Research on Decision-making Model for Maintenance Mode Risks of Equipment Components within Task Cycle

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Research on Decision-making Model for Maintenance
Mode Risks of Equipment Components within Task
Cycle
Jia Liu1,2, Jianwei Lv1,*and Jianjun Yang1
1Dept of Management Science, Naval Univ. of Engineering, Wuhan 430033, China
2Institute of Navy Equipment and Technology, Beijing China, 102442
*Corresponding author
Abstract—To develop scientific and reasonable maintenance
decision-making scheme for equipment during task execution,
select a suitable maintenance mode for components, control and
reduce the risk of equipment failure to the maximum, this paper
analyzes the basic types of maintenance mode for equipment
components within task cycle, as well as their influence on the
risk of equipment failure. Taking the risk, probability,
consequence and detectability of failure as the decision-making
indicators, the logical judgment method is employed to create the
logical judgment diagram of decision-making risks for
maintenance mode of equipment components within task cycle. If
any maintenance mode cannot be judged through logical
judgment diagram, the safety, task and economic risks are taken
as the decision-making indicators, and the fuzzy theory and
analytic network process are combined to build a decision-
making model for maintenance mode risks of equipment based
on analytic network process, so as to introduce the decision-
making method for optimal maintenance mode.
Keywords-task cycle; maintenance mode; risks; decision-
making
I. INTRODUCTION
Decision-making on maintenance risks has an aim to select
the maintenance mode reasonably for avoiding the risk of