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Computers & Industrial Engineering 151 (2021) 106924
Available online 22 October 2020
0360-8352/© 2020 Elsevier Ltd. All rights reserved.
Integrated optimization of quality and maintenance: A literature review
Ameneh Farahani
a
, Hamid Tohidi
b
,
*
a
Department of Industrial Engineering, Roudehen Branch, Islamic Azad University, Roudehen, Iran
b
Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
ARTICLE INFO
Keywords:
Maintenance
Production
Quality
Repair
Review
ABSTRACT
Nowadays, getting new markets depends on customer satisfaction. Quality is the most important factor in
customer satisfaction. Quality in production includes understanding the customer needs correctly, designing the
product according to the perceived needs, precisely designing the production process, and delivery time ac-
cording to the desired time of the customer. In order to produce according to the specied technical charac-
teristics, integrated maintenance and quality control planning are required. Also, for timely delivery of the
product, integrated production and maintenance planning are necessary. Therefore, production systems need
integrated optimization of production planning, maintenance and quality control to achieve quality goals that
lead to customer satisfaction. This paper provides a comprehensive literature review on the papers that optimize
decisions for either maintenance and quality or maintenance, quality, and production. Reviewed papers are
tabulated based on important and distinctive features. Also, the contribution of each paper is listed in the tables.
These tables facilitate the comparison of the work done in this area and will help the quick access of the reader to
his favourite eld. In writing review papers, this method of presentation can be a contribution. In the end, the
trend in research on integrated optimization of maintenance, quality and production has been determined, and
the gaps in this eld are presented for future research.
1. Introduction
Production planning, maintenance, and quality control are three
main tasks in manufacturing systems that, in the past, these were opti-
mized separately, while these three tasks interact mutually. Many re-
searchers believe that in the models that these three tasks are not
considered simultaneously, they are not globally optimal.
Production planning is the process of deciding on the resources an
organization needs for its future production operations. Production
planning is usually done at three levels: strategic level (long-term),
tactical level (aggregate production) and operational level (production
schedule). In the papers that focus on production planning, in general,
two main issues are considered. The rst issue determines the economic
production quantity (EPQ) and inventory level. The second issue is
scheduling and sequence of production operations, which assigns the
available production capacity and determines the sequence of produc-
tion operations and their start time. These two issues are included in
tactical and operational production planning, respectively.
Most production scheduling models assume that machines are al-
ways available; however, in real production environments, the machine
breaks down and may not be available at some time. It is not optimal to
carry out production planning on machines, regardless of deterioration
and break down of them. Maintenance includes all technical and
managerial activities during the life of the equipment, the purpose of
which is to maintain or restore the equipment so that it can provide the
expected task with the acceptable quality level. In maintenance plan-
ning, machine maintenance scheduling is done to prevent sudden
equipment failure. When the machine is not in good condition and needs
maintenance, the products are not favourable in terms of quality, and
the rate of production of the non-conformity products increases. When
an unplanned stop occurs due to a sudden machine breakdown, the
current production schedule is not performed, and customer orders are
delayed, and modifying the production schedule in an emergency usu-
ally imposes a high cost on the system. The maintenance will reduce
process variation and help increase product quality. The additional
maintenance will lead to increased costs, and delayed maintenance will
increase the process variability. Maintenance planning is the best bal-
ance between the cost of maintenance and quality-related costs.
The choice of a maintenance policy is limited by production sched-
uling decisions, quality control and inventory, so the specic interaction
* Corresponding author.
E-mail addresses: st.a_farahani@riau.ac.ir (A. Farahani), H_tohidi@azad.ac.ir (H. Tohidi).
Contents lists available at ScienceDirect
Computers & Industrial Engineering
journal homepage: www.elsevier.com/locate/caie
https://doi.org/10.1016/j.cie.2020.106924
Received 2 June 2019; Received in revised form 29 June 2020; Accepted 16 October 2020
Computers & Industrial Engineering 151 (2021) 106924
2
of maintenance with production planning and quality control is novel. In
the short term, production scheduling seeks to assign operations and
their sequence without sudden equipment failure. In the long term,
aggregate planning seeks to offset demand if the equipment is stopped
by determining the optimal level of inventory. Preventive maintenance
planning may interfere with optimal delivery time. When a piece of
equipment is not in good production condition, the quality of the process
output is not acceptable in terms of quality control.
Quality control strives to achieve a level of quality that is compatible
with product features and process capability. The goal of a quality
control system is to ensure that the quality level is optimal so that the
costs of sampling error are minimized. The quality of a product can be
determined by a large number of characteristics. In quality control, some
key features must be conrmed that ensure the quality of the product.
Changing these characteristics within a specic limit indicates that the
quality of the product is good, and when it goes beyond these limits, the
production process becomes unacceptable. Quality control methods
include acceptance sampling, process control. Inspections can be per-
formed during (process control) or after the production process
(acceptance sampling).
There are two failure modes for the machine: One mode is that the
machine stops quickly and the other mode is that the machine is out of
control but has not stopped yet and production continues. In the second
stage, non-conformity products are produced until inspection shows that
the process is out of control. When a non-conformity product is pro-
duced, the cause is searched, which can be due to changes in raw ma-
terials, environmental factors, operators, and machine failure. If the
cause is a failure machine, the machine will be repaired. Therefore,
quality control is in direct interaction with maintenance and production
planning.
Therefore, the direct relationship between quality control, main-
tenanace, and production have led researchers to develop integrated
models of maintenance, quality and production in recent years.
Ben-Daya and Rahim (Ben-Daya and Rahim, 2001) provide a review
of the literature related to integrated production planning, quality
control and maintenance. They emphasize the need to present inte-
grated models. Pandey et al. (Pandey et al., 2010) review the papers on
integrated scheduling of production, repair, and quality. They are stated
that existing integrated approaches are more about either maintenance
and quality, or the production and maintenance, and there are no in-
tegrated models about scheduling of production, maintenance, and
quality.
Hadidi et al. (Hadidi et al., 2012) review models that integrate
different aspects of repair, quality, production, and inventory, they
divide the integration approach into two categories, the rst category is
the interrelated models that consider one of the three tasks of the pro-
duction system (production, maintenance, quality) as the objective and
other tasks as constraints, and the second category is integrated models
that optimize either two or three tasks of a system as the objective
simultaneously, and decision variables relate to all tasks (production,
maintenance and quality).
In the present paper, we review papers that optimize either quality
and maintenance decisions, or quality, maintenance, and production
decisions taking into account their interaction on each other during
production. With our knowledge, there is no review paper in this eld
since 2012.
The main contribution of the present paper is a comprehensive re-
view of published papers in the eld of optimization of maintenance and
quality, as well as maintenance, quality, and production by considering
the interaction of these three tasks on each other. The main features of
the papers are tabulated in such a way that access to the work done is
facilitated. The contribution of each paper is also listed in the tables. In
the review papers, this method of presentation can be a contribution.
The rst paper, which considered integrated repairs and quality de-
cisions, was published in 1988. So the present review includes papers
from 1998 to May 3, 2019, by searching keywords (statistical process
control and maintenance; control chart and maintenance; quality and
maintenance; acceptance sampling and maintenance; acceptance sam-
pling and repair; statistical process control and repair; control chart and
repair; quality and repair) from Scopus, Web of Science and Google
Scholar. The present paper has also listed the papers in which decision
variables only are related to one aspect of the three main tasks (quality,
maintenance, and production), and these decision variables are opti-
mized to the interaction of other tasks. The present paper reviews the
papers (Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-Daya,
1998; Chiu and Huang, 1995; Chiu and Huang, 1996; Ben-Daya, 1999;
Ben-Daya and Rahim, 2000; Cassady et al., 2000; Rahim and Ben-Daya,
2001; Linderman et al., 2005; Wang and Sheu, 2003; Kuo, 2006; Makis
and Fung, 1995; Ben-Daya and Makhdoum, 1998; Lee and Rahim, 2001;
Yeung et al., 2007; Makis and Fung, 1998; Alfares et al., 2005; Wu and
Makis, 2008; Radhoui et al., 2009; Lin et al., 2011; Wu and Wang, 2011;
Wang, 2011; Mehrafrooz and Noorossana, 2011; Ho and Quinino, 2012;
Wang, 2012; Kim and Makis, 2012; Chen, 2013; Xiang, 2013; Liu et al.,
2013; Zhong et al., 2016; Yin et al., 2015; Yin et al., 2015; Lu et al.,
2016; Nourelfath et al., 2016; Salmasnia et al., 2017; Fakher et al., 2018;
Zhong and Ma, 2017; Lesage and Dehombreux, 2012; Li et al., 2017; Liu
et al., 2017; Li et al., 2017; Zhou et al., 2017; Li et al., 2018; Bahria et al.,
2018; Salmasnia et al., 2018; Salmasnia et al., 2018; Tasias and Nenes,
2018; Wan et al., 2018; Salmasnia et al., 2018; Salmasnia et al., 2019;
Tagaras, 1988; Wang and Chen, 1995; Chiang and Yuan, 2001; Zhou and
Zhu, 2008; Wang et al., 2009; Panagiotidou and Tagaras, 2010; Char-
ongrattanasakul and Pongpullponsak, 2011; Pandey et al., 2011; Pandey
et al., 2012; Panagiotidou and Tagaras, 2012 ; Tambe and Kulkarni,
2014 ; Zhang et al., 2015; Makis, 2015; Tambe and Kulkarni, 2015;
Ardakan et al., 2016; Jafari and Makis, 2016; Jafari and Makis, 2016;
Bouslah et al., 2016; Khrueasom and Pongpullponsak, 2017; Tambe and
Kulkarni, 2016; Jain and Lad, 2017; Bouslah et al., 2016; Bouslah et al.,
2018; Rasay et al., 2018; Latrous et al., 2018; Farahani et al., 2019; Li
et al., 2019; Hsu and Kuo, 1995; Chiu and Huang, 1996; Yerel et al.,
2007; Panagiotidou and Tagaras, 2007; Panagiotidou and Tagaras,
2008; Chang et al., 2009; Panagiotidou and Nenes, 2009; Nenes and
Panagiotidou, 2011; Pandey et al., 2010; Mehdi et al., 2010; Engin,
2010; Radhoui et al., 2010; Rahim and Shakil, 2011; Colledani and
Tolio, 2012; Morales, 2013; Dhouib et al., 2012; Rivera-G´
omez et al.,
2013; Shrivastava et al., 2016; Dan et al., 2016; Rasay et al., 2018; Yin
and Makis, 2010; Azadeh et al., 2017; Cheng et al., 2018; Rasay et al.,
2018; Wan et al., 2018; Pasha and Moghadam, 2018; Duan et al., 2019;
Wang et al., 2019; Beheshti Fakher et al., 2017; Kouki et al., 2014;
Deloux et al., 2009; Nguyen et al., 2019; Pan et al., 2012; Maillart et al.,
2009; Zhou and Liu, 2016; Lampreia et al., 2018; Lesage and Dehom-
breux, 2012; Rivera-Gomez et al., 2013; Alsyouf et al., 2016; Yang and
Table 1
. Journal perspective (journals with three or more publications).
Number of
papers
Journal
12 Computers & Industrial Engineering
12 European Journal of Operational Research
10 Reliability Engineering & System Safety
9 International Journal of Production Research
5 The International Journal of Advanced Manufacturing
Technology
5 Journal of the Operational Research Society
4 IIE transactions
4 International Journal of Production Economics
3 Journal of quality in maintenance engineering
3 International Journal of Quality & Reliability Management
3 Quality and Reliability Engineering International
3 Journal of Manufacturing systems
3 Communications in Statistics-Theory and Methods
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
3
Zeng, 2018 Apr; Zhang et al., 2018; Bahria et al., 2019; He et al., 2019;
Lin, 2004; Le and Tan, 2013; Ivy and Nembhard, 2005; Ji-Wen et al.,
2010; Chan, 2003; Chan and Wu, 2009; Azizi, 2015; Gupta et al., 2009;
Katter et al., 1997; Alsyouf et al., 2015; Yeong et al., 2013; Ali et al.,
2020).
Table 1 provides information on journals that have published papers
in the eld of optimization, either maintenance and quality, or main-
tenance, quality, and production. The Computers & Industrial Engi-
neering and the European Journal of Operational Research have
published the most number of papers in this eld. Table 1 lists the
journals that have published either three or more papers in this eld.
Concerning the year of publication, as can be seen in Fig. 1, the
number of papers published in the eld of integrated optimization has
increased in the years 2011–2019 with a steep slope. Thus, the tendency
to study the integrated optimization of either two main tasks (mainte-
nance and quality) or three main tasks (production, maintenance, and
quality) on the oor of the workshop has increased in recent years.
The integrated concepts presented in the papers are listed in Table 2,
which include the integrity of maintenance and the quality; integrity of
maintenance, the quality and the production; integrity of maintenance,
the quality, the production and the inventory; integrity of maintenance,
the quality, and the inventory. According to Table 2, 63% of the papers
are related to the integrated optimization of maintenance and quality,
and 31% are related to the integrated optimization of maintenance,
quality, and production.
The papers are generally divided into three categories: research, case
study, and review. Table 3 lists the review papers and the case study. As
can be seen in Table 3, 0.08% of papers are case studies, and 0.02% are
review papers.
The rest of the paper is presented as follows. Section 2 describes the
tabulation of the papers according to their distinctive features in quality,
maintenance, and production. Finally, in Section 3, the conclusion and
potential areas for future research are presented.
2. Description of the tabulation of papers
In this section, the important and distinctive features of the papers
are tabulated and compared. These papers optimize either decisions of
quality and maintenance or quality, maintenance, and production by
considering the interaction of these three tasks on each other so that the
reader can easily understand the research done in this area.
2.1. Tabulation based on quality policy
In quality control, the purpose is to maintain specic standards, di-
agnose, correct the process deviations, and evaluate the performance of
the production system. Statistical Quality Control (SQC) is a branch of
quality control that includes collecting, analyzing, and interpreting the
data for use in quality control activities. Statistical quality control is
divided into three main parts: Statistical Process Control (SPC), Design
of Experiments (DOE), and acceptance sampling. In acceptance sam-
pling, which is an inspection method, an appropriate plan is selected,
taking into account the balance between producer and consumer risk
and the cost of sampling. Accordingly, the decision is made to accept or
reject a stack. This approach is usually used after production.
Design of experiments is an active method, by deliberately and
purposefully modifying the levels of factors, their effects on the response
Table 2
. Integrated concepts.
Maintenance, Quality (Rahim and Banerjee, 1993; Chiu and Huang, 1995;
Chiu and Huang, 1996; Ben-Daya and Rahim, 2000;
Cassady et al., 2000; Linderman et al., 2005; Kuo,
2006; Lee and Rahim, 2001; Yeung et al., 2007; Wu
and Makis, 2008; Wu and Wang, 2011; Wang, 2011;
Mehrafrooz and Noorossana, 2011; Ho and Quinino,
2012; Wang, 2012; Kim and Makis, 2012; Xiang,
2013; Liu et al., 2013; Zhong et al., 2016; Yin et al.,
2015; Yin et al., 2015; Lu et al., 2016; Zhong and Ma,
2017; Lesage and Dehombreux, 2012; Li et al., 2017;
Liu et al., 2017; Li et al., 2017; Zhou et al., 2017; Li
et al., 2018; Bahria et al., 2018; Salmasnia et al.,
2018; Tasias and Nenes, 2018; Wan et al., 2018;
Salmasnia et al., 2019; Tagaras, 1988; Wang and
Chen, 1995; Chiang and Yuan, 2001; Zhou and Zhu,
2008; Panagiotidou and Tagaras, 2010;
Charongrattanasakul and Pongpullponsak, 2011;
Pandey et al., 2012; Panagiotidou and Tagaras, 2012
; Zhang et al., 2015; Makis, 2015; Ardakan et al.,
2016; Khrueasom and Pongpullponsak, 2017; Jain
and Lad, 2017; Rasay et al., 2018; Latrous et al.,
2018; Farahani et al., 2019; Li et al., 2019; Chiu and
Huang, 1996; Yerel et al., 2007; Panagiotidou and
Tagaras, 2008; Chang et al., 2009; Panagiotidou and
Nenes, 2009; Nenes and Panagiotidou, 2011; Pandey
et al., 2010; Morales, 2013; Shrivastava et al., 2016;
Dan et al., 2016; Yin and Makis, 2010; Rasay et al.,
2018; Pasha and Moghadam, 2018; Duan et al., 2019;
Deloux et al., 2009; Nguyen et al., 2019; Maillart
et al., 2009; Lampreia et al., 2018; Lesage and
Dehombreux, 2012; Alsyouf et al., 2016; Yang and
Zeng, 2018 Apr; Zhang et al., 2018; He et al., 2019;
Le and Tan, 2013; Ivy and Nembhard, 2005; Ji-Wen
et al., 2010; Chan, 2003; Chan and Wu, 2009; Gupta
et al., 2009; Ali et al., 2020)
Maintenance, Quality,
Production
(Rahim and Ben-Daya, 2001; Wang and Sheu, 2003;
Makis and Fung, 1995; Ben-Daya and Makhdoum,
1998; Makis and Fung, 1998; Lin et al., 2011; Chen,
2013; Nourelfath et al., 2016; Salmasnia et al., 2017;
Fakher et al., 2018; Salmasnia et al., 2018; Salmasnia
et al., 2018; Wang et al., 2009; Pandey et al., 2011;
Tambe and Kulkarni, 2014 ; Tambe and Kulkarni,
2015; Jafari and Makis, 2016; Jafari and Makis,
2016; Bouslah et al., 2016; Tambe and Kulkarni,
2016; Bouslah et al., 2016; Bouslah et al., 2018; Hsu
and Kuo, 1995; Mehdi et al., 2010; Engin, 2010;
Radhoui et al., 2010; Rahim and Shakil, 2011;
Colledani and Tolio, 2012; Rivera-G´
omez et al.,
2013; Rasay et al., 2018; Azadeh et al., 2017; Cheng
et al., 2018; Wan et al., 2018; Wang et al., 2019;
Beheshti Fakher et al., 2017; Kouki et al., 2014; Pan
et al., 2012; Zhou and Liu, 2016; Rivera-Gomez et al.,
2013; Lin, 2004)
Maintenance, Quality,
Production, Inventory
(Alfares et al., 2005; Dhouib et al., 2012; Bahria
et al., 2019)
Maintenance, Quality,
Inventory
(Rahim, 1994; Rahim and Ben-Daya, 1998; Ben-
Daya, 1999; Radhoui et al., 2009)
17
32
84
0
20
40
60
80
100
1988-2000 2001-2010 2011-2019
Number of papers
Time intervals
Fig. 1. . Number of papers published in different time intervals.
Table 3
. List of review papers and case studies.
Case study (Li et al., 2019; Yerel et al., 2007; Colledani and Tolio, 2012;
Lampreia et al., 2018; Lesage and Dehombreux, 2012; Alsyouf et al.,
2016; Chan and Wu, 2009; Azizi, 2015; Gupta et al., 2009; Katter
et al., 1997; Alsyouf et al., 2015)
Review
paper
Pandey et al., 2010, Hadidi et al., 2012, Cassady et al., 2000
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
4
variable, measured and evaluated, and the optimal levels of inuencing
factors are determined. This approach is commonly used in process
design and pre-production.
Statistical process control is a statistical technique that is used to
reduce dispersion and, consequently, to improve quality. The tools of
this method include histogram (steam-and-leaf plot), check sheet, Pareto
chart, cause, and effect chart, scatter chart, defect concentration dia-
gram, and control chart. The rst six tools are mostly used in the process
design or to discover the cause of the failure. But the control charts are
used to detect the process variations during the production process.
The control charts are divided into three main classes, include the
Shewhart chart, the Cumulative Sum (CUSUM) chart, and the Expo-
nential Weighted Moving Average (EWMA) chart.
Each of these classes can be categorized using three important fea-
tures: either parametric or non-parametric (if the distribution of obser-
vations is assumed to be known (normal), then the control chart is
parametric; otherwise, the control chart is non-parametric), either uni-
variate or multivariate (if a single variable causes the process to be out of
control, the control chart is univariate, and if two or more variables
cause the process to be out of control, it is called a multivariate control
chart), either discrete (attribute) or continuous (variable) (if the quali-
tative characteristic is measurable, the control chart is continuous, and if
it is countable, the control chart is discrete).
The parametric control charts monitor the mean and/or standard
deviation of the process, while non-parametric control charts monitor
the shape (centre) and/or scale (dispersion) parameter of a process.
Shewhart control charts reveal the medium to large variations of the
process (
σ
≥1.5). The CUSUM chart and EWMA chart detect the small
variations of the process (
σ
≤1.5). The types of parametric control
charts can be considered in the setting of non-parametric charts.
The cost of quality is dened in two ways: the cost of obtaining good
quality, which is the cost of quality assurance, and the cost associated
with poor quality products, which is known as the cost of non-
conformity. The cost of quality assurance includes the cost of quality
planning, product design, training, information costs, inspection and
testing, the cost of equipment and inspection operators. Poor quality
costs refer to non-conformity costs. This cost is the difference between
the cost of producing a product or providing a service and the cost of a
defect. Defective costs include internal and external costs. Internal costs
are related to the production of poor-quality products before the product
reaches the customer. These costs include waste costs, rework, process
defect check, process stop, price reduction. External costs include the
cost of responding to the customer complaint, product return costs,
warranty acceptance costs, and lost sales costs.
The cost of a quality program includes the cost of prevention and the
cost of evaluation. Therefore, in general, the cost of quality is formulated
as follows:
The expected cost of quality assurance =Expected cost of inspection
(cost of stopping the process, inspection and restart) +Expected cost of
producing non-conformity products (cost of rejection, rework, waste
costs, increase the cost of repairs, cost of failure)
The cost of the inspection is calculated according to the number of
inspections in a period and the number of samples taken from the line.
As the number of inspections increases, the cost of inspection increases,
but the cost of producing non-conformity products decreases faster than
increasing inspection cost, and at one point, the cost of the inspection is
not compensated by reducing the cost of producing non-conformity
products. This point is the optimal number of inspections.
In acceptance sampling, the goal is to minimize the expected cost of
sampling errors (producer and consumer risk). Therefore, for the spec-
ied quality level with the determined risks, the decision to reject or
accept the shipment is made based on the sampling plan.
The production lines are sampled to ensure the quality of the prod-
ucts produced both during production and after production. The time for
sampling is one of the important characteristics that papers can be
categorized based on it. As can be seen in Table 4, in some papers, the
time is taken to sampling, but in some papers, to simplify the model, it is
ignored.
The quality control policies used in papers generally include control
charts and acceptance sampling. As described in the above, the control
charts used in reviewed papers are categorized according to important
features in Table 5. The quality control policy in some papers is based on
the loss function. The loss function is a function that calculates possible
deviations from the target value. The papers are listed in Table 6 based
Table 5
. Classication of control charts.
Parametric Variable Univariate X Bar (X), X−R ,X−S, CUSUM, EWMA, X−S2, Shewhart individual-residual joint, Reliability control chart (RCC), time-based (t) (time-
between-event (TBE) control chart)
Parametric Variable Multivariate Chi square
χ
2, Multivariate Bayesian, Hotelling’s T2, VP-T2 Hotelling, Multivariate Exponentially Weighted Moving Average
(MEWMA), Multivariate cumulative sum (MCUSUM)
Parametric Attribute Univariate Number of Nonconforming (np), p, EWMA, CUSUM, Likelihood ratio, Cumulative Count of Conforming (CCC)
Parametric Attribute Multivariate Multivariate np, MEWMA, MCUSUM
Non-
parametric
Kolmogorov-Smirnov
Table 4
. Duration of sampling.
Negligible (Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-Daya,
1998; Chiu and Huang, 1995; Chiu and Huang, 1996; Ben-Daya,
1999; Ben-Daya and Rahim, 2000; Cassady et al., 2000; Rahim and
Ben-Daya, 2001; Linderman et al., 2005; Wang and Sheu, 2003; Kuo,
2006; Makis and Fung, 1995; Ben-Daya and Makhdoum, 1998; Lee
and Rahim, 2001; Yeung et al., 2007; Makis and Fung, 1998; Alfares
et al., 2005; Wu and Makis, 2008; Radhoui et al., 2009; Lin et al.,
2011; Wu and Wang, 2011; Wang, 2011; Mehrafrooz and
Noorossana, 2011; Ho and Quinino, 2012; Wang, 2012; Kim and
Makis, 2012; Chen, 2013; Xiang, 2013; Liu et al., 2013; Zhong et al.,
2016; Yin et al., 2015; Yin et al., 2015; Lu et al., 2016; Nourelfath
et al., 2016; Salmasnia et al., 2017; Fakher et al., 2018; Zhong and
Ma, 2017; Lesage and Dehombreux, 2012; Liu et al., 2017; Li et al.,
2017; Zhou et al., 2017; Li et al., 2018; Bahria et al., 2018; Salmasnia
et al., 2018; Salmasnia et al., 2018; Tasias and Nenes, 2018; Wan
et al., 2018; Salmasnia et al., 2018; Salmasnia et al., 2019; Ali et al.,
2020)
Not
negligible
(Tagaras, 1988; Wang and Chen, 1995; Chiang and Yuan, 2001; Zhou
and Zhu, 2008; Wang et al., 2009; Panagiotidou and Tagaras, 2010;
Charongrattanasakul and Pongpullponsak, 2011; Pandey et al.,
2011; Pandey et al., 2012; Panagiotidou and Tagaras, 2012 ; Tambe
and Kulkarni, 2014 ; Zhang et al., 2015; Makis, 2015; Tambe and
Kulkarni, 2015; Ardakan et al., 2016; Jafari and Makis, 2016; Jafari
and Makis, 2016; Bouslah et al., 2016; Khrueasom and
Pongpullponsak, 2017; Tambe and Kulkarni, 2016; Jain and Lad,
2017; Bouslah et al., 2016; Bouslah et al., 2018; Latrous et al., 2018;
Farahani et al., 2019; Li et al., 2019)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
5
on the type of quality control policy.
In recent years, the economic design of control charts with variable
parameters have been considered. As shown in Table 6, these charts
include Variable-parameter (VP) Shewhart (adaptive) control chart,
Adaptive chart, Adaptive synthetic X control chart and VP−T2 Hotelling
control chart.
In real production systems, more than one cause usually causes the
process to be out of control, and these causes usually affect each other
and are not independent of each other. Another distinctive feature of
papers can be the number of causes that can be a single cause or several
causes. The papers are listed in Table 7 based on the number of causes.
Economic and economic-statistical schemes are two ways to design
control charts. The economic scheme ignores the statistical properties in
designing the control chart, whereas the economic-statistical scheme
considers the statistical properties in the control chart design. An
economic-statistical scheme usually designs more realistic control
charts. Papers are listed in Table 8 according to the type of design.
An important factor in using control charts is the parameter design of
control charts. The parameters of the control charts include sample size,
sampling interval, and control limit. These parameters can be xed or
variable. In the xed state, the parameters of the control charts are
Table 6
Type of quality control policy.
X Bar (X) (Rahim and Banerjee, 1993; Rahim, 1994;
Rahim and Ben-Daya, 1998; Chiu and
Huang, 1996; Ben-Daya, 1999; Ben-Daya
and Rahim, 2000; Cassady et al., 2000;
Rahim and Ben-Daya, 2001; Linderman
et al., 2005; Ben-Daya and Makhdoum,
1998; Lee and Rahim, 2001; Yeung et al.,
2007; Mehrafrooz and Noorossana, 2011;
Ho and Quinino, 2012; Xiang, 2013; Liu
et al., 2013; Yin et al., 2015; Salmasnia
et al., 2017; Lesage and Dehombreux, 2012;
Li et al., 2017; Liu et al., 2017; Bahria et al.,
2018; Salmasnia et al., 2018; Tagaras, 1988;
Zhou and Zhu, 2008; Panagiotidou and
Tagaras, 2010; Pandey et al., 2011; Pandey
et al., 2012; Zhang et al., 2015; Jain and
Lad, 2017; Latrous et al., 2018; Farahani
et al., 2019; Chiu and Huang, 1996; Chang
et al., 2009; Pandey et al., 2010; Engin,
2010; Rahim and Shakil, 2011; Dan et al.,
2016; Pan et al., 2012; Maillart et al., 2009;
Lesage and Dehombreux, 2012; Zhang et al.,
2018; Bahria et al., 2019)
MEWMA (Yin et al., 2015; Yin et al., 2015;
Charongrattanasakul and Pongpullponsak,
2011; Lampreia et al., 2018)
Loss function (Lu et al., 2016; Zhong and Ma, 2017; Li
et al., 2017; Zhou and Zhu, 2008;
Shrivastava et al., 2016; Dan et al., 2016;
Zhou and Liu, 2016; Ji-Wen et al., 2010)
Acceptance sampling (Wang and Sheu, 2003; Kuo, 2006; Makis
and Fung, 1995; Makis and Fung, 1998;
Alfares et al., 2005; Radhoui et al., 2009; Lin
et al., 2011; Wang, 2011; Chen, 2013;
Nourelfath et al., 2016; Fakher et al., 2018;
Chiang and Yuan, 2001; Wang et al., 2009;
Tambe and Kulkarni, 2014 ; Tambe and
Kulkarni, 2015; Bouslah et al., 2016; Tambe
and Kulkarni, 2016; Bouslah et al., 2016;
Bouslah et al., 2018; Hsu and Kuo, 1995;
Mehdi et al., 2010; Radhoui et al., 2010;
Dhouib et al., 2012; Rivera-G´
omez et al.,
2013; Azadeh et al., 2017; Cheng et al.,
2018; Wang et al., 2019; Beheshti Fakher
et al., 2017; Kouki et al., 2014; Rivera-
Gomez et al., 2013; Yang and Zeng, 2018
Apr; Ivy and Nembhard, 2005)
Multivariate Bayesian (Wang, 2012; Makis, 2015; Jafari and
Makis, 2016; Jafari and Makis, 2016; Yin
and Makis, 2010; Duan et al., 2019)
CUSUM (Li et al., 2017; Li et al., 2018; Shrivastava
et al., 2016; Lampreia et al., 2018)
x−Rcontrol chart (Yerel et al., 2007; Lesage and Dehombreux,
2012)
Chi square (
χ
2) control chart (Wu and Makis, 2008; Salmasnia et al.,
2018; Rasay et al., 2018; Rasay et al., 2018)
Variable –parameter (VP) Shewhart
(adaptive) control chart
(Tasias and Nenes, 2018; Salmasnia et al.,
2019; Panagiotidou and Nenes, 2009)
Bayesian control chart (Kim and Makis, 2012; Li et al., 2019; Nenes
and Panagiotidou, 2011)
Np (Number of Nonconforming)
control chart
(Wang, 2011; Wang and Chen, 1995; Yang
and Zeng, 2018 Apr)
On-line inspection (Panagiotidou and Tagaras, 2008)
Static chart (Wu and Wang, 2011)
Adaptive chart (Wu and Wang, 2011)
CCC (Cumulative Count of
Conforming) control chart
(Chan, 2003; Chan and Wu, 2009)
General (Panagiotidou and Tagaras, 2012 ; Rasay
et al., 2018; Deloux et al., 2009)
Reliability control chart (Alsyouf et al., 2016)
Kolmogorov-Smirnov control chart (Khrueasom and Pongpullponsak, 2017)
Likelihood ratio control chart (Zhong et al., 2016)
T2Hotellingcontrol chart (Latrous et al., 2018; Pasha and Moghadam,
2018)
x−Scontrol chart (Morales, 2013)
(Chiu and Huang, 1995)
Table 7
. Number of causes.
A single
cause
(Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-Daya,
1998; Chiu and Huang, 1995; Chiu and Huang, 1996; Ben-Daya,
1999; Ben-Daya and Rahim, 2000; Rahim and Ben-Daya, 2001;
Linderman et al., 2005; Wang and Sheu, 2003; Makis and Fung, 1995;
Ben-Daya and Makhdoum, 1998; Lee and Rahim, 2001; Yeung et al.,
2007; Alfares et al., 2005; Lin et al., 2011; Wang, 2011; Mehrafrooz
and Noorossana, 2011; Ho and Quinino, 2012; Wang, 2012; Chen,
2013; Xiang, 2013; Liu et al., 2013; Zhong et al., 2016; Yin et al.,
2015; Lesage and Dehombreux, 2012; Li et al., 2017; Liu et al., 2017;
Li et al., 2017; Zhou et al., 2017; Li et al., 2018; Bahria et al., 2018;
Salmasnia et al., 2018; Salmasnia et al., 2018; Wan et al., 2018;
Salmasnia et al., 2018; Salmasnia et al., 2019; Tagaras, 1988; Wang
and Chen, 1995; Chiang and Yuan, 2001; Zhou and Zhu, 2008; Wang
et al., 2009; Panagiotidou and Tagaras, 2010; Charongrattanasakul
and Pongpullponsak, 2011; Pandey et al., 2011; Pandey et al., 2012;
Tambe and Kulkarni, 2014 ; Zhang et al., 2015; Tambe and Kulkarni,
2016; Jain and Lad, 2017; Bouslah et al., 2016; Farahani et al., 2019;
Li et al., 2019; Hsu and Kuo, 1995; Chiu and Huang, 1996; Chang
et al., 2009; Panagiotidou and Nenes, 2009; Nenes and Panagiotidou,
2011; Pandey et al., 2010; Engin, 2010; Rahim and Shakil, 2011;
Morales, 2013; Dhouib et al., 2012; Shrivastava et al., 2016; Dan
et al., 2016; Rasay et al., 2018; Rasay et al., 2018; Wan et al., 2018;
Pasha and Moghadam, 2018; Wang et al., 2019; Deloux et al., 2009;
Nguyen et al., 2019; Pan et al., 2012; Zhou and Liu, 2016; Lampreia
et al., 2018; Yang and Zeng, 2018 Apr; Zhang et al., 2018; Bahria
et al., 2019; He et al., 2019; Ivy and Nembhard, 2005; Ji-Wen et al.,
2010; Yeong et al., 2013; Ali et al., 2020)
Several
causes
(Wu and Makis, 2008; Wu and Wang, 2011; Wang, 2012; Kim and
Makis, 2012; Yin et al., 2015; Lu et al., 2016; Salmasnia et al., 2017;
Zhong and Ma, 2017; Tasias and Nenes, 2018; Makis, 2015; Tambe
and Kulkarni, 2015; Ardakan et al., 2016; Jafari and Makis, 2016;
Bouslah et al., 2018; Rasay et al., 2018; Yin and Makis, 2010; Gupta
et al., 2009)
Table 6 (continued )
x−S2control chart
Shewhart individual control chart (Zhou et al., 2017)
Shewhart individual-residual joint
control chart
(Zhong and Ma, 2017)
adaptive synthetic X control chart (Wan et al., 2018)
VP −T2Hotellingcontrol chart (Salmasnia et al., 2018)
TBE(Time Between Events) control
chart (Time-based (t-chart))
(Wan et al., 2018; He et al., 2019; Gupta
et al., 2009; Ali et al., 2020)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
6
constant in the sampling period, but in the variable state, each param-
eter can change according to a specic criterion (the time, the failure
rate). Variable parameters appear to be appropriate for processes whose
failure rate varies over time. Papers based on this feature are shown in
Table 9.
When the accuracy and precision of the process are appropriate, the
process is in control. The accuracy of the process is measured by the
mean process, and the precision is measured by the standard deviation.
The inaccuracy is due to the large changes that occur between the
samples taken, and the imprecision is due to the changes within each
sample. When the process is out of control, both/either the mean and/or
standard deviation of the process changes, according to this feature, the
papers are listed in Table 10.
The process starts in the in-control state, and after some time, it shifts
to an out-of-control state. In the out of control state, the process still
works, but the quality characteristic of the process is out of the control.
In the failure state, the process stops. The papers are tabulated according
to the number of out-of-control modes and the failure mode in Table 11.
In production processes, several out-of-control modes and failure mode
is closer to the reality of systems, but for simplifying the problem, some
modes are not considered in some papers.
The qualitative variables of the papers are presented in Tables 12–14.
As can be seen in these tables, the parameters of the control chart (the
sample size, the control limit, the sampling interval) are the most vari-
ables in the papers in the quality policy.
2.2. Tabulation of maintenance policy
All components of the operating system, including machinery and
equipment, wear out and deteriorate when performing tasks. A machine
breaks down when a fault in any of its important components causes the
Table 9
. The parameters of the control charts.
Fixed Variable
Sampling
interval
(Chiu and Huang, 1995; Chiu and
Huang, 1996; Cassady et al., 2000;
Rahim and Ben-Daya, 2001;
Linderman et al., 2005; Makis and
Fung, 1995; Yeung et al., 2007;
Makis and Fung, 1998; Alfares
et al., 2005; Wu and Makis, 2008;
Radhoui et al., 2009; Wu and Wang,
2011; Wang, 2011; Mehrafrooz and
Noorossana, 2011; Wang, 2012;
Kim and Makis, 2012; Xiang, 2013;
Liu et al., 2013; Yin et al., 2015; Yin
et al., 2015; Nourelfath et al., 2016;
Fakher et al., 2018; Lesage and
Dehombreux, 2012; Li et al., 2017;
Liu et al., 2017; Li et al., 2017;
Bahria et al., 2018; Tagaras, 1988;
Wang and Chen, 1995; Zhou and
Zhu, 2008; Charongrattanasakul
and Pongpullponsak, 2011; Pandey
et al., 2011; Pandey et al., 2012;
Tambe and Kulkarni, 2014 ; Zhang
et al., 2015; Makis, 2015; Tambe
and Kulkarni, 2015; Ardakan et al.,
2016; Jafari and Makis, 2016;
Jafari and Makis, 2016; Bouslah
et al., 2016; Khrueasom and
Pongpullponsak, 2017; Tambe and
Kulkarni, 2016; Farahani et al.,
2019; Li et al., 2019; Chiu and
Huang, 1996; Pandey et al., 2010;
Engin, 2010; Rahim and Shakil,
2011; Morales, 2013; Shrivastava
et al., 2016; Dan et al., 2016; Yin
and Makis, 2010; Duan et al., 2019;
Deloux et al., 2009; Pan et al., 2012;
Yang and Zeng, 2018 Apr; Zhang
et al., 2018; Bahria et al., 2019; He
et al., 2019; Yeong et al., 2013; Ali
et al., 2020)
(Rahim and Banerjee, 1993;
Rahim, 1994; Rahim and Ben-
Daya, 1998; Chiu and Huang,
1995; Ben-Daya, 1999; Ben-
Daya and Rahim, 2000; Wang
and Sheu, 2003; Kuo, 2006;
Ben-Daya and Makhdoum,
1998; Lee and Rahim, 2001;
Wu and Wang, 2011; Ho and
Quinino, 2012; Nourelfath
et al., 2016; Salmasnia et al.,
2017; Fakher et al., 2018;
Zhou et al., 2017; Li et al.,
2018; Salmasnia et al., 2018;
Salmasnia et al., 2018; Tasias
and Nenes, 2018; Wan et al.,
2018; Salmasnia et al., 2018;
Salmasnia et al., 2019;
Panagiotidou and Tagaras,
2010; Jain and Lad, 2017;
Rasay et al., 2018; Latrous
et al., 2018; Panagiotidou and
Nenes, 2009; Nenes and
Panagiotidou, 2011; Rahim
and Shakil, 2011; Morales,
2013; Rasay et al., 2018;
Rasay et al., 2018; Pasha and
Moghadam, 2018; Beheshti
Fakher et al., 2017)
Sampling
size
(Rahim and Banerjee, 1993; Rahim,
1994; Rahim and Ben-Daya, 1998;
Chiu and Huang, 1995; Chiu and
Huang, 1996; Ben-Daya, 1999; Ben-
Daya and Rahim, 2000; Cassady
et al., 2000; Rahim and Ben-Daya,
2001; Linderman et al., 2005; Ben-
Daya and Makhdoum, 1998; Lee
and Rahim, 2001; Yeung et al.,
2007; Alfares et al., 2005; Wu and
Makis, 2008; Radhoui et al., 2009;
Wu and Wang, 2011; Wang, 2011;
Mehrafrooz and Noorossana, 2011;
Ho and Quinino, 2012; Wang,
2012; Kim and Makis, 2012; Xiang,
2013; Liu et al., 2013; Zhong et al.,
2016; Yin et al., 2015; Yin et al.,
2015; Salmasnia et al., 2017;
Lesage and Dehombreux, 2012; Li
et al., 2017; Liu et al., 2017; Li
et al., 2017; Zhou et al., 2017; Li
et al., 2018; Bahria et al., 2018;
Salmasnia et al., 2018; Tagaras,
1988; Wang and Chen, 1995; Zhou
and Zhu, 2008; Panagiotidou and
Tagaras, 2010;
Charongrattanasakul and
Pongpullponsak, 2011; Pandey
et al., 2011; Pandey et al., 2012;
Tambe and Kulkarni, 2014 ; Zhang
et al., 2015; Makis, 2015; Tambe
and Kulkarni, 2015; Ardakan et al.,
2016; Jafari and Makis, 2016;
Jafari and Makis, 2016; Bouslah
(Kuo, 2006; Salmasnia et al.,
2018; Salmasnia et al., 2018;
Tasias and Nenes, 2018;
Salmasnia et al., 2018;
Salmasnia et al., 2019;
Bouslah et al., 2016; Jain and
Lad, 2017; Panagiotidou and
Nenes, 2009; Nenes and
Panagiotidou, 2011; Rahim
and Shakil, 2011; Maillart
et al., 2009)
(continued on next page)
Table 8
. Types of designs.
Economic (Rahim and Ben-Daya, 2001; Wang and Sheu, 2003; Makis and
Fung, 1998; Alfares et al., 2005; Wu and Makis, 2008; Radhoui
et al., 2009; Lin et al., 2011; Liu et al., 2013; Yin et al., 2015;
Wan et al., 2018; Tagaras, 1988; Wang et al., 2009; Tambe and
Kulkarni, 2014 ; Tambe and Kulkarni, 2015; Bouslah et al., 2016;
Bouslah et al., 2018; Hsu and Kuo, 1995; Chiu and Huang, 1996;
Panagiotidou and Tagaras, 2008; Chang et al., 2009;
Panagiotidou and Nenes, 2009; Nenes and Panagiotidou, 2011;
Mehdi et al., 2010; Radhoui et al., 2010; Dhouib et al., 2012;
Rivera-G´
omez et al., 2013; Shrivastava et al., 2016; Dan et al.,
2016; Yin and Makis, 2010; Cheng et al., 2018; Wan et al., 2018;
Wang et al., 2019; Kouki et al., 2014; Nguyen et al., 2019; Zhou
and Liu, 2016; Rivera-Gomez et al., 2013; Ivy and Nembhard,
2005; Ji-Wen et al., 2010; Chan, 2003; Chan and Wu, 2009;
Yeong et al., 2013)
Economic/
Statistical
(Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-Daya,
1998; Chiu and Huang, 1995; Chiu and Huang, 1996; Ben-Daya,
1999; Ben-Daya and Rahim, 2000; Rahim and Ben-Daya, 2001;
Linderman et al., 2005; Ben-Daya and Makhdoum, 1998; Lee and
Rahim, 2001; Yeung et al., 2007; Wu and Makis, 2008; Wu and
Wang, 2011; Wang, 2011; Mehrafrooz and Noorossana, 2011;
Ho and Quinino, 2012; Wang, 2012; Xiang, 2013; Liu et al.,
2013; Zhong et al., 2016; Yin et al., 2015; Salmasnia et al., 2017;
Zhong and Ma, 2017; Li et al., 2017; Liu et al., 2017; Li et al.,
2017; Zhou et al., 2017; Li et al., 2018; Bahria et al., 2018;
Salmasnia et al., 2018; Salmasnia et al., 2018; Tasias and Nenes,
2018; Salmasnia et al., 2018; Salmasnia et al., 2019; Wang and
Chen, 1995; Zhou and Zhu, 2008; Panagiotidou and Tagaras,
2010; Charongrattanasakul and Pongpullponsak, 2011; Pandey
et al., 2011; Pandey et al., 2012; Zhang et al., 2015; Makis, 2015;
Ardakan et al., 2016; Jafari and Makis, 2016; Tambe and
Kulkarni, 2016; Farahani et al., 2019; Li et al., 2019; Pandey
et al., 2010; Engin, 2010; Rahim and Shakil, 2011; Rasay et al.,
2018; Yin and Makis, 2010; Rasay et al., 2018; Pasha and
Moghadam, 2018; Deloux et al., 2009; Yang and Zeng, 2018 Apr;
Zhang et al., 2018; Bahria et al., 2019; He et al., 2019; Yeong
et al., 2013; Ali et al., 2020)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
7
machine to stop or produce a number of defective units. The goal of an
effective maintenance policy is to keep the equipment in optimal oper-
ating condition and ensure reliable performance.
There are two general policies in maintenance planning: corrective
maintenance (repair after the failure of the machine), preventive
maintenance (repair before the failure of the machine). In the corrective
maintenance, the machine continues to operate until it breaks down,
and then the repairs are done. In preventive maintenance, the condition
of the machine before failure is assessed using a criterion (time, usage,
condition, or alarm) and if needed, it will be repaired.
In maintenance planning, the goal is usually to minimize costs and
the objective function is usually dened as follows:
Minimize (total maintenance cost in the time) =Inspection cost +
Number of preventive maintenances * Average cost +The average
number of failures * Average cost +Cost of stopping production
(duration of failure or preventive maintenance if production needs to be
stopped).
The inputs of this function are statistical distribution of equipment
failure and repair times, inspection and repair costs and lost production
costs, and the limitations of this function are the aggregate production
plan, available resources and acceptable quality level. The output of this
objective function is an inspection schedule and preventive maintenance
and repair in the event of a breakdown.
If preventive maintenance is not performed, the total cost of repairs
will be at the time of equipment failure (which will usually be a high
cost), but if preventive maintenance is done, as the number of preventive
maintenance increases, the cost of preventive maintenance will increase,
but the cost of failure will decrease faster than increasing preventive
maintenance cost, and at one point, the cost of preventive maintenance
is not offset by the reduction in breakdown costs. This point is the
optimal number of preventive maintenances. Therefore, preventive
maintenance is used to reduce the frequency of failures.
The production line stops when the machine breaks down or some-
times during preventive maintenance. The duration of the stop affects
the cost of maintenance. The papers have tried to get closer to the reality
of production environments by considering the time for repairs. The
time for maintenance is one of the important characteristics that papers
can be categorized based on it. As can be seen in Table 15, in some
Table 9 (continued )
Fixed Variable
et al., 2016; Khrueasom and
Pongpullponsak, 2017; Tambe and
Kulkarni, 2016; Bouslah et al.,
2016; Rasay et al., 2018; Latrous
et al., 2018; Farahani et al., 2019; Li
et al., 2019; Chiu and Huang, 1996;
Pandey et al., 2010; Engin, 2010;
Rahim and Shakil, 2011; Morales,
2013; Shrivastava et al., 2016; Dan
et al., 2016; Rasay et al., 2018; Yin
and Makis, 2010; Rasay et al., 2018;
Pasha and Moghadam, 2018; Duan
et al., 2019; Deloux et al., 2009; Pan
et al., 2012; Zhang et al., 2018;
Bahria et al., 2019; Yeong et al.,
2013; Ali et al., 2020)
Control
limit
(Rahim and Banerjee, 1993; Rahim,
1994; Rahim and Ben-Daya, 1998;
Chiu and Huang, 1995; Chiu and
Huang, 1996; Ben-Daya, 1999; Ben-
Daya and Rahim, 2000; Cassady
et al., 2000; Rahim and Ben-Daya,
2001; Linderman et al., 2005; Ben-
Daya and Makhdoum, 1998; Lee
and Rahim, 2001; Yeung et al.,
2007; Wu and Wang, 2011; Wang,
2011; Mehrafrooz and Noorossana,
2011; Ho and Quinino, 2012;
Wang, 2012; Kim and Makis, 2012;
Xiang, 2013; Liu et al., 2013; Zhong
et al., 2016; Yin et al., 2015; Yin
et al., 2015; Salmasnia et al., 2017;
Lesage and Dehombreux, 2012; Li
et al., 2017; Liu et al., 2017; Li
et al., 2017; Zhou et al., 2017; Li
et al., 2018; Bahria et al., 2018;
Salmasnia et al., 2018; Tagaras,
1988; Wang and Chen, 1995; Zhou
and Zhu, 2008; Panagiotidou and
Tagaras, 2010;
Charongrattanasakul and
Pongpullponsak, 2011; Pandey
et al., 2011; Pandey et al., 2012;
Zhang et al., 2015; Makis, 2015;
Ardakan et al., 2016; Jafari and
Makis, 2016; Jafari and Makis,
2016; Khrueasom and
Pongpullponsak, 2017; Bouslah
et al., 2016; Rasay et al., 2018;
Latrous et al., 2018; Farahani et al.,
2019; Li et al., 2019; Chiu and
Huang, 1996; Pandey et al., 2010;
Engin, 2010; Rahim and Shakil,
2011; Morales, 2013; Shrivastava
et al., 2016; Dan et al., 2016; Rasay
et al., 2018; Yin and Makis, 2010;
Rasay et al., 2018; Pasha and
Moghadam, 2018; Duan et al.,
2019; Deloux et al., 2009; Pan et al.,
2012; Zhang et al., 2018; Bahria
et al., 2019; He et al., 2019; Yeong
et al., 2013; Ali et al., 2020)
(Salmasnia et al., 2018;
Salmasnia et al., 2018; Tasias
and Nenes, 2018; Wan et al.,
2018; Salmasnia et al., 2019;
Jain and Lad, 2017;
Panagiotidou and Nenes,
2009; Rahim and Shakil,
2011; Maillart et al., 2009)
Table 10
. The type of process deviations.
Process mean (Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-
Daya, 1998; Chiu and Huang, 1995; Chiu and Huang, 1996;
Ben-Daya, 1999; Ben-Daya and Rahim, 2000; Cassady et al.,
2000; Rahim and Ben-Daya, 2001; Linderman et al., 2005;
Ben-Daya and Makhdoum, 1998; Lee and Rahim, 2001;
Yeung et al., 2007; Wu and Makis, 2008; Mehrafrooz and
Noorossana, 2011; Ho and Quinino, 2012; Kim and Makis,
2012; Xiang, 2013; Liu et al., 2013; Yin et al., 2015; Yin et al.,
2015; Lu et al., 2016; Salmasnia et al., 2017; Zhong and Ma,
2017; Lesage and Dehombreux, 2012; Li et al., 2017; Liu
et al., 2017; Li et al., 2017; Zhou et al., 2017; Li et al., 2018;
Bahria et al., 2018; Salmasnia et al., 2018; Salmasnia et al.,
2018; Tasias and Nenes, 2018; Wan et al., 2018; Salmasnia
et al., 2018; Salmasnia et al., 2019; Tagaras, 1988; Zhou and
Zhu, 2008; Panagiotidou and Tagaras, 2010; Pandey et al.,
2011; Pandey et al., 2012; Zhang et al., 2015; Makis, 2015;
Ardakan et al., 2016; Jain and Lad, 2017; Rasay et al., 2018;
Latrous et al., 2018; Farahani et al., 2019; Chiu and Huang,
1996; Panagiotidou and Nenes, 2009; Nenes and
Panagiotidou, 2011; Pandey et al., 2010; Engin, 2010; Rahim
and Shakil, 2011; Morales, 2013; Shrivastava et al., 2016;
Dan et al., 2016; Rasay et al., 2018; Yin and Makis, 2010;
Rasay et al., 2018; Pasha and Moghadam, 2018; Duan et al.,
2019; Pan et al., 2012; Zhou and Liu, 2016; Zhang et al.,
2018; Bahria et al., 2019; He et al., 2019; Yeong et al., 2013;
Ali et al., 2020)
Process standard
deviation
(Chiu and Huang, 1995; Salmasnia et al., 2018; Tasias and
Nenes, 2018; Morales, 2013)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
8
papers, the time is considered to perform maintenance, but in some
papers, it is ignored.
In the maintenance planning, the best and most effective mainte-
nance techniques for each equipment are determined. The goal is to
achieve the desired reliability at the lowest possible cost. In the past, it
was believed that equipment would wear out over time, so preventive
maintenance would be carried out based on time and usage, but research
shows that equipment failure is not linearly related to its lifespan. So, in
recent years, to reduce costs, often condition monitoring is done.
Table 16 shows the type of maintenance in the papers. It should be noted
that to maintain the authenticity of the words of the papers, the same
title mentioned for repairs in the paper is given in the tables. In the
following, each type is described.
Preventive Maintenance (PM) is done before the equipment breaks
down to avoid the high costs of machine failure, stop production, and
the production of non-conformity products. Determining the condition
of a machine for maintenance may be optical or require special equip-
ment testing. The breakdown status of a piece of equipment may or may
not have any symptoms. Therefore, there is no need for preventive
maintenance for equipment that does not show signs of failure. In this
equipment, the distribution of the probability of failure is dened. PM
includes Time-based Maintenance (TBM), Aged-Based Maintenance
(ABM), Quality-Based Maintenance (QBM), Usage-Based Maintenance
(UBM), Condition-Based Maintenance (CBM), Predictive Maintenance
and Detective Maintenance. Alarms used for preventive maintenance are
either based on monitoring equipment conditions or based on machine
output (control charts). PM usually performs when the correct alarm is
received from the machine, and the maintenance returns the process to
the in-control state. PM can be turned the process into either the as good
as a new state or a state between the previous state and the as good as a
new state (better than the state before the repairs). If the correct alarms
are not obtained from the system, at the end of the planning period,
Planned Maintenance performs, which usually turns the process into the
as good as new state.
When a false alarm is received from the machine, Compensation
Maintenance performs. Reactive Maintenance performs when the cor-
rect alarms are received from the machine. Selective maintenance is
doing in such a way that a subset of operations for repairs should be
select at the same time, which is usually appropriate when there is either
a resource constraint or time constraint or budget. In condition-based
maintenance (CBM), repairs perform after receiving signals of the ma-
chine. In condition-based maintenance, the monitoring of the conditions
for repairs is similar to the quality control charts. Aged-based mainte-
nance is doing based on the age of the equipment. When the machine is
stopped by a breakdown, Corrective Maintenance (CM) is performed.
In the repair, the process can be turned into the as good as new state
or become a state between the previous state and the as good as new
state (better than the state before the maintenance). In the Restoration,
Table 11
. Number of process modes.
An in-control mode, An out of
control mode, A failure mode
(Makis and Fung, 1995; Wu and Makis, 2008; Wu
and Wang, 2011; Wang, 2011; Mehrafrooz and
Noorossana, 2011; Ho and Quinino, 2012; Wang,
2012; Zhong et al., 2016; Yin et al., 2015; Fakher
et al., 2018; Lesage and Dehombreux, 2012; Liu
et al., 2017; Salmasnia et al., 2018; Tasias and
Nenes, 2018; Wan et al., 2018; Salmasnia et al.,
2019; Panagiotidou and Tagaras, 2010;
Charongrattanasakul and Pongpullponsak, 2011;
Pandey et al., 2011; Pandey et al., 2012;
Panagiotidou and Tagaras, 2012 ; Tambe and
Kulkarni, 2014 ; Makis, 2015; Jafari and Makis,
2016; Jafari and Makis, 2016; Bouslah et al.,
2016; Tambe and Kulkarni, 2016; Jain and Lad,
2017; Latrous et al., 2018; Li et al., 2019;
Panagiotidou and Tagaras, 2008; Panagiotidou
and Nenes, 2009; Nenes and Panagiotidou, 2011;
Dhouib et al., 2012; Shrivastava et al., 2016; Dan
et al., 2016; Yin and Makis, 2010; Azadeh et al.,
2017; Cheng et al., 2018; Duan et al., 2019; Wang
et al., 2019; Beheshti Fakher et al., 2017; Kouki
et al., 2014; Lesage and Dehombreux, 2012; Yang
and Zeng, 2018 Apr; Ji-Wen et al., 2010; Gupta
et al., 2009)
An in-control mode, An out of
control mode
(Rahim and Banerjee, 1993; Rahim, 1994; Rahim
and Ben-Daya, 1998; Chiu and Huang, 1995; Chiu
and Huang, 1996; Ben-Daya, 1999; Ben-Daya and
Rahim, 2000; Cassady et al., 2000; Rahim and
Ben-Daya, 2001; Linderman et al., 2005; Wang
and Sheu, 2003; Kuo, 2006; Ben-Daya and
Makhdoum, 1998; Lee and Rahim, 2001; Yeung
et al., 2007; Makis and Fung, 1998; Alfares et al.,
2005; Radhoui et al., 2009; Lin et al., 2011; Chen,
2013; Nourelfath et al., 2016; Salmasnia et al.,
2017; Zhong and Ma, 2017; Li et al., 2017; Zhou
et al., 2017; Salmasnia et al., 2018; Salmasnia
et al., 2018; Wang and Chen, 1995; Zhou and Zhu,
2008; Ardakan et al., 2016; Khrueasom and
Pongpullponsak, 2017; Rasay et al., 2018; Hsu
and Kuo, 1995; Chiu and Huang, 1996;
Panagiotidou and Tagaras, 2007; Chang et al.,
2009; Engin, 2010; Rahim and Shakil, 2011;
Morales, 2013; Rasay et al., 2018; Pasha and
Moghadam, 2018; Pan et al., 2012; Maillart et al.,
2009; Zhang et al., 2018; Lin, 2004; Ivy and
Nembhard, 2005; Chan and Wu, 2009; Yeong
et al., 2013; Ali et al., 2020)
An in-control mode, Several out
of control modes, A failure
mode
(Kim and Makis, 2012; Xiang, 2013; Lu et al.,
2016; Tagaras, 1988; Chiang and Yuan, 2001;
Farahani et al., 2019; Colledani and Tolio, 2012;
Deloux et al., 2009; Nguyen et al., 2019; Zhou and
Liu, 2016; Le and Tan, 2013)
An in-control mode, Several out
of control modes
(Wang et al., 2009; Zhang et al., 2015)
An in-control mode, A failure
mode
(Rivera-G´
omez et al., 2013; Wan et al., 2018)
Table 13
. (continued) The qualitative variables that are less used in papers.
A binary decision variable indicating whether
or not sampling occurs at the beginning of
the ith period
(Yeung et al., 2007)
Level of quality control (Bouslah et al., 2018)
The threshold level of the rate of non-
conforming units
(Radhoui et al., 2009; Hsu and
Kuo, 1995; Mehdi et al., 2010)
The time of the rst inspection (Salmasnia et al., 2017;
Panagiotidou and Tagaras, 2012)
The sampling rate (Zhang et al., 2015; Bouslah et al.,
2016)
Clearance number, Inspection stopping
threshold
(Bouslah et al., 2016)
Scheduled duration without monitoring,
Scheduled monitoring duration
(Yin et al., 2015)
Minimum and maximum thresholds for the rate
of nonconforming items
(Azadeh et al., 2017)
Table 12
. The qualitative variables that are less used in papers.
The number of production lot to
sampling
(Hsu and Kuo, 1995)
The optimal stopping time for control
policy
(Duan et al., 2019)
Value of the inspection quality level (Nguyen et al., 2019)
Optimal inspection strategy (Chan, 2003; Chan and Wu, 2009)
Weighting parameter (Yin et al., 2015)
The decision interval (control limit) (Li et al., 2017; Li et al., 2018;
Shrivastava et al., 2016)
Design parameter of an error function (Salmasnia et al., 2018)
Failure rate threshold beyond which PM
activities should be performed
(Ben-Daya and Makhdoum, 1998; Lu
et al., 2016; Radhoui et al., 2010)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
9
Overhaul, Major Repair, Perfect Corrective, Perfect Preventive, Full
perfect, Total Maintenance, Preventive Replacement, Corrective
Replacement, Complete Repair and Replacement, the process turns into
the as good as new state.
In using the control chart, if the stoppage is due to a single obser-
vation out of the control limits, corrective maintenance of type A per-
forms, and if the stoppage is due to a sequence of several observations
between the warning and control limits, corrective maintenance of type
B performs. The repairs of A and B are imperfect with measurable per-
formances. By the Block Replacement with Minimal Repair, a
manufacturing system component is replaced based on two occurrences:
either the failure of the component or preset block replacement times (if
the age of the manufacturing system component is no less than a
threshold value), Otherwise, a minimal repair will be taken to restore
the manufacturing system component.
The Minimal Maintenance, the Minimal Corrective, and the Imper-
fect Preventive are imperfect (the state between as-good-as-new state
and previous state). The Delayed Maintenance policy allows a delay time
Table 14
. The qualitative variables used in most papers.
The sample size (Rahim and Banerjee, 1993; Rahim, 1994; Rahim
and Ben-Daya, 1998; Chiu and Huang, 1995;
Chiu and Huang, 1996; Ben-Daya, 1999; Ben-
Daya and Rahim, 2000; Cassady et al., 2000;
Rahim and Ben-Daya, 2001; Linderman et al.,
2005; Kuo, 2006; Lee and Rahim, 2001; Yeung
et al., 2007; Wu and Wang, 2011; Xiang, 2013;
Liu et al., 2013; Yin et al., 2015; Yin et al., 2015;
Salmasnia et al., 2017; Zhong and Ma, 2017;
Lesage and Dehombreux, 2012; Li et al., 2017;
Liu et al., 2017; Li et al., 2017; Li et al., 2018;
Bahria et al., 2018; Salmasnia et al., 2018;
Salmasnia et al., 2018; Tasias and Nenes, 2018;
Wan et al., 2018; Salmasnia et al., 2018;
Salmasnia et al., 2019; Tagaras, 1988; Wang and
Chen, 1995; Zhou and Zhu, 2008; Panagiotidou
and Tagaras, 2010; Charongrattanasakul and
Pongpullponsak, 2011; Pandey et al., 2011;
Pandey et al., 2012; Panagiotidou and Tagaras,
2012 ; Tambe and Kulkarni, 2014 ; Zhang et al.,
2015; Tambe and Kulkarni, 2015; Ardakan et al.,
2016; Khrueasom and Pongpullponsak, 2017;
Tambe and Kulkarni, 2016; Jain and Lad, 2017;
Bouslah et al., 2016; Rasay et al., 2018; Latrous
et al., 2018; Farahani et al., 2019; Chiu and
Huang, 1996; Chang et al., 2009; Panagiotidou
and Nenes, 2009; Nenes and Panagiotidou, 2011;
Rahim and Shakil, 2011; Morales, 2013;
Shrivastava et al., 2016; Dan et al., 2016; Rasay
et al., 2018; Yin and Makis, 2010; Rasay et al.,
2018; Pasha and Moghadam, 2018; Pan et al.,
2012; Maillart et al., 2009; Yang and Zeng, 2018
Apr; Zhang et al., 2018; Bahria et al., 2019;
Yeong et al., 2013)
The control limit (Rahim and Banerjee, 1993; Rahim, 1994; Rahim
and Ben-Daya, 1998; Chiu and Huang, 1995;
Chiu and Huang, 1996; Ben-Daya, 1999; Ben-
Daya and Rahim, 2000; Cassady et al., 2000;
Rahim and Ben-Daya, 2001; Linderman et al.,
2005; Ben-Daya and Makhdoum, 1998; Lee and
Rahim, 2001; Yeung et al., 2007; Wu and Makis,
2008; Ho and Quinino, 2012; Wang, 2012;
Xiang, 2013; Liu et al., 2013; Zhong et al., 2016;
Yin et al., 2015; Yin et al., 2015; Salmasnia et al.,
2017; Zhong and Ma, 2017; Lesage and
Dehombreux, 2012; Li et al., 2017; Liu et al.,
2017; Li et al., 2017; Bahria et al., 2018;
Salmasnia et al., 2018; Salmasnia et al., 2018;
Tasias and Nenes, 2018; Wan et al., 2018;
Salmasnia et al., 2018; Salmasnia et al., 2019;
Tagaras, 1988; Zhou and Zhu, 2008;
Panagiotidou and Tagaras, 2010; Pandey et al.,
2011; Pandey et al., 2012; Panagiotidou and
Tagaras, 2012 ; Makis, 2015; Ardakan et al.,
2016; Jafari and Makis, 2016; Khrueasom and
Pongpullponsak, 2017; Jain and Lad, 2017;
Rasay et al., 2018; Latrous et al., 2018; Farahani
et al., 2019; Li et al., 2019; Chiu and Huang,
1996; Chang et al., 2009; Panagiotidou and
Nenes, 2009; Rahim and Shakil, 2011; Morales,
2013; Dan et al., 2016; Rasay et al., 2018; Yin
and Makis, 2010; Rasay et al., 2018; Wan et al.,
2018; Pasha and Moghadam, 2018; Duan et al.,
2019; Deloux et al., 2009; Nguyen et al., 2019;
Pan et al., 2012; Maillart et al., 2009; Yang and
Zeng, 2018 Apr; Zhang et al., 2018; Bahria et al.,
2019; He et al., 2019; Yeong et al., 2013; Ali
et al., 2020)
The sampling interval
(inspection interval)
(Rahim and Banerjee, 1993; Rahim, 1994; Rahim
and Ben-Daya, 1998; Chiu and Huang, 1995;
Chiu and Huang, 1996; Ben-Daya, 1999; Ben-
Daya and Rahim, 2000; Cassady et al., 2000;
Rahim and Ben-Daya, 2001; Linderman et al.,
2005; Wang and Sheu, 2003; Kuo, 2006; Makis
and Fung, 1995; Ben-Daya and Makhdoum,
1998; Lee and Rahim, 2001; Wu and Makis,
Table 14 (continued )
2008; Lin et al., 2011; Wu and Wang, 2011;
Wang, 2011; Mehrafrooz and Noorossana, 2011;
Ho and Quinino, 2012; Wang, 2012; Chen, 2013;
Xiang, 2013; Liu et al., 2013; Zhong et al., 2016;
Yin et al., 2015; Yin et al., 2015; Nourelfath et al.,
2016; Zhong and Ma, 2017; Li et al., 2017; Liu
et al., 2017; Li et al., 2017; Li et al., 2018; Bahria
et al., 2018; Salmasnia et al., 2018; Salmasnia
et al., 2018; Tasias and Nenes, 2018; Wan et al.,
2018; Salmasnia et al., 2018; Salmasnia et al.,
2019; Tagaras, 1988; Wang and Chen, 1995;
Zhou and Zhu, 2008; Wang et al., 2009;
Panagiotidou and Tagaras, 2010;
Charongrattanasakul and Pongpullponsak, 2011;
Pandey et al., 2011; Panagiotidou and Tagaras,
2012 ; Tambe and Kulkarni, 2014 ; Makis, 2015;
Tambe and Kulkarni, 2015; Ardakan et al., 2016;
Khrueasom and Pongpullponsak, 2017; Tambe
and Kulkarni, 2016; Jain and Lad, 2017; Rasay
et al., 2018; Latrous et al., 2018; Farahani et al.,
2019; Chiu and Huang, 1996; Chang et al., 2009;
Panagiotidou and Nenes, 2009; Nenes and
Panagiotidou, 2011; Engin, 2010; Morales, 2013;
Shrivastava et al., 2016; Dan et al., 2016; Rasay
et al., 2018; Yin and Makis, 2010; Rasay et al.,
2018; Pasha and Moghadam, 2018; Pan et al.,
2012; Zhang et al., 2018; Bahria et al., 2019; Lin,
2004; Yeong et al., 2013; Ali et al., 2020)
The number of the sampling
(inspections) until
maintenance
(Rahim and Banerjee, 1993; Rahim, 1994; Rahim
and Ben-Daya, 1998; Ben-Daya, 1999; Wang and
Sheu, 2003; Ben-Daya and Makhdoum, 1998;
Makis and Fung, 1998; Alfares et al., 2005; Lin
et al., 2011; Chen, 2013; Zhong et al., 2016;
Nourelfath et al., 2016; Salmasnia et al., 2017; Li
et al., 2017; Bahria et al., 2018; Wang et al.,
2009; Panagiotidou and Tagaras, 2010; Pandey
et al., 2012; Rasay et al., 2018; Rahim and Shakil,
2011; Pasha and Moghadam, 2018; Beheshti
Fakher et al., 2017; Lin, 2004)
The inspection period (Lesage and Dehombreux, 2012; Chiang and
Yuan, 2001; Rasay et al., 2018; Rasay et al.,
2018; Deloux et al., 2009)
Number of sampling taken
before Planned maintenance
(Rahim and Ben-Daya, 2001; Zhong and Ma,
2017; Charongrattanasakul and Pongpullponsak,
2011; Ardakan et al., 2016; Khrueasom and
Pongpullponsak, 2017; Dan et al., 2016)
Warning limit (Ben-Daya and Makhdoum, 1998; Salmasnia
et al., 2018; Salmasnia et al., 2018; Tasias and
Nenes, 2018; Salmasnia et al., 2019;
Charongrattanasakul and Pongpullponsak, 2011;
Makis, 2015; Panagiotidou and Nenes, 2009)
The acceptance number (Wang and Chen, 1995; Tambe and Kulkarni,
2014 ; Makis, 2015; Tambe and Kulkarni, 2016;
Bouslah et al., 2016; Yang and Zeng, 2018 Apr)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
10
for the detection and maintenance after an alarm. In the Time-based
Preventive Replacement policy, repairs are doing at specied times.
The Autonomous Maintenance which continuously and automatically
improves the process and prevents breakdowns and defects.
In general, the types of maintenances mentioned above are divided
into two categories: repairs before the failure or alarm and repairs after
the failure or alarm, according to Table 17.
After the repair, the equipment turns into either the as-good-as-new
state, or the state between as-good-as-new state and previous state
(better than the previous state). The rst is called perfect repair and the
second is imperfect repair. Papers based on the result of repair can be
divided into two categories, perfect or imperfect, which are listed in
Table 18.
Optimal equipment conditions deteriorate over time. The pattern of
failure of machines and the process of deterioration should be studied.
The deteriorating process of machines is listed in Tables 19 and 20. More
equipment failure patterns can be considered according to Markov’s
process, in which the state of the machine at any given moment depends
only on its current state. Markov chain is a discrete-time stochastic
process in which the future status of a system depends only on the
current state of the system. However, in a continuous-time Markov
chain, the time of each state is exponentially distributed. In each Markov
chain, if the probability of transition from a state to another state is
independent of time (or stage), then the Markov chain will be homo-
geneous. In the semi-Markov chains, the probability of a change in status
depends on the amount of time that has elapsed since the entry into the
current state. In the partially observable Markov Decision, the states are
only partially observable. The observations of the state cannot accu-
rately determine the state of the system.
Table 16
Type of maintenance.
Reactive (Linderman et al., 2005; Yin et al., 2015; Zhou et al.,
2017; Salmasnia et al., 2018; Zhou and Zhu, 2008;
Charongrattanasakul and Pongpullponsak, 2011;
Ardakan et al., 2016; Khrueasom and Pongpullponsak,
2017; Rasay et al., 2018; Rasay et al., 2018; Wan et al.,
2018; Pan et al., 2012)
Condition-based (Wu and Makis, 2008; Wang, 2012; Liu et al., 2013; Liu
et al., 2017; Panagiotidou and Tagaras, 2010; Zhang
et al., 2015; Bouslah et al., 2016; Li et al., 2019;
Panagiotidou and Nenes, 2009; Rasay et al., 2018; Yin
and Makis, 2010; Cheng et al., 2018; Wan et al., 2018;
Deloux et al., 2009; Nguyen et al., 2019; Maillart et al.,
2009; Zhou and Liu, 2016; Lampreia et al., 2018)
Preventive (Chiu and Huang, 1995; Chiu and Huang, 1996; Ben-
Daya, 1999; Ben-Daya and Rahim, 2000; Cassady et al.,
2000; Wang and Sheu, 2003; Ben-Daya and
Makhdoum, 1998; Lee and Rahim, 2001; Yeung et al.,
2007; Radhoui et al., 2009; Lin et al., 2011; Mehrafrooz
and Noorossana, 2011; Chen, 2013; Xiang, 2013;
Zhong et al., 2016; Yin et al., 2015; Lu et al., 2016;
Nourelfath et al., 2016; Salmasnia et al., 2017; Fakher
et al., 2018; Liu et al., 2017; Bahria et al., 2018;
Salmasnia et al., 2018; Salmasnia et al., 2018; Tasias
and Nenes, 2018; Wan et al., 2018; Salmasnia et al.,
2018; Salmasnia et al., 2019; Tagaras, 1988;
Panagiotidou and Tagaras, 2010; Pandey et al., 2011;
Pandey et al., 2012; Makis, 2015; Jafari and Makis,
2016; Jafari and Makis, 2016; Bouslah et al., 2016;
Bouslah et al., 2018; Rasay et al., 2018; Latrous et al.,
2018; Farahani et al., 2019; Li et al., 2019; Hsu and
Kuo, 1995; Yerel et al., 2007; Panagiotidou and
Tagaras, 2007; Chang et al., 2009; Panagiotidou and
Nenes, 2009; Nenes and Panagiotidou, 2011; Pandey
et al., 2010; Mehdi et al., 2010; Radhoui et al., 2010;
Rahim and Shakil, 2011; Colledani and Tolio, 2012;
Morales, 2013; Dhouib et al., 2012; Dan et al., 2016;
Rasay et al., 2018; Yin and Makis, 2010; Azadeh et al.,
2017; Rasay et al., 2018; Wan et al., 2018; Pasha and
Moghadam, 2018; Duan et al., 2019; Kouki et al., 2014;
Zhou and Liu, 2016; Lesage and Dehombreux, 2012;
Rivera-Gomez et al., 2013; Alsyouf et al., 2016; Yang
and Zeng, 2018 Apr; Zhang et al., 2018; Bahria et al.,
2019; He et al., 2019)
Repair (Rahim and Banerjee, 1993; Rahim, 1994; Rahim and
Ben-Daya, 1998; Chiu and Huang, 1995; Chiu and
Huang, 1996; Ben-Daya, 1999; Ben-Daya and Rahim,
2000; Rahim and Ben-Daya, 2001; Wang and Sheu,
2003; Kuo, 2006; Ben-Daya and Makhdoum, 1998;
Wang and Chen, 1995; Chiang and Yuan, 2001; Tambe
and Kulkarni, 2014 ; Chiu and Huang, 1996; Rahim and
Shakil, 2011; Pasha and Moghadam, 2018; Lin, 2004;
Le and Tan, 2013; Ali et al., 2020)
Replacement (Rahim, 1994; Rahim and Ben-Daya, 1998; Wu and
Makis, 2008; Li et al., 2017; Liu et al., 2017; Li et al.,
2018; Chiang and Yuan, 2001; Tambe and Kulkarni,
2014 ; Jafari and Makis, 2016; Jafari and Makis, 2016;
Tambe and Kulkarni, 2016; Li et al., 2019; Nguyen
et al., 2019; Lin, 2004; Le and Tan, 2013; Ivy and
Nembhard, 2005; Ali et al., 2020)
Compensation (Mehrafrooz and Noorossana, 2011; Yin et al., 2015;
Zhong and Ma, 2017; Li et al., 2017; Zhou and Zhu,
2008; Charongrattanasakul and Pongpullponsak,
2011; Khrueasom and Pongpullponsak, 2017; Rasay
et al., 2018)
Restoration (Makis and Fung, 1998; Alfares et al., 2005; Nourelfath
et al., 2016; Tagaras, 1988; Rahim and Shakil, 2011;
Dhouib et al., 2012)
Age-replacement (Rahim and Banerjee, 1993; Lee and Rahim, 2001;
Yeung et al., 2007; Makis, 2015; Ji-Wen et al., 2010)
Planned (Linderman et al., 2005; Mehrafrooz and Noorossana,
2011; Zhong et al., 2016; Zhong and Ma, 2017; Li et al.,
2017; Zhou et al., 2017; Li et al., 2018; Zhou and Zhu,
2008; Charongrattanasakul and Pongpullponsak,
2011; Ardakan et al., 2016; Khrueasom and
Pongpullponsak, 2017; Dan et al., 2016; Pan et al.,
2012)
(continued on next page)
Table 15
. Duration of repair.
Not
negligible
(Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-Daya,
1998; Chiu and Huang, 1995; Chiu and Huang, 1996; Ben-Daya,
1999; Ben-Daya and Rahim, 2000; Cassady et al., 2000; Rahim and
Ben-Daya, 2001; Linderman et al., 2005; Kuo, 2006; Ben-Daya and
Makhdoum, 1998; Lee and Rahim, 2001; Makis and Fung, 1998;
Radhoui et al., 2009; Mehrafrooz and Noorossana, 2011; Yin et al.,
2015; Yin et al., 2015; Lu et al., 2016; Fakher et al., 2018; Zhong and
Ma, 2017; Lesage and Dehombreux, 2012; Li et al., 2017; Li et al.,
2017; Zhou et al., 2017; Li et al., 2018; Bahria et al., 2018; Salmasnia
et al., 2018; Tasias and Nenes, 2018; Wan et al., 2018; Salmasnia
et al., 2018; Tagaras, 1988; Wang and Chen, 1995; Chiang and Yuan,
2001; Zhou and Zhu, 2008; Wang et al., 2009; Panagiotidou and
Tagaras, 2010; Charongrattanasakul and Pongpullponsak, 2011;
Pandey et al., 2011; Pandey et al., 2012; Panagiotidou and Tagaras,
2012 ; Tambe and Kulkarni, 2014 ; Zhang et al., 2015; Makis, 2015;
Tambe and Kulkarni, 2015; Ardakan et al., 2016; Jafari and Makis,
2016; Jafari and Makis, 2016; Bouslah et al., 2016; Khrueasom and
Pongpullponsak, 2017; Tambe and Kulkarni, 2016; Jain and Lad,
2017; Bouslah et al., 2016; Bouslah et al., 2018; Latrous et al., 2018;
Farahani et al., 2019; Li et al., 2019; Hsu and Kuo, 1995; Chiu and
Huang, 1996; Yerel et al., 2007; Panagiotidou and Tagaras, 2007;
Panagiotidou and Tagaras, 2008; Chang et al., 2009; Panagiotidou
and Nenes, 2009; Nenes and Panagiotidou, 2011; Pandey et al.,
2010; Mehdi et al., 2010; Engin, 2010; Radhoui et al., 2010; Rahim
and Shakil, 2011; Colledani and Tolio, 2012; Morales, 2013; Dhouib
et al., 2012; Rivera-G´
omez et al., 2013; Shrivastava et al., 2016; Dan
et al., 2016; Rasay et al., 2018; Yin and Makis, 2010; Azadeh et al.,
2017; Cheng et al., 2018; Rasay et al., 2018; Wan et al., 2018; Pasha
and Moghadam, 2018; Duan et al., 2019; Wang et al., 2019; Beheshti
Fakher et al., 2017)
Negligible (Wang and Sheu, 2003; Makis and Fung, 1995; Yeung et al., 2007;
Alfares et al., 2005; Wu and Makis, 2008; Lin et al., 2011; Wu and
Wang, 2011; Wang, 2011; Ho and Quinino, 2012; Wang, 2012; Kim
and Makis, 2012; Chen, 2013; Xiang, 2013; Liu et al., 2013; Lu et al.,
2016; Nourelfath et al., 2016; Salmasnia et al., 2017; Liu et al., 2017;
Li et al., 2018; Salmasnia et al., 2018; Wang et al., 2009; Morales,
2013; Dhouib et al., 2012; Beheshti Fakher et al., 2017; Kouki et al.,
2014; Deloux et al., 2009; Nguyen et al., 2019; Ali et al., 2020)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
11
In a shock model, a system is subjected to random shocks in the in-
control state. These shocks cause damage to the system. The amount
of damage is a random variable. The delay time divides the failure
process into two stages: the rst step from the new state to the out of
control state and the second step from the out of control state to the
failure state. The second step is called the failure delay time. In the
Geometric process, the mean lifetime sequence of a system decreases
geometrically as the number of repairs increases. The Gamma process
assumes that shocks follow a gamma distribution. The failure rate is the
number of times a system or a component fails per unit of time. This rate
can be either xed or increasing over time.
The length of time it takes for a machine to break down follows a
Table 16 (continued )
Corrective (Cassady et al., 2000; Yeung et al., 2007; Radhoui
et al., 2009; Mehrafrooz and Noorossana, 2011; Kim
and Makis, 2012; Xiang, 2013; Zhong et al., 2016; Yin
et al., 2015; Salmasnia et al., 2017; Zhong and Ma,
2017; Lesage and Dehombreux, 2012; Li et al., 2017; Li
et al., 2018; Bahria et al., 2018; Salmasnia et al., 2018;
Tasias and Nenes, 2018; Wan et al., 2018; Salmasnia
et al., 2019; Panagiotidou and Tagaras, 2010; Pandey
et al., 2011; Panagiotidou and Tagaras, 2012 ; Tambe
and Kulkarni, 2014 ; Tambe and Kulkarni, 2015; Jafari
and Makis, 2016; Bouslah et al., 2016; Tambe and
Kulkarni, 2016; Bouslah et al., 2016; Bouslah et al.,
2018; Latrous et al., 2018; Farahani et al., 2019; Hsu
and Kuo, 1995; Panagiotidou and Nenes, 2009; Nenes
and Panagiotidou, 2011; Pandey et al., 2010; Radhoui
et al., 2010; Colledani and Tolio, 2012; Dan et al.,
2016; Rasay et al., 2018; Yin and Makis, 2010; Azadeh
et al., 2017; Cheng et al., 2018; Duan et al., 2019;
Beheshti Fakher et al., 2017; Kouki et al., 2014; Lesage
and Dehombreux, 2012; Alsyouf et al., 2016; Yang and
Zeng, 2018 Apr; Zhang et al., 2018; Bahria et al., 2019;
He et al., 2019)
Minor repair (Wu and Wang, 2011; Wang, 2011; Chan, 2003; Chan
and Wu, 2009)
Major repair (Wu and Wang, 2011; Wang, 2011; Chan, 2003; Chan
and Wu, 2009)
Aged-based (Xiang, 2013; Jafari and Makis, 2016; Tambe and
Kulkarni, 2016; Beheshti Fakher et al., 2017)
Overhaul (Bouslah et al., 2016; Mehdi et al., 2010; Rivera-G´
omez
et al., 2013; Cheng et al., 2018; Wang et al., 2019;
Maillart et al., 2009; Rivera-Gomez et al., 2013)
Predictive (Yin et al., 2015; Yin et al., 2015; Li et al., 2017; Li
et al., 2018; Dan et al., 2016; Deloux et al., 2009)
Minimal repair (Lin et al., 2011; Lu et al., 2016; Fakher et al., 2018;
Wang et al., 2009; Panagiotidou and Tagaras, 2012 ;
Wang et al., 2019; Beheshti Fakher et al., 2017;
Maillart et al., 2009; Rivera-Gomez et al., 2013)
Perfect corrective (Panagiotidou and Tagaras, 2008)
Minimal maintenance (Panagiotidou and Tagaras, 2008)
Perfect preventive (Panagiotidou and Tagaras, 2012 ; Panagiotidou and
Tagaras, 2008)
Selective (Tambe and Kulkarni, 2014 ; Tambe and Kulkarni,
2015; Tambe and Kulkarni, 2016)
Time-based preventive (Makis and Fung, 1995; Lesage and Dehombreux,
2012; Bouslah et al., 2016)
Minimal corrective (Pandey et al., 2012; Shrivastava et al., 2016)
‘A’ corrective (Ho and Quinino, 2012)
‘B’ corrective (Ho and Quinino, 2012)
Full preventive (Kim and Makis, 2012)
Total maintenance (Engin, 2010)
Preventive replacement (Liu et al., 2013; Jain and Lad, 2017; Deloux et al.,
2009)
Corrective replacement (Jain and Lad, 2017; Deloux et al., 2009)
Block replacement with
minimal repair
(Ji-Wen et al., 2010)
Delayed (Zhang et al., 2015)
Autonomous (Azizi, 2015)
Quality based (Lesage and Dehombreux, 2012)
Imperfect preventive (Shrivastava et al., 2016; Wang et al., 2019)
Complete repair (Fakher et al., 2018; Wang et al., 2009)
Table 18
. The repair result.
Perfect (Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-Daya, 1998;
Chiu and Huang, 1995; Chiu and Huang, 1996; Ben-Daya, 1999; Ben-
Daya and Rahim, 2000; Cassady et al., 2000; Linderman et al., 2005;
Wang and Sheu, 2003; Makis and Fung, 1995; Lee and Rahim, 2001;
Yeung et al., 2007; Makis and Fung, 1998; Alfares et al., 2005; Wu and
Makis, 2008; Radhoui et al., 2009; Lin et al., 2011; Wu and Wang, 2011;
Wang, 2011; Mehrafrooz and Noorossana, 2011; Wang, 2012; Kim and
Makis, 2012; Xiang, 2013; Liu et al., 2013; Zhong et al., 2016; Yin et al.,
2015; Yin et al., 2015; Nourelfath et al., 2016; Salmasnia et al., 2017;
Fakher et al., 2018; Zhong and Ma, 2017; Lesage and Dehombreux,
2012; Liu et al., 2017; Li et al., 2017; Zhou et al., 2017; Li et al., 2018;
Bahria et al., 2018; Salmasnia et al., 2018; Salmasnia et al., 2018; Tasias
and Nenes, 2018; Wan et al., 2018; Salmasnia et al., 2018; Salmasnia
et al., 2019; Tagaras, 1988; Wang and Chen, 1995; Chiang and Yuan,
2001; Zhou and Zhu, 2008; Wang et al., 2009; Panagiotidou and
Tagaras, 2010; Charongrattanasakul and Pongpullponsak, 2011;
Panagiotidou and Tagaras, 2012 ; Tambe and Kulkarni, 2014 ; Zhang
et al., 2015; Makis, 2015; Tambe and Kulkarni, 2015; Ardakan et al.,
2016; Jafari and Makis, 2016; Jafari and Makis, 2016; Khrueasom and
Pongpullponsak, 2017; Tambe and Kulkarni, 2016; Jain and Lad, 2017;
Bouslah et al., 2016; Bouslah et al., 2018; Rasay et al., 2018; Latrous
et al., 2018; Farahani et al., 2019; Li et al., 2019; Hsu and Kuo, 1995;
Chiu and Huang, 1996; Panagiotidou and Tagaras, 2007; Panagiotidou
and Tagaras, 2008; Panagiotidou and Nenes, 2009; Nenes and
Panagiotidou, 2011; Pandey et al., 2010; Mehdi et al., 2010; Engin,
2010; Radhoui et al., 2010; Rahim and Shakil, 2011; Colledani and
Tolio, 2012; Dhouib et al., 2012; Rivera-G´
omez et al., 2013; Shrivastava
et al., 2016; Dan et al., 2016; Rasay et al., 2018; Yin and Makis, 2010;
Azadeh et al., 2017; Cheng et al., 2018; Rasay et al., 2018; Wan et al.,
2018; Pasha and Moghadam, 2018; Duan et al., 2019; Wang et al., 2019;
Kouki et al., 2014; Deloux et al., 2009; Nguyen et al., 2019; Pan et al.,
2012; Maillart et al., 2009; Rivera-Gomez et al., 2013; Alsyouf et al.,
2016; Yang and Zeng, 2018 Apr; Zhang et al., 2018; Bahria et al., 2019;
He et al., 2019; Le and Tan, 2013; Ivy and Nembhard, 2005; Ji-Wen
et al., 2010; Chan, 2003; Chan and Wu, 2009; Ali et al., 2020)
Imperfect (Ben-Daya, 1999; Ben-Daya and Rahim, 2000; Wang and Sheu, 2003;
Ben-Daya and Makhdoum, 1998; Lee and Rahim, 2001; Lin et al., 2011;
Wang, 2011; Ho and Quinino, 2012; Chen, 2013; Xiang, 2013; Lu et al.,
2016; Nourelfath et al., 2016; Fakher et al., 2018; Li et al., 2017; Liu
et al., 2017; Li et al., 2018; Tasias and Nenes, 2018; Wan et al., 2018;
Chiang and Yuan, 2001; Wang et al., 2009; Pandey et al., 2011; Pandey
et al., 2012; Panagiotidou and Tagaras, 2012 ; Tambe and Kulkarni,
2014 ; Tambe and Kulkarni, 2015; Jafari and Makis, 2016; Jafari and
Makis, 2016; Tambe and Kulkarni, 2016; Jain and Lad, 2017; Bouslah
et al., 2016; Farahani et al., 2019; Panagiotidou and Tagaras, 2008;
Chang et al., 2009; Pandey et al., 2010; Radhoui et al., 2010; Morales,
2013; Rivera-G´
omez et al., 2013; Shrivastava et al., 2016; Azadeh et al.,
2017; Cheng et al., 2018; Pasha and Moghadam, 2018; Wang et al.,
2019; Beheshti Fakher et al., 2017; Kouki et al., 2014; Maillart et al.,
2009; Zhou and Liu, 2016; Rivera-Gomez et al., 2013; Le and Tan, 2013;
Ji-Wen et al., 2010)
Table 17
. Classication of types of repairs (before and after failure).
Before the failure or alarm
(both true and false)
Aged-based maintenance, Time-based Preventive
Replacement policy, Replacement, Repair,
Restoration, Age-replacement, Planned maintenance,
Imperfect preventive, Complete Repair.
After the failure or alarm
(both true and false)
Reactive maintenance, Corrective Maintenance,
Compensation Maintenance, Condition-based
maintenance, Restoration, Overhaul, Major Repair,
Minor repair Perfect Corrective, Perfect Preventive,
Full preventive, Total Maintenance, Preventive
Replacement, Corrective Replacement, Complete
Repair, Replacement, “A” Corrective maintenance,
“B” Corrective maintenance, Block Replacement with
Minimal Repair, Delayed Maintenance policy,
Minimal Maintenance, Minimal Corrective, Repair,
Restoration, Predictive maintenance, Minimal repair,
Selective, Autonomous Maintenance, Quality based.
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
12
distribution function, which depends on the working machine charac-
teristics, the manufacturing process, how the parts are combined, and
other characteristics. The lifespan of the equipment can be calculated
using these functions, and therefore the probability of failure in a period
is determined.
The in-control time follows a distribution with either an increasing
failure rate or a xed failure rate. The types of distributions presented in
papers are listed in Table 21. The exponential distribution is a memo-
ryless distribution and is a suitable distribution for the in-control time.
In this distribution, the probability of machine failure at any time
regardless of the duration of the time it has worked is calculated. In
equipment that the main causes of failure are accidental, this distribu-
tion is appropriate. The negative exponential distribution is suitable for
equipment where the failure of a part causes the whole device to fail. If
the failure rate increases with the lifespan of a piece of equipment, the
distribution of the Weibull is appropriate for the in-control time distri-
bution. In this distribution, the failure of a system is due to the most
signicant failure between multiple failures. When the equipment con-
sists of several components and the time to failure of each component
follows the exponential distribution, the time to equipment failure is
considered as the gamma distribution.
The variables related to repairs are listed in Tables 22 and 23. As can
be seen in the tables, the preventive maintenance interval and the
optimal repair threshold have the most repetitions in the papers.
2.3. Tabulation based on production policy
The most obvious issue in preparing a production plan is determining
the length of the planning horizon. Production programs are divided
into short-term, medium-term and long-term plans based on the length
of the planning horizon. Typically, a long-term plan is considered to be
ve years or more, which is the minimum time to change the available
capacity. For a 1–24-month planning horizon, medium-term production
plans are prepared within the framework of long-term plans. In this type
Table 21
. Distribution of time until process shift.
Exponential (Kuo, 2006; Makis and Fung, 1995; Makis and Fung, 1998;
Alfares et al., 2005; Wu and Makis, 2008; Mehrafrooz and
Noorossana, 2011; Kim and Makis, 2012; Xiang, 2013; Liu
et al., 2013; Zhong et al., 2016; Zhong and Ma, 2017; Liu
et al., 2017; Zhou et al., 2017; Salmasnia et al., 2018;
Salmasnia et al., 2018; Salmasnia et al., 2019; Tagaras,
1988; Wang and Chen, 1995; Zhang et al., 2015; Makis,
2015; Jafari and Makis, 2016; Farahani et al., 2019; Hsu and
Kuo, 1995; Chiu and Huang, 1996; Chang et al., 2009;
Panagiotidou and Nenes, 2009; Nenes and Panagiotidou,
2011; Engin, 2010; Dhouib et al., 2012; Dan et al., 2016; Yin
and Makis, 2010; Deloux et al., 2009; Alsyouf et al., 2016;
Zhang et al., 2018; He et al., 2019; Le and Tan, 2013; Ivy and
Nembhard, 2005; Ji-Wen et al., 2010; Yeong et al., 2013)
Weibull (Cassady et al., 2000; Linderman et al., 2005; Lee and
Rahim, 2001; Yeung et al., 2007; Yin et al., 2015; Yin et al.,
2015; Lu et al., 2016; Salmasnia et al., 2017; Lesage and
Dehombreux, 2012; Li et al., 2017; Li et al., 2017; Li et al.,
2018; Wan et al., 2018; Salmasnia et al., 2018; Zhou and
Zhu, 2008; Charongrattanasakul and Pongpullponsak,
2011; Pandey et al., 2011; Pandey et al., 2012; Tambe and
Kulkarni, 2014 ; Tambe and Kulkarni, 2015; Ardakan et al.,
2016; Tambe and Kulkarni, 2016; Jain and Lad, 2017;
Bouslah et al., 2018; Pandey et al., 2010; Dan et al., 2016;
Wang et al., 2019; Beheshti Fakher et al., 2017; Pan et al.,
2012; Zhou and Liu, 2016; Yang and Zeng, 2018 Apr; Gupta
et al., 2009)
General (Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-
Daya, 1998; Chiu and Huang, 1995; Chiu and Huang, 1996;
Ben-Daya, 1999; Ben-Daya and Rahim, 2000; Rahim and
Ben-Daya, 2001; Wang and Sheu, 2003; Makis and Fung,
1995; Ben-Daya and Makhdoum, 1998; Lin et al., 2011;
Chen, 2013; Nourelfath et al., 2016; Wan et al., 2018; Wang
et al., 2009; Panagiotidou and Tagaras, 2010; Panagiotidou
and Tagaras, 2012 ; Jafari and Makis, 2016; Bouslah et al.,
2016; Rasay et al., 2018; Panagiotidou and Tagaras, 2007;
Panagiotidou and Tagaras, 2008; Rahim and Shakil, 2011;
Morales, 2013; Shrivastava et al., 2016; Rasay et al., 2018;
Rasay et al., 2018; Lin, 2004)
Not known (Radhoui et al., 2009; Wang, 2011; Ho and Quinino, 2012;
Wang, 2012; Khrueasom and Pongpullponsak, 2017;
Latrous et al., 2018; Radhoui et al., 2010; Bahria et al.,
2019)
Erlang (Duan et al., 2019)
General Exponential (Ali et al., 2020)
Marshall–Olkin
bivariate
(Li et al., 2019)
Negative exponential (Tambe and Kulkarni, 2015; Tambe and Kulkarni, 2016;
Wan et al., 2018)
Non-negative
exponential
(Tasias and Nenes, 2018; Zhang et al., 2015; Pasha and
Moghadam, 2018)
Table 19
. Type of machine deterioration process.
Continuous-time Markov
chain
(Wu and Makis, 2008; Kim and Makis, 2012; Liu
et al., 2013; Chiang and Yuan, 2001; Makis, 2015;
Jafari and Makis, 2016; Jafari and Makis, 2016;
Farahani et al., 2019; Wan et al., 2018; Le and Tan,
2013)
Continuous time-
homogeneous Semi-Markov
(Duan et al., 2019)
Markov chain (Wang and Sheu, 2003; Makis and Fung, 1998; Ho
and Quinino, 2012; Zhou et al., 2017; Salmasnia
et al., 2018; Wan et al., 2018; Salmasnia et al.,
2019; Tagaras, 1988; Zhang et al., 2015;
Panagiotidou and Nenes, 2009; Colledani and
Tolio, 2012; Maillart et al., 2009; Ivy and
Nembhard, 2005)
The shock model (Pasha and Moghadam, 2018)
Continuous time
homogeneous Markov
chain
(Zhong et al., 2016; Li et al., 2019; Yin and Makis,
2010)
The delay time (Wang, 2012)
Discrete-time Markov chain (Linderman et al., 2005; Yeung et al., 2007)
Semi-Markov decision process (Xiang, 2013; Tasias and Nenes, 2018; He et al.,
2019)
Partially Observable Markov
Decision
(Nguyen et al., 2019)
Geometric process (Wang, 2011; Ho and Quinino, 2012; Liu et al.,
2017)
Gamma process (Lu et al., 2016; Cheng et al., 2018; Yang and Zeng,
2018 Apr)
Table 20
. (continued) Type of machine deterioration process.
Increasing failure
rate
(Rahim and Banerjee, 1993; Rahim, 1994; Rahim and Ben-
Daya, 1998; Chiu and Huang, 1995; Chiu and Huang, 1996;
Ben-Daya, 1999; Ben-Daya and Rahim, 2000; Rahim and Ben-
Daya, 2001; Ben-Daya and Makhdoum, 1998; Lee and Rahim,
2001; Yeung et al., 2007; Radhoui et al., 2009; Lin et al., 2011;
Kim and Makis, 2012; Chen, 2013; Yin et al., 2015; Yin et al.,
2015; Lu et al., 2016; Nourelfath et al., 2016; Lesage and
Dehombreux, 2012; Li et al., 2017; Wan et al., 2018; Salmasnia
et al., 2018; Zhou and Zhu, 2008; Wang et al., 2009; Pandey
et al., 2011; Tambe and Kulkarni, 2014 ; Tambe and Kulkarni,
2015; Bouslah et al., 2016; Jain and Lad, 2017; Bouslah et al.,
2016; Bouslah et al., 2018; Rasay et al., 2018; Li et al., 2019;
Panagiotidou and Tagaras, 2007; Panagiotidou and Tagaras,
2008; Panagiotidou and Nenes, 2009; Nenes and Panagiotidou,
2011; Mehdi et al., 2010; Radhoui et al., 2010; Rahim and
Shakil, 2011; Dhouib et al., 2012; Rivera-G´
omez et al., 2013;
Dan et al., 2016; Rasay et al., 2018; Rasay et al., 2018; Pasha
and Moghadam, 2018; Wang et al., 2019; Kouki et al., 2014;
Maillart et al., 2009; Zhou and Liu, 2016; Rivera-Gomez et al.,
2013; Bahria et al., 2019; Lin, 2004; Ali et al., 2020)]
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
13
of planning, it is assumed that the capacity is constant. A medium-term
plan is prepared based on an annual forecast and available production
resources (labour, inventory, current production costs, suppliers and
collateral contract).
Production scheduling for short periods of less than a month provides
short-term programs. It assigns orders to individuals, and machines also
determine the sequence of tasks. In the integrated optimization models
presented in the papers, considering the production decisions, the pro-
duction schedule is considered. Production scheduling decisions require
sufcient attention to the interactions between the scheduling system
and other decision-making systems such as forecasting, aggregation
planning, inventory control, quality control, and maintenance planning.
The goal of scheduling is to achieve the customer’s delivery date, reduce
completion time, reduce delay delivery, reduce response time, reduce
system time, reduce overtime, increase manpower efciency and ma-
chine efciency, reduce machine idle time and reduce work-in-process
inventory. The output of the production schedule is the assignment of
jobs to production resources and the determination of their sequence in
each resource. Production scheduling constraints include capacity con-
straints, aggregate plan decisions for inventory, labour force, over time,
maintenance, availability, and work-in-process inventory.
Production scheduling variables include the exact size of the daily
workforce, production rate in regular time and overtime and activity
lower than normal, assignment of orders to resources (labour, ma-
chines), prioritizing jobs on resources.
The general production scheduling formula, which is one of the NP-
Hard problems, is as follows:
Minz =∑
K
k=1
∑
n
i=1
xiok (1)
S.T:
∑
K
k=1
(xijk −tijk) ≥ ∑
K
h=1
xij−1h;1≤i≤n,2<j≤m,1≤j−1≤m−1,h∕= k
(2)
∑
K
k=1
(xijk −tijk) ≥ 0;1≤i≤n,j=1(3)
∑
m
q=1
xpqk −∑
m
j=1
xijk +M(1−yipk)≥tpqk ;1≤i,p≤n,i∕= p,1≤k≤K(4)
Table 22
. The variables related to repairs.
The number of preventive
maintenances
(Fakher et al., 2018; Li et al., 2017;
Salmasnia et al., 2018; Tagaras, 1988; Wan
et al., 2018)
Determine the optimal maintenance
strategy
(Chen, 2013; Tambe and Kulkarni, 2016; Le
and Tan, 2013; Ji-Wen et al., 2010; Chan,
2003; Chan and Wu, 2009)
Preventive maintenance interval (Ben-Daya and Rahim, 2000; Cassady et al.,
2000; Yeung et al., 2007; Xiang, 2013; Lu
et al., 2016; Wan et al., 2018; Zhou and
Zhu, 2008; Panagiotidou and Tagaras,
2010; Pandey et al., 2011; Pandey et al.,
2012; Panagiotidou and Tagaras, 2012 ;
Jain and Lad, 2017; Rasay et al., 2018;
Farahani et al., 2019; Pandey et al., 2010;
Shrivastava et al., 2016; Pan et al., 2012;
Zhou and Liu, 2016; Zhang et al., 2018; He
et al., 2019; Yeong et al., 2013; Ali et al.,
2020)
The age threshold (Dhouib et al., 2012)
The threshold of condition-based
preventive maintenance
(Zhou and Liu, 2016)
F-stopping time (the rst sampling
epochat which full preventive
maintenance should take place)
(Kim and Makis, 2012)
Preventive replacement time (Makis and Fung, 1995)
Replacement times for critical
components
(Alsyouf et al., 2016)
The decision on maintenance actions
for each component
(Tambe and Kulkarni, 2014 ; Tambe and
Kulkarni, 2015)
Scheduled minimal maintenance time
if a quality shift occurs
(Panagiotidou and Tagaras, 2008)
The preventive maintenance threshold (Li et al., 2017; Chang et al., 2009; Cheng
et al., 2018; Deloux et al., 2009; Yang and
Zeng, 2018 Apr)
The type of maintenance (Maillart et al., 2009)
The machine efciency (Engin, 2010)
Probability of a shift in the jth interval (Beheshti Fakher et al., 2017)
Number of machines to be assigned
per operator
(Engin, 2010)
The effectiveness of a type A
corrective maintenance
(Ho and Quinino, 2012)
Expected number of failures (Beheshti Fakher et al., 2017)
The exponential weight constant (Charongrattanasakul and
Pongpullponsak, 2011)
Preventive maintenance level (Fakher et al., 2018; Jafari and Makis,
2016; Beheshti Fakher et al., 2017)
Initial age of machine in the rst
period
(Beheshti Fakher et al., 2017)
Opportunistic maintenance level (Jafari and Makis, 2016)
The machine mode (Rivera-Gomez et al., 2013; He et al., 2019)
The Average delay time (Zhang et al., 2015)
The optimal repair level (Wang and Sheu, 2003)
The maintenance action period (Bouslah et al., 2016; Lesage and
Dehombreux, 2012; Deloux et al., 2009)
A binary variable for performing an
overhaul
(Wang et al., 2019)
A binary variable for performing
preventive maintenance
(Wang et al., 2019)
Available production time on the
machine
(Beheshti Fakher et al., 2017)
Critical preventive maintenance age of
machine
(Bouslah et al., 2018)
Age of machine (Li et al., 2018; Beheshti Fakher et al.,
2017; Rivera-Gomez et al., 2013)
Table 23
. (continued) The variables related to repairs.
The number of preventive
maintenances
(Fakher et al., 2018; Li et al., 2017; Salmasnia
et al., 2018; Tagaras, 1988; Wan et al., 2018)
The number of age-based
maintenances
(Li et al., 2018)
Repair threshold (Chiang and Yuan, 2001)
The cost of actual PM activities (Ben-Daya and Rahim, 2000)
The maintenance level (Pasha and Moghadam, 2018)
The equipment inspection
interval
(Yang and Zeng, 2018 Apr)
Overhaul threshold (Bouslah et al., 2016; Cheng et al., 2018)
The overhaul rate (Rivera-G´
omez et al., 2013)
Replacement threshold (Chiang and Yuan, 2001; Nguyen et al., 2019)
The optimal virtual age
threshold
(Wang and Sheu, 2003)
The optimal probability
threshold
(Ivy and Nembhard, 2005)
Preventive maintenance interval
in the in-control state
(Panagiotidou and Tagaras, 2007; Panagiotidou
and Tagaras, 2008)
The age limit (Li et al., 2019)
Number of preventive
maintenance activities
(Ben-Daya and Makhdoum, 1998)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
14
∑
m
q=1
xpqk −∑
m
j=1
xijk +Myipk ≥tijk;1≤i,p≤n,1≤j,q≤m,i∕= p,1≤k≤K
(5)
xijk ≥0,yipk =0or1(6)
k,h:Machine 1 ≤k,h≤K;
i,p: Job 1 ≤i,p≤n;
j,j−1,q:Operation 1 ≤j≤m;
tijk: Time to perform operation j of job i by machine k;
M: Big number;
xiok: Completion time of the last operation of the job i on the machine
k;
xijk: Completion time of the operation j of the job i on the machine k;
yipk: A binary variable that it is one, if the jobs i and p are assigned to
the machine k, respectively and zero otherwise;
Equation (1) is the objective function that minimizes the completion
time. Equations (2) and (3) ensure the sequence of operations on jobs.
Equations (4) and (5) ensure that no two operations are assigned to one
machine at the same time. Equation (6) determines the type of variables
that are positive integer and binary, respectively.
The types of manufacturing systems in the papers include a single
machine (a production process), two-machine, the multi-machine that
are presented in Table 24.
In mass production, the production schedule tries to balance the
production line by grouping the production activities into stations. In
the lean and agile production, production scheduling determines prod-
uct type, production lot size, and assignment sequence.
The variables related to production in the papers are presented in
Table 25. As can be seen in the tables, the most repetitions are related to
the lot size and production quantity, respectively.
2.4. Tabulation based on the objective function and solving approach
Revenue is the most important goal of any production system, and
this goal is achieved by minimizing production costs. Therefore, in
planning the three main tasks of the workshop oor (production, repair
and quality), the objective function is dened based on the protability
of the system by minimizing costs, maximizing prots, and determining
optimal policies. Papers are listed in Table 26, based on the objective
Table 24
. Type of production system.
Single machine (Rahim and Banerjee, 1993; Rahim, 1994; Rahim and
Ben-Daya, 1998; Chiu and Huang, 1995; Chiu and
Huang, 1996; Ben-Daya, 1999; Ben-Daya and Rahim,
2000; Cassady et al., 2000; Rahim and Ben-Daya,
2001; Linderman et al., 2005; Wang and Sheu, 2003;
Kuo, 2006; Makis and Fung, 1995; Ben-Daya and
Makhdoum, 1998; Lee and Rahim, 2001; Yeung et al.,
2007; Makis and Fung, 1998; Alfares et al., 2005; Wu
and Makis, 2008; Radhoui et al., 2009; Lin et al.,
2011; Wu and Wang, 2011; Wang, 2011; Mehrafrooz
and Noorossana, 2011; Ho and Quinino, 2012; Wang,
2012; Kim and Makis, 2012; Xiang, 2013; Yin et al.,
2015; Yin et al., 2015; Lu et al., 2016; Nourelfath
et al., 2016; Salmasnia et al., 2017; Fakher et al.,
2018; Lesage and Dehombreux, 2012; Li et al., 2017;
Liu et al., 2017; Li et al., 2017; Zhou et al., 2017; Li
et al., 2018; Bahria et al., 2018; Salmasnia et al.,
2018; Tasias and Nenes, 2018; Wan et al., 2018;
Salmasnia et al., 2018; Tagaras, 1988; Wang and
Chen, 1995; Chiang and Yuan, 2001; Zhou and Zhu,
2008; Wang et al., 2009; Panagiotidou and Tagaras,
2010; Charongrattanasakul and Pongpullponsak,
2011; Pandey et al., 2011; Pandey et al., 2012;
Panagiotidou and Tagaras, 2012 ; Tambe and
Kulkarni, 2014 ; Zhang et al., 2015; Tambe and
Kulkarni, 2015; Ardakan et al., 2016; Jafari and
Makis, 2016; Bouslah et al., 2016; Tambe and
Kulkarni, 2016; Jain and Lad, 2017; Bouslah et al.,
2016; Latrous et al., 2018; Farahani et al., 2019; Hsu
and Kuo, 1995; Chiu and Huang, 1996; Yerel et al.,
2007; Panagiotidou and Tagaras, 2007; Panagiotidou
and Tagaras, 2008; Chang et al., 2009; Panagiotidou
and Nenes, 2009; Nenes and Panagiotidou, 2011;
Pandey et al., 2010; Mehdi et al., 2010; Radhoui et al.,
2010; Rahim and Shakil, 2011; Rivera-G´
omez et al.,
2013; Shrivastava et al., 2016; Dan et al., 2016; Rasay
et al., 2018; Yin and Makis, 2010; Cheng et al., 2018;
Wan et al., 2018; Duan et al., 2019; Kouki et al., 2014;
Deloux et al., 2009; Nguyen et al., 2019; Pan et al.,
2012; Maillart et al., 2009; Rivera-Gomez et al., 2013;
Yang and Zeng, 2018 Apr; Zhang et al., 2018; He
et al., 2019; Ivy and Nembhard, 2005; Chan, 2003;
Chan and Wu, 2009; Gupta et al., 2009; Ali et al.,
2020)
Batch production on a
machine
(Kuo, 2006; Zhang et al., 2015; Wang et al., 2019;
Bahria et al., 2019)
A production facility
consists of two units
(Jafari and Makis, 2016)
A manufacturing cell (Dhouib et al., 2012)
Multi-machine in series (Colledani and Tolio, 2012; Azadeh et al., 2017)
A supply chain system (Zhong et al., 2016)
Two-unit series systems (Liu et al., 2013; Salmasnia et al., 2018; Salmasnia
et al., 2019; Rasay et al., 2018)
Multi-machine (parallel
machines)
(Beheshti Fakher et al., 2017)
Two-stage dependent
process
(Zhong and Ma, 2017; Rasay et al., 2018)
Multi-station discrete
manufacturing
(Ji-Wen et al., 2010)
Two-machine (Bouslah et al., 2018)
Multi-machine (Engin, 2010; Zhou and Liu, 2016)
Table 25
. The variables related to production.
Production quantity (Rahim, 1994; Rahim and Ben-Daya, 1998;
Lin et al., 2011; Chen, 2013; Nourelfath
et al., 2016; Wang et al., 2019; Lin, 2004)
The lot size (Makis and Fung, 1995; Makis and Fung,
1998; Fakher et al., 2018; Jafari and Makis,
2016; Jafari and Makis, 2016; Bouslah et al.,
2016; Cheng et al., 2018; Beheshti Fakher
et al., 2017)
Production time cycle (Ben-Daya, 1999; Ben-Daya and Rahim,
2000; Alfares et al., 2005; Rasay et al., 2018;
Rasay et al., 2018)
Cycle time (Alfares et al., 2005; Engin, 2010)
The size of the buffer stock (Radhoui et al., 2009; Mehdi et al., 2010;
Radhoui et al., 2010; Azadeh et al., 2017;
Bahria et al., 2019)
The security stock hedging level (Dhouib et al., 2012)
The production rate (Rivera-G´
omez et al., 2013)
Inventory of conforming product (Fakher et al., 2018)
The stock level (Rivera-Gomez et al., 2013)
The production level of product (Beheshti Fakher et al., 2017)
Surplus inventory threshold (Bouslah et al., 2016; Bouslah et al., 2016)
The number of produced batches
before a preventive maintenance
(Kouki et al., 2014)
Inventory level (Nourelfath et al., 2016; Bouslah et al.,
2018; Cheng et al., 2018; Wang et al., 2019;
Beheshti Fakher et al., 2017)
Backorder level (Nourelfath et al., 2016; Fakher et al., 2018;
Wang et al., 2019; Beheshti Fakher et al.,
2017)
Binary variable for the setup of
product
(Nourelfath et al., 2016; Fakher et al., 2018;
Wang et al., 2019; Beheshti Fakher et al.,
2017)
Inventory of nonconforming product (Fakher et al., 2018)
The maximum buffer size (Zhou and Liu, 2016)
Batch sequence (Pandey et al., 2011; Tambe and Kulkarni,
2014 ; Tambe and Kulkarni, 2015; Tambe
and Kulkarni, 2016)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
15
Table 27
. The solution approach.
The search
methods
Numerical search (Wang and Sheu, 2003;
Yeung et al., 2007; Wu and
Makis, 2008; Lin et al., 2011;
Wang, 2011; Chen, 2013;
Xiang, 2013; Lu et al., 2016;
Zhong and Ma, 2017; Liu
et al., 2017; Bahria et al.,
2018; Tasias and Nenes,
2018; Tagaras, 1988;
Panagiotidou and Tagaras,
2012 ; Hsu and Kuo, 1995;
Panagiotidou and Nenes,
2009; Nenes and
Panagiotidou, 2011; Mehdi
et al., 2010; Dhouib et al.,
2012; Rivera-G´
omez et al.,
2013; Kouki et al., 2014;
Rivera-Gomez et al., 2013;
Alsyouf et al., 2016; Bahria
et al., 2019; Lin, 2004; Chan,
2003; Chan and Wu, 2009;
Ali et al., 2020)
The pattern search technique of
Hooke and Jeeves (Hooke and
Jeeves, 1961)
(Rahim and Banerjee, 1993;
Rahim, 1994; Rahim and
Ben-Daya, 1998; Chiu and
Huang, 1995; Chiu and
Huang, 1996; Ben-Daya,
1999; Ben-Daya and Rahim,
2000; Rahim and Ben-Daya,
2001; Linderman et al.,
2005; Ben-Daya and
Makhdoum, 1998; Lee and
Rahim, 2001; Ardakan et al.,
2016; Chiu and Huang,
1996; Chang et al., 2009)
The pattern search (Li et al., 2017; Pan et al.,
2012)
Gird search approach (Zhou et al., 2017; Tagaras,
1988; Zhou and Zhu, 2008;
Jain and Lad, 2017; Rasay
et al., 2018; Wan et al., 2018;
Nguyen et al., 2019)
The enumeration procedure (Radhoui et al., 2009; Li
et al., 2017; Li et al., 2018;
Pandey et al., 2011)
The stepwise partial
particularization procedure
(Wang et al., 2009)
A heuristic search (Alfares et al., 2005; Wu and
Wang, 2011; Mehrafrooz and
Noorossana, 2011;
Nourelfath et al., 2016;
Wang and Chen, 1995;
Tambe and Kulkarni, 2016;
Bouslah et al., 2016)
An iterative algorithm (Kim and Makis, 2012;
Chiang and Yuan, 2001;
Makis, 2015; Jafari and
Makis, 2016; Jafari and
Makis, 2016; Maillart et al.,
2009; Zhou and Liu, 2016; Le
and Tan, 2013)
A regression-based approach (Ho and Quinino, 2012;
Pandey et al., 2012; Azadeh
et al., 2017)
A dynamic search algorithm (He et al., 2019)
Exhaustive search (Tasias and Nenes, 2018;
Panagiotidou and Tagaras,
2010; Panagiotidou and
Tagaras, 2008)
The expectation–maximization
(EM) algorithm
(Li et al., 2019; Duan et al.,
2019)
Markov chain approximation (Yin et al., 2015)
Simulation Simulation (Cassady et al., 2000;
Radhoui et al., 2009; Wang,
2012; Yin et al., 2015; Lesage
and Dehombreux, 2012; Li
(continued on next page)
Table 26
. Type of object function.
Minimize the expected cost per time
unit
(Rahim and Banerjee, 1993; Rahim, 1994;
Rahim and Ben-Daya, 1998; Chiu and
Huang, 1995; Chiu and Huang, 1996; Ben-
Daya, 1999; Ben-Daya and Rahim, 2000;
Cassady et al., 2000; Rahim and Ben-Daya,
2001; Wang and Sheu, 2003; Makis and
Fung, 1995; Ben-Daya and Makhdoum,
1998; Lee and Rahim, 2001; Yeung et al.,
2007; Makis and Fung, 1998; Alfares et al.,
2005; Wu and Makis, 2008; Radhoui et al.,
2009; Lin et al., 2011; Wu and Wang, 2011;
Wang, 2011; Mehrafrooz and Noorossana,
2011; Ho and Quinino, 2012; Wang, 2012;
Kim and Makis, 2012; Chen, 2013; Xiang,
2013; Liu et al., 2013; Zhong et al., 2016;
Yin et al., 2015; Yin et al., 2015; Lu et al.,
2016; Nourelfath et al., 2016; Salmasnia
et al., 2017; Zhong and Ma, 2017; Lesage
and Dehombreux, 2012; Li et al., 2017; Liu
et al., 2017; Li et al., 2017; Zhou et al.,
2017; Li et al., 2018; Bahria et al., 2018;
Salmasnia et al., 2018; Salmasnia et al.,
2018; Tasias and Nenes, 2018; Wan et al.,
2018; Salmasnia et al., 2018; Salmasnia
et al., 2019; Tagaras, 1988; Wang and
Chen, 1995; Chiang and Yuan, 2001; Zhou
and Zhu, 2008; Wang et al., 2009;
Charongrattanasakul and Pongpullponsak,
2011; Pandey et al., 2011; Pandey et al.,
2012; Tambe and Kulkarni, 2014 ; Makis,
2015; Tambe and Kulkarni, 2015; Ardakan
et al., 2016; Jafari and Makis, 2016; Jafari
and Makis, 2016; Bouslah et al., 2016;
Tambe and Kulkarni, 2016; Jain and Lad,
2017; Bouslah et al., 2016; Bouslah et al.,
2018; Farahani et al., 2019; Chang et al.,
2009; Panagiotidou and Nenes, 2009;
Pandey et al., 2010; Mehdi et al., 2010;
Engin, 2010; Radhoui et al., 2010; Rahim
and Shakil, 2011; Morales, 2013; Dhouib
et al., 2012; Rivera-G´
omez et al., 2013;
Shrivastava et al., 2016; Dan et al., 2016;
Yin and Makis, 2010; Azadeh et al., 2017;
Cheng et al., 2018; Wan et al., 2018; Pasha
and Moghadam, 2018; Duan et al., 2019;
Wang et al., 2019; Beheshti Fakher et al.,
2017; Kouki et al., 2014; Deloux et al.,
2009; Nguyen et al., 2019; Pan et al., 2012;
Maillart et al., 2009; Zhou and Liu, 2016;
Rivera-Gomez et al., 2013; Alsyouf et al.,
2016; Yang and Zeng, 2018 Apr; Zhang
et al., 2018; Bahria et al., 2019; He et al.,
2019; Lin, 2004; Le and Tan, 2013; Ivy and
Nembhard, 2005; Ji-Wen et al., 2010;
Chan, 2003; Chan and Wu, 2009; Yeong
et al., 2013; Ali et al., 2020)
The expected long-run average prot
per time unit of the production
system is maximized
(Fakher et al., 2018; Panagiotidou and
Tagaras, 2010; Panagiotidou and Tagaras,
2012 ; Zhang et al., 2015; Rasay et al.,
2018; Latrous et al., 2018; Hsu and Kuo,
1995; Chiu and Huang, 1996; Panagiotidou
and Tagaras, 2007; Panagiotidou and
Tagaras, 2008; Rasay et al., 2018; Rasay
et al., 2018)
Determining maintenance policy (Li et al., 2019; Gupta et al., 2009)
The long-run expected availability
maximization
(Tasias and Nenes, 2018)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
16
function. As can be seen in the table, the objective function of most
papers is minimizing the expected cost per unit time.
Optimization problems include linear and nonlinear problems with
continuous and discrete variables. Combinational optimization is the
search for the optimal point of functions with discrete variables. The
scheduling problems are combinational optimization. These problems
are NP-hard. Optimization problems solving methods are generally
divided into four categories: enumerative methods, computational
methods, heuristic and meta-heuristic methods.
In enumerative methods, only one point belonging to the domain
space of the objective function is examined in each iteration. These
methods are easier to implement than other methods, but they require
signicant calculations. In these methods, there is no mechanism to
reduce the search domain, and the search space with this method is very
large.
Most optimization computational methods use objective function
gradients to guide search. The presence or absence of optimization
constraints plays a key role in these methods. For this reason, these
Table 28
. The main contributions.
(Rahim and Banerjee,
1993)
The work of Banerjee and Rahim (Banerjee and Rahim,
1988) has been developed in such a way that a general
distribution is assumed for in-control periods with an
increasing failure rate (non-Markovian shock model) and
the possibility of age-dependent repair before failure is
considered.
(Rahim, 1994) This paper generalizes the model in Lee and Rosenblatt (
Lee and Rosenblatt, 1987), and Banerjee and Rahim (
Banerjee and Rahim, 1988). An integrated model is
developed for both the inventory and quality control for a
class of deteriorating processes where the in-control
period follows a probability distribution with an
increasing failure rate.
(Rahim and Ben-Daya,
1998)
This model generalizes Rahim (Rahim, 1994) ’s model to
cases where production ceases not only for a true alarm
but also for a false alarm.
(Chiu and Huang, 1995) The relationship between control charts X and S2and
preventive maintenance is discussed.
(Chiu and Huang, 1996) In this paper, Banerjee and Rahim (Banerjee and Rahim,
1988) ’s model taking into account the preventive
maintenance policy, is optimized, and the results with
the results of Banerjee and Rahim (Banerjee and Rahim,
1988) are compared.
(Ben-Daya, 1999) An integrated model for the joint optimization of the
economic production quantity, the economic design of
x-control chart and the optimal maintenance level are
developed for the rst time.
(Ben-Daya and Rahim,
2000)
A model for the joint optimization of maintenance level
and the economic design of x-control chart is presented,
in the proposed model, the preventive maintenance
changes the shift rate of the equipment to the out-of-
control state by an amount proportional to the preventive
maintenance level.
(Cassady et al., 2000) A strategy is dened for monitoring and controlling a
manufacturing process through the simultaneous
implementation of a statistical process control chart and
a preventive policy; This research has utilized the X chart
and modied age-replacement preventive maintenance
policy simultaneously to improve the performance of a
manufacturing process.
(Rahim and Ben-Daya,
2001)
A generalized integrated model is developed to
determine optimal production quantity, inspection
schedules, and control chart design parameters, where
both product and process are subject to deterioration.
(Linderman et al., 2005) An integrated approach for both maintenance and
process control is provided, Adaptive maintenance is
considered, and Planned maintenance is doing at regular
intervals to prevent breakdowns when the process
instability is determined by the SPC, adaptive
maintenance performs.
(Wang and Sheu, 2003) The effects of the general time to shift distributions, two
types of process inspection errors, and general repair
policy on the optimal production/inspection/
maintenance policy are considered.
(Kuo, 2006) An integrated model for both maintenance and product
quality control is presented in a discrete-time Markovian
process, both scheduling of the sampling and the sample
size are directly included in the action space of dynamic
programming model, the system is formulated as a
partially observable Markov decision process.
(Makis and Fung, 1995) The problem of the joint determination of the lot size,
inspection interval, and preventive replacement time is
considered for a production facility subject to random
failure.
(Ben-Daya and
Makhdoum, 1998)
The integrated model is developed for the joint
determination of Economic Production Quantity (EPQ),
preventive maintenance level, and the economic design
parameters of the control chart. This paper explores the
alternatives of the maintenance policies; a Weibull model
is used to illustrate the PM policies and to investigate
their effect on the EPQ and quality control costs.
(Lee and Rahim, 2001) The effect of both age-dependent maintenance cost and a
salvage value of the equipment has been studied on the
economic design of the X control chart.
(Yeung et al., 2007)
(continued on next page)
Table 27 (continued )
et al., 2017; Wan et al., 2018;
Pandey et al., 2011; Pandey
et al., 2012; Tambe and
Kulkarni, 2014 ; Zhang et al.,
2015; Tambe and Kulkarni,
2015; Bouslah et al., 2016;
Tambe and Kulkarni, 2016;
Jain and Lad, 2017; Bouslah
et al., 2016; Bouslah et al.,
2018; Latrous et al., 2018;
Pandey et al., 2010; Radhoui
et al., 2010; Rivera-G´
omez
et al., 2013; Shrivastava
et al., 2016; Yin and Makis,
2010; Azadeh et al., 2017;
Cheng et al., 2018; Zhou and
Liu, 2016; Zhang et al., 2018;
Ivy and Nembhard, 2005; Ali
et al., 2020)
Mathematical
planning
Dynamic programming (Kuo, 2006)
Mathematical planning (Engin, 2010)
The exact solution (Liu et al., 2013; Zhong et al.,
2016; Nourelfath et al.,
2016; Fakher et al., 2018;
Zhong and Ma, 2017; Liu
et al., 2017; Farahani et al.,
2019; Panagiotidou and
Tagaras, 2007; Shrivastava
et al., 2016; Yin and Makis,
2010; Rasay et al., 2018;
Pasha and Moghadam, 2018;
Ji-Wen et al., 2010)
Meta-heuristic Genetic algorithm (Yin et al., 2015; Wan et al.,
2018; Charongrattanasakul
and Pongpullponsak, 2011;
Tambe and Kulkarni, 2015;
Khrueasom and
Pongpullponsak, 2017; Dan
et al., 2016; Wang et al.,
2019; Beheshti Fakher et al.,
2017; Yang and Zeng, 2018
Apr)
A tabu search algorithm (Rahim and Shakil, 2011;
Morales, 2013; Beheshti
Fakher et al., 2017)
Simulated annealing algorithm (Tambe and Kulkarni, 2014 ;
Tambe and Kulkarni, 2015;
Tambe and Kulkarni, 2016)
The particle swarm optimization
algorithm
(Salmasnia et al., 2017;
Salmasnia et al., 2018;
Salmasnia et al., 2018;
Salmasnia et al., 2018;
Salmasnia et al., 2019)
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
17
methods are divided into two categories: constrained and
unconstrained.
Unconstrained optimization methods, depending on the number of
variables, including optimizing one-variable and multi-variable func-
tions. The optimization methods of one-variable functions are divided
into three categories: zero-order, rst-order, and second-order methods.
Zero-order methods only require the calculation of the objective func-
tion at different points; However, rst-order methods use the objective
function and its derivative, and second-order methods use the objective
function and its rst and second derivatives. In optimizing multivariate
functions that are widely used in engineering, minimizing or maxi-
mizing a quantity is done with a large amount of design variable.
Constrained optimization methods are divided into three categories:
linear programming, direct and indirect methods. Linear programming
problems in which objective functions and constraints are linear. Linear
programming is a branch of mathematical programming. In the direct
methods, the optimal point is searched directly, and unconstrained
optimization methods are not used. In indirect methods, unconstrained
optimization algorithms are used to solve generalized optimization
problems with constraints.
One way to solve combinational optimization problems is to consider
all possible answers and calculate the objective functions related to it,
and nally, choose the best answer. It is clear that this approach ulti-
mately leads to the exact answer to the problem. But in practice, due to a
large number of possible answers, it is impossible to use it.
Due to the problems related to the complete counting method, it has
always been emphasized to create more effective and efcient methods.
In this context, various algorithms have emerged, the most famous of
which is the Simplex method for solving linear programming and Branch
and Bound method for solving linear programming with integer vari-
ables. For large-scale problems, the Simplex method works very well,
but the branch and Bound method lose its efciency and does not
perform better than the full count. For the above reasons, there has
recently been a greater focus on heuristic or metaheuristic methods or
random search.
Heuristic search methods are methods that can provide a good
answer (close to optimal) at a logical time for a problem. Heuristic
search methods are mainly based on enumerative methods, except that
they use additional information to guide the search.
Heuristic algorithms are designed for a specic problem. Therefore,
these algorithms cannot be used to solve various problems. But meta-
heuristic algorithms are quite general in terms of application and can
solve very complex problems. Most of these methods are accidental and
inspired by nature.
Simulation is used when the problem is very complex or has so many
variables that mathematical modelling cannot be used. In the simula-
tion, using the system’s past behaviours, its behavioural distribution is
obtained using statistical science, and the model is adjusted based on
past behaviour. Papers, according to the solution approach, are listed in
Table 27.
Table 29
. (continued) The main contributions.
(Wu and Makis, 2008) A multivariate SPC chart for CBM is considered in both
economic and economic-statistics design.
(Radhoui et al., 2009) The maintenance performs when the rate of non-
conforming items generated is higher than the specied
threshold.
(Lin et al., 2011) An integrated model of production lot-sizing,
maintenance, and quality are developed considering the
possibilities of inspection errors, preventive
maintenance (PM) errors, and minimal repairs for an
imperfect production system with increasing hazard
rates.
(Wu and Wang, 2011) The cost model is formulated for a three-state system
monitored by an adaptive control chart with variable
parameters and a control chart with static parameters.
(Wang, 2011) Optimization of maintenance using the np control chart
is done, and the concepts of minor and major repairs are
introduced, the type of machine deterioration process is
Geometric process.
(Mehrafrooz and
Noorossana, 2011)
This paper combines PM with an adaptive SPC; the
assumptions of this model are similar to the model
Panagiotidu and Nenes (Panagiotidou and Nenes,
2009), except that this model incorporates planned
maintenance.
(Ho and Quinino, 2012) An integrated economic model is proposed by
incorporating the following two dimensions. On-line
process control and a corrective maintenance program,
this paper considers the variable inspection interval and
perfect maintenance.
(Wang, 2012) A Markovian process is not used to model a three-stage
system. Instead, a two-stage failure process with
arbitrary random sojourn times in each stage is used,
two monitoring policy are considered including age-
based monitoring policy and block-based monitoring
policy.
(Kim and Makis, 2012) The model is a generalization of a recent model
considered by Makis (Makis, 2008 Apr), failure is
considered in this paper, a partially observable
deteriorating system subject to random failure is
modelled, the process state follows an unobservable
continuous time-homogeneous Markov chain.
(Chen, 2013) The features of imperfect rework and PM errors into an
EPQ framework are integrated
(Xiang, 2013) An integrated model is developed for a production
process that deteriorates according to a discrete-time
Markov chain; the PM restores the production
equipment to any state between the current state and
the as-good-as-new state, and the CM is perfect at more
cost.
(Liu et al., 2013) The economic and economic-statistical designs of a X
control chart for two-identical unit series systems with
condition-based maintenance is studied.
(Zhong et al., 2016) A supply chain system is considered as a maintainable
system, and a cost model has constructed for the
integration of the likelihood rate control chart and
perform maintenance in the supply chain.
(Yin et al., 2015) The assumption of the failure mechanism from
traditional quality shift to a combination of quality shift
and equipment failure is extended, an integrated model
of SPC and maintenance when designing the MEWMA
control chart is considered.
(Yin et al., 2015) An integrated model of SPC and maintenance decisions
by considering the delayed monitoring policy is
presented.
(Lu et al., 2016) A joint model of PM and quality is considered for a
deteriorating single-machine manufacturing system,
process variables affecting product quality are
identied, a process model is developed to
quantitatively describe the impact of process variables
on product quality and an integrated reliability model is
built for the machine based on the proportional hazard
model (PHM) considering effects of the degradation
states of quality-related components on machine
reliability, the quality loss is measured by Taguchi loss
function, a PM policy is designed, in which imperfect
PM for the machine and perfect PM for the quality-
(continued on next page)
Table 28 (continued )
Optimization of X control chart, in conjunction with an
age-replacement preventive maintenance policy, is
considered.
(Makis and Fung, 1998) The effect of machine failures is studied on the optimal
lot size and the optimal number of inspections in a
production cycle.
(Alfares et al., 2005) A model is formulated to integrate several realistic
aspects, including item and process deterioration,
varying demand and production rates, quality,
inspection, and maintenance.
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
18
2.5. The main contributions of papers
The main contributions of the papers are presented in Tables 28–35.
These tables easily show the progress of the work done in this area.
3. Conclusion and potential areas for future research
In this paper, a comprehensive review has been done on the papers
that optimize the decisions of either quality and maintenance or quality,
maintenance, and production, taking into account their interaction with
each other. This review includes the papers from 1998 to May 3, 2019.
In present paper are also listed papers in which decision variables only
are related to one aspect of the three main tasks (quality, maintenance,
and production), and these decision variables are optimized by the
interaction of other tasks. With our knowledge, there is no review paper
in this eld since 2012. The main contribution of this paper is to tabulate
the important features of papers in three elds of quality, repair, and
production. These tables facilitate quick access to the work done in this
area. Also, according to the analysis presented, research trends in this
area have been determined. Research gaps and areas that need further
research have been identied for future research.
Fig. 2 provides an overview of quality, repair, and production pol-
icies in the papers. In this diagram, the most frequently considered
features in the papers are listed. The percentages of these features are
shown in Fig. 2.
According to Fig. 2, it can be seen that the most tendency of papers in
quality policy is as follows: ignoring the sampling duration, applying X
control chart and acceptance sampling for quality control respectively, a
single cause for being out of control, Economic/Statistical design for
determining parameters of control chart, xed parameters for the con-
trol charts, deviation of the process mean when the system is out of
control, the process modes are either an in-control mode, an out-of-
control mode and a failure mode or an in-control mode and an out
control mode. In the production eld, 83% of papers consider a single
machine production system.
In the eld of repairs, the tendency of papers includes the following:
the duration of the repairs has not been ignored, the type of repairs is
either preventive or corrective maintenance respectively, the result of
the repair is perfect, the process of machine deterioration has an
increasing failure rate, the time-to-failure distribution is either the
exponential or the Weibull distribution, respectively.
The objective function in 83% of papers is to minimize the expected
cost per time unit. The approach of solving in 61% of papers is the search
method.
Based on the analysis performed and the trends of the papers, many
contributions can be made in this eld, and there are many research
gaps in this area, several recommendations for future research are pre-
sented in the following:
•It is recommended to present the integrated optimization models
with other decisions, including demand, routing, and priorities of
machines for production and maintenance.
Table 30
. (continued) The main contributions.
(Fakher et al., 2018) An optimization model is presented that integrates
production, maintenance, and quality policies in a multi-
product capacitated lot-sizing problem; this model
maximizes the expected prot.
(Zhong and Ma, 2017) The integration of the Shewhart individual-residual
(ZX−Ze) joint control chart and maintenance are studied
for two-stage dependent processes, which are in series.
(Lesage and
Dehombreux, 2012)
Based on the model by Cassady et al. (Cassady et al.,
2000), an integrated model of maintenance and quality
control based on Monte Carlo Experiments is developed,
and the issue has come close to the reality of industrial
environments.
(Li et al., 2017) A joint optimization model of SPC and predictive
maintenance policy is proposed, which considers
machine health conditions.
(Liu et al., 2017) An integrated model of statistical process control and
condition-based maintenance for a deteriorating system
is proposed.
(Li et al., 2017) The integrated optimization of maintenance policy and
quality control has been studied based on the economic
design of the CUSUM control chart for the process of a
small quality shift.
(Zhou et al., 2017) This paper has combined the queueing theory and control
chart to model the customer delay time and the CBM.
(Li et al., 2018) The economic design of CUSUM chart and age-based
imperfect preventive maintenance policy is presented.
(Bahria et al., 2018) A mathematical model and a solving procedure are
presented, which allow nding the optimal parameters of
the control chart minimizing the average total cost per
time unit, including maintenance and quality costs.
(Salmasnia et al., 2018) The VP −T2 Hotelling chart is used to monitor multiple
quality characteristics. The parameters of this control
chart are variable.
(Salmasnia et al., 2018) The economic-statistical design of an adaptive non-
central chi-square chart with maintenance policy is
studied for joint monitoring mean and variability of two-
unit series systems.
(Tasias and Nenes,
2018)
The development of an advanced monitoring scheme for
the joint economic-statistical optimization of quality and
preventive maintenance actions is presented.
(Wan et al., 2018) An integrated model of Maintenance Management (MM)
and quality control policy is developed with an adaptive
synthetic X chart.
(Salmasnia et al., 2018) An integrated mathematical model is presented that
integrates the concepts of production cycle length,
maintenance policy, and designing the control chart.
(Salmasnia et al., 2019) The economic-statistical design of a VP-Shewhart chart is
integrated with condition-based maintenance for two-
unit series systems.
(Tagaras, 1988) A cost model has been formulated for the simultaneous
optimization of process control and maintenance
activities.
(Wang and Chen, 1995) The np-control chart design has been considered under
the fuzzy environment.
(Chiang and Yuan,
2001)
A state-dependent maintenance policy is proposed for a
multi-state continuous-time Markovian deteriorating
system subject to aging and fatal shocks.
(Zhou and Zhu, 2008) An integrated model of control chart and maintenance
management is developed based on the integrated model
proposed by Linderman et al. (Linderman et al., 2005),
the control chart is used to monitoring the conditions of
the machine that is subject to deterioration, and planned
maintenance is also used to prevent equipment failure.
Based on the Alexander et al. (Alexander et al., 1995) cost
model, the economic behaviour of the integrated model
is investigated.
(Wang et al., 2009) An extended integrated model of jointing determination
of EPQ and the optimal PM strategy is presented, the
length of inspection time is as one of the factors in this
model.
Table 29 (continued )
integrated components are considered, a predetermined
threshold for PM is dened.
(Nourelfath et al., 2016) A model has been introduced that integrates
production, maintenance, and quality for an imperfect
process in a multi-period multi-product lot-sizing.
(Salmasnia et al., 2017) An integrated model of economic production quantity,
statistical process monitoring, and maintenance
considering multiple assignable causes are proposed.
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
19
•In recent years manufacturing system decisions have been optimized
in the form of supply chains. Optimizing integrated production,
repair, and quality decisions in the multi-layer supply chain can be
done in future research.
•The constraints should be considered in the integrated optimization
models, which include repair resources, warehouse space, buffer
capacity, raw materials, delivery time.
•In the manufacturing systems such as ow shop and job shop, no
paper optimizes the decisions of quality and repairs or the decisions
of quality, repairs, and production simultaneously, that it can be
done in the future research.
•The real environments of production are always subject to uncer-
tainty in maintenance, quality, and production. Stochastic, fuzzy,
and robust optimization can be used in the integrated optimization
models.
•In most papers, numerical examples are made using theoretical data.
Case study papers could be presented to determine the applicability
of models in different elds.
•Many control charts assume that the underlying form of the process
distributions is known. In real environments and in practice, the
specied distribution may be inaccurate, whereby parametric con-
trol charts work poorly and unreliably. In this case, non-parametric
control charts (without distribution) can work well, so the use of
non-parametric control charts in integrated optimization models is
recommended.
•In some production processes, small and large variations need to be
controlled simultaneously. New hybrid charts must be designed
using the combination of Shewhart’s control charts and small
variations-sensitive control charts for these processes.
•When several quality characteristics in a process need to be
controlled, and some of these characteristics affect another, some of
which are variable quality characteristics and some attribute quality
characteristics, it is recommended to design a new hybrid control
chart to control the quality characteristics with these features.
•In none of the integrated papers, human resource planning is not
considered to interact with the planning of production, quality, and
repairs. It is recommended to present this model for future research.
•Customer satisfaction is the most important goal of production.
Customers are the only source of return on capital. Therefore, it
should be considered in the objective function. Integrated Optimi-
zation of quality, repair, and production decisions by considering the
cost (prot) and without considering customer satisfaction is not a
global optimization.
Table 31
. (continued) The main contributions.
(Panagiotidou and Tagaras,
2010)
Joint optimization of SPC and CBM are done in a
general setting without restrictive assumptions,
the close relationship between SPC and CBM
provides a practical view of the effects of some of
the key features of the problem on this optimal
joint design.
(Charongrattanasakul and
Pongpullponsak, 2011)
An integrated model has been developed
between the Statistical Process Control and
Planned Maintenance using the EWMA control
chart; the warning limit is considered to increase
the control policy from four to six.
(Pandey et al., 2011) A model has been developed for integrating
maintenance scheduling, process quality control
policy decisions, and production.
(Pandey et al., 2012) A new integrated model is presented for joint
optimization of preventive maintenance interval
and control parameters considering the Taguchi
loss function. Two types of maintenance policies
are considered: minimal corrective
maintenance, imperfect preventive
maintenance. This model considers imperfect
maintenance.
(Panagiotidou and Tagaras,
2012)
An integrated model is presented without
making any specic assumption about the form
of the quality shift and failure time distributions.
(Tambe and Kulkarni, 2014) An integrated model is developed for the joint
analysis and optimization of maintenance
decisions, process quality control and
production scheduling for a multi-component
multi-product manufacturing system, the
combined approach of selective maintenance
with production scheduling is used.
(Zhang et al., 2015) A delayed maintenance policy based on
X−control chart is proposed for the joint
optimization of SPC and CBM policy, the
operational state probabilities during the
delayed period are estimated by Bayesian
theory, a Markov model is built for the
monitoring-maintenance process.
(Makis, 2015) A novel sampling methodology is proposed,
which is characterized by two sampling intervals
and two control thresholds.
(Tambe and Kulkarni, 2015) A methodology is developed for optimizing
maintenance and quality plan with the
constraint on schedule, availability, repair time
and detection time for a single machine, the
integrated approach of selective maintenance
with production scheduling and the consequence
of maintenance actions on the product quality
are considered.
(Ardakan et al., 2016) The integrated economic design of MEWMA
control chart is presented using maintenance
policies.
(Jafari and Makis, 2016) The development of the EMQ model is done
considering production system deterioration and
CBM.
(Jafari and Makis, 2016) A jointly optimal lot-sizing and maintenance
policy are developed for a two-unit production
facility using a multivariate Bayesian control
approach.
(Bouslah et al., 2016) New models are presented to the joint economic
design of type-1 continuous sampling plan,
production, inventory, and preventive
maintenance for deteriorating production
processes subject to an AOQL constraint. The
well-known hedging point policy (HPP) is
employed to control the production rate over
time, time-based preventive maintenance and
condition-based predictive maintenance are two
used repair policies.
(Khrueasom and
Pongpullponsak, 2017)
An integrated approach for controlling the
process is developed based on the EWMA control
chart, the integrated model of
Charnograttanasakul and Pongpullponsak (
Charongrattanasakul and Pongpullponsak,
2009; Charongrattanasakul and
Table 31 (continued )
Pongpullponsak, 2011), and the Kolmogorov-
Smirnov control chart of Khrueasom and
Pongpullponsak (Khrueasom and
Pongpullponsak, 2014).
(Tambe and Kulkarni, 2016) An integrated model has been developed that
simultaneously optimizes the maintenance,
production scheduling, and quality control
decisions, the integration of selective
maintenance with production scheduling is
done.
(Jain and Lad, 2017) A method for dynamic optimization of
maintenance planning and quality control is
presented, a new tool condition monitoring
(TCM) system is proposed for instantaneous
diagnostic.
(Bouslah et al., 2016) For the rst time, the joint design and
optimization of production, PM, and quality
control have studied using acceptance sampling
plans. A dynamic stochastic model is presented
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
20
Table 32
. (continued) The main contributions.
(Bouslah et al., 2018) An integrated model is developed for the joint design of
production, quality, and maintenance control policies of
multistage systems by incorporating failure correlation
into the joint design of these control policies for
production lines with degrading machines.
(Rasay et al., 2018) An integrated model of PM and quality control about the
chi-square control chart for a two-step process is
presented; there is no restriction to the failure
mechanism of each stage.
(Latrous et al., 2018) An integration model is considered for condition-based
maintenance and a multivariate control chart, a
comparative study is done for univariate control chart vs
multivariate control chart.
(Farahani et al., 2019) All process modes, including in control mode, out of
control modes, sampling mode, preventive maintenance
at various levels, corrective maintenance, and
inspection for the false alarm, are considered as a
continuous-time Markov chain.
(Li et al., 2019) A Bayesian control scheme is presented for early fault
detection of the gear system with dependent competing
risks.
(Hsu and Kuo, 1995) The performance of an inspection and maintenance
policy is analyzed by 100% sampling of a production lot
after producing n parts and then initiates a preventive/
corrective maintenance activity when the fraction of bad
parts in the sample reaches a given threshold.
(Chiu and Huang, 1996) A more realistic assumption is considered that the cost of
repair and the net hourly out-of-control income are
functions of detection delay.
(Yerel et al., 2007) A combination of a mean quality control chart and the
Kolmogorov-Smirnov test is used for the Colemanite
Mineral Processing Plant.
(Panagiotidou and
Tagaras, 2007)
In this paper does not require any of the distributions of
the times to quality shift and failure to be exponential.
(Panagiotidou and
Tagaras, 2008)
In addition to in control and out of control states, the
failure state is also considered, a maintenance policy,
including both perfect and imperfect maintenance, are
studied, distribution of time to quality shifts, and
failures is General distribution.
(Chang et al., 2009) In the proposed model, preventive maintenance can
reduce the occurrence rate to an out-of-control state by
an amount proportional to the maintenance level on the
quality control costs.
(Panagiotidou and
Nenes, 2009)
This paper Combines PM actions with an adaptive SPC
tool.
(Nenes and
Panagiotidou, 2011)
The Bayesian One-sided chart is used to control the
average process with maintenance that extends the work
of the Panagiotidou and Nense (Panagiotidou and
Nenes, 2009).
(Pandey et al., 2010) A model is developed for obtaining optimal preventive
maintenance intervals based on block replacement
policy to incorporate the effect of rejection cost.
(Mehdi et al., 2010) The joint quality control and preventive maintenance
policies have been developed for a production system
producing conforming and non-conforming units.
(Engin, 2010) Economic X control chart design methodology has been
used to estimate and optimize machine efciency in the
case of multi-machine assignments.
(Radhoui et al., 2010) The joint quality control and preventive maintenance
policies have been proposed by determining the optimal
size of the buffer stock and the rate of nonconforming
units based on which maintenance actions are to be
performed.
(Rahim and Shakil,
2011)
An integrated model of economic production quantity
(EPQ), economical design of an X control chart and
preventive maintenance (PM) is presented under non-
uniform quality control parameters.
(Colledani and Tolio,
2012)
A general theory is proposed to analyze the production
rate of conforming parts in manufacturing systems with
progressively deteriorating machines and preventive
maintenance.
(Morales, 2013) The Economic Statistical Design (ESD) of joint X−S
control charts have been used to monitor mean and
variability in the production process.
Table 33
(continued) The main contributions.
(Dhouib et al., 2012) The joint optimization of production-inventory control and
preventive maintenance policy is considered for a
manufacturing cell comprising an imperfect process.
(Rivera-G´
omez et al.,
2013)
A stochastic dynamic programming model is developed
with two decision variables, the production rate and the
quality decision related to the overhaul strategy, which
counters the effect of the deterioration.
(Shrivastava et al.,
2016)
An integrated approach for optimization of maintenance
and process control policy is proposed with a CUSUM
chart.
(Dan et al., 2016) An optimal economic approach is proposed by integrating
statistical process control and preventive maintenance; the
ve scenarios are dened.
(Rasay et al., 2018) The proposed model by Wu and Makis (Wu and Makis,
2008) is developed. This extension includes: no restrictive
is on the deterioration mechanism of the system,
developing the integrated CBM and SPC model is based on
the recursive equations and renewal reward process, the
proposed model is applicable for different types of
inspection policy.
(Yin and Makis, 2010) The economic and economic statistical design of the
multivariate Bayesian control chart is proposed for a three-
state CBM model by considering the control limit policy
structure.
(Azadeh et al., 2017) Joint optimization of quality control and maintenance
strategies is presented for a multi-machine production line
that produces both conforming and non-conforming units.
(Cheng et al., 2018) An integrated strategy is studied for production planning,
quality control, inventory control, and CBM for an
imperfect production system.
(Rasay et al., 2018) The development of an integrated model is done for SPC
and MM, while no restrictive assumption is considered
about the deterioration mechanism of the units of the
system, and the model can be applied to different types of
inspection policies.
(Wan et al., 2018) The TBE control chart, the customer delay cost, and the
cost of lost sales are considered explicitly.
(Pasha and
Moghadam, 2018)
The general approach of Ben-Daya and Rahim (Ben-Daya
and Rahim, 2000) and Rahim and Banerjee (Rahim and
Banerjee, 1993) is applied for multivariate process control.
(Duan et al., 2019) The Bayesian estimation and control methods are applied
to multivariate deteriorating data for the machine tool.
(Wang et al., 2019) The integration problem of production, maintenance, and
quality is considered for a capacitated lot-sizing
production system subject to deterioration.
(Beheshti Fakher et al.,
2017)
A model has been developed for integrated optimization of
lot- size, PM planning and process inspections in a multi-
product multi-machine production system, the non-
uniform inspections and different levels of PM are
considered.
(Kouki et al., 2014) The maintenance strategy is optimized with considering
the deteriorated product degree by determining the
optimal number of batches produced before undertaking a
preventive maintenance action.
(Deloux et al., 2009) A predictive maintenance policy is considered for a
continuously deteriorating system subject to stress; CBM
policy is used to inspect and replace the system according
to the observed deterioration level.
(Nguyen et al., 2019) Dynamic condition-based maintenance and a monitoring
policy are studied using the partially observable Markov
decision process (POMDP) model for a system subject to a
continuous degradation process and imperfect inspection
representative by observation noises.
(Pan et al., 2012) The concept of quality loss and maintenance policy to an
imperfect process are introduced in order to ll the gap
between the classic EPQ model with the assumption of the
perfect production process and the real manufacturing
situation, the control chart and maintenance policies are
presented in an EPQ model simultaneously.
(Maillart et al., 2009) A substantial improvement is made over the Markov chain
approach of Yeung et al. (Yeung et al., 2007); this model
allows the sampling parameters to adapt dynamically and
includes the option for minimal repair.
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
21
•In order to reduce production costs, dispersed production
geographically, and agile production philosophy, it is suggested that
in integrated optimization models, the production systems with
rework, the multi-period multi-product manufacturing systems,
geographically dispersed production systems be considered.
•The solution approach is heavily skewed toward the numerical
search approach. It is recommended to use a decomposition algo-
rithm and hybrid techniques that are suitable for solving large
problems. The integrated optimization problems are linked with
scheduling problems. So, optimization problems are NP-hard. It is
impossible to optimize them using exact methods for problems with
larger dimensions; the computational time needed to solve these
problems is not acceptable. Meta-heuristic algorithms can be used to
solve them. Meta-heuristic algorithms can obtain near-optimal so-
lutions at an acceptable time. As seen in the review of solving
methods, the Genetic algorithm, the Tabu Search algorithm, the
Simulated Annealing algorithm, and the Particle Swarm Optimiza-
tion algorithm have been used to solve these problems. It is recom-
mended to use the other Meta-heuristic algorithms, which have good
results in the eld of combination problems and hybrid Meta-
heuristic algorithms.
•In some production processes, considering the same distribution for
the in-control time in all production cycles may be far from the re-
ality of production. Considering different distributions in different
cycles can be done in future research
•In many papers, the quality of the solution method is not compared
to others. This comparison could be useful to get a better grasp of the
quality of the solution approach and evaluation and validation of the
proposed model.
•Green production is a new tendency in production systems to elim-
inate different production wastes in terms of environmental issues. In
spite of the importance of green production, in none of the reviewed
papers have been seen.
•Integrated production, repair, and quality decisions can be optimized
with objective function based on lean production (waste reduction).
•For closer to the reality of the system deterioration process, it is
recommended to consider hybrid deterioration processes (the
integrity of the shock model, the delay time, and the geometric
process).
CRediT authorship contribution statement
Ameneh Farahani: Visualization, Investigation, Writing - review &
editing. Hamid Tohidi: Conceptualization, Methodology, Writing -
original draft.
Table 34
(continued) The main contributions.
(Zhou and Liu, 2016) An integrated maintenance arrangement and buffer
setting model considering quality loss for degradation
systems are proposed. The upstream machines, the
downstream machines, and buffer size into
considerations simultaneously are taken, a cost-saving
function is proposed to trigger the opportunistic
maintenance.
(Lampreia et al., 2018) The CUSUM and the EWMA control charts are developed
and applied to water electro pump vibration control.
(Lesage and
Dehombreux, 2012)
This paper evaluates the role of quality control in repair
strategies, data mining, and cause and effect diagram is
used, the originality of this paper is the implementation
of integrated models in the industry.
(Rivera-Gomez et al.,
2013)
Models of Radhoui et al. (Mehdi et al., 2010) and
Deyahem Nodem et al. (Nodem et al., 2011) have been
developed, the simultaneous optimization of production
planning, preventive maintenance, and overhaul control
is presented for the case of a single machine subject to
random failures and deterioration, a maintenance
efciency parameter is used to decrease the level of
deterioration if preventive maintenance is carried out, a
semi-Markov model is formulated, and a stochastic
dynamic programming model is presented.
(Alsyouf et al., 2016) How to assess the rate of occurrence of failure (ROCOF)
of a multi-component repairable system and improve its
reliability are presented, a control chart was developed to
monitor the time between failures.
(Yang and Zeng, 2018
Apr)
Periodic equipment inspection and product quality
control are integrated. The np-control chart is used to
monitor the shift of product quality, and the
deterioration state of the equipment is introduced to
determine whether the equipment requires maintenance.
(Zhang et al., 2018) Taguchi loss function is used to depict the inuence of
different process shift on quality cost, and the joint
optimization design of the control chart and maintenance
policy is considered under random shifts.
(Bahria et al., 2019) The preventive and corrective maintenance actions are
triggered by the process control with the control chart, a
buffer stock is considered to ensure continuous supply
during maintenance actions, besides the control limits on
the control chart, the surveillance limits (lower than the
control limits) will trigger PM actions.
(He et al., 2019) A reliability-oriented joint optimization model of PM and
quality control policy is proposed with TBE control chart
by focusing on the inuences of machine performance
and manufacturing quality on the produced product
reliability degradation.
(Lin, 2004) The preventive maintenance error factor is added to the
two process states of the imperfect process model.
(Le and Tan, 2013) The inspection-maintenance scheme is investigated for a
system that suffers from degradation.
(Ivy and Nembhard,
2005)
The methods are developed for determining and
evaluating maintenance policies for deteriorating
systems under conditions of limited and costly
information, and these models are integrated with noisy
data observations, statistical quality control (SQC), and
partially observable Markov decision processes
(POMDPs).
(Ji-Wen et al., 2010) Three distinctive multi-component maintenance policies
have been modelled and analyzed by incorporating the
economic effects of maintenance activities, product
deviation related to the quality loss, and obsolescence at
the time of disposal.
(Chan, 2003) The cumulative count of conforming chart (CCC chart) is
applied in inspection and maintenance planning for
systems where minor inspection, major inspection, minor
maintenance, and major maintenance are available.
(Chan and Wu, 2009) The concept of cumulative count of conforming chart
(CCC chart) is used in inspection and maintenance
planning for systems where minor inspection, major
inspection, minor maintenance, and major maintenance
are available. The above concepts are illustrated by a
real-life example in the maintenance of buses in a bus
company.
Table 35
(continued) The main contributions.
(Azizi, 2015) The integration between the Statistical Process Control (SPC),
Overall Equipment Efciency (OEE), and Autonomous
Maintenance (AM) are proposed to achieve continuous
improvement in the production capability.
(Gupta et al.,
2009)
The chart control principle developed by Xie et al. (Xie et al.,
2002) is applied for a case study.
(Katter et al.,
1997)
The use of control charts for laser condition monitoring is
studied.
(Alsyouf et al.,
2015)
A statistical process control (SPC) chart is designed for
monitoring the time-between-failure of a repairable system.
(Yeong et al.,
2013)
A new methodology is proposed for determining the optimal cost
and parameters of the synthetic X-chart under different quality
loss functions.
(Ali et al., 2020) Integrated optimization of repair and quality decisions is
performed by proposing some new control charts based on an
exponential class of distributions.
A. Farahani and H. Tohidi
Computers & Industrial Engineering 151 (2021) 106924
22
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76%
23%
16%
69%
56%
33%
27%
83%
65%
32%
23%
82%
60%
63%
86%
88%
94%
43%
43%
87%
61%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Maintenance duraon: Not negligible
Prevenve maintenance
Types of maintenance : Correcve maintenance
The repair result: Perfect
Type of machine deterioraon process : Increasing…
Exponenal
Distribuon of me to failure: Weibull
Type of producon systems : Single machine
Sampling duraon : Negligible
X bar
Types of quality control policy : Acceptance sampling
Number of causes: Single cause
Types of design: Economic/Stasca
Fixed sampling…
Fixed sampling size
Characteriscs of the control charts: Fixed control limit
The type of process deviaons: Process mean
An in control mode, An out control…
Number of process modes: An in control mode, An…
The object funcon : Minimize the expected cost per…
The soluon approach : Search method
Repair ProduconQuality
Model
Features
Fig. 2. . Features with the most frequent.
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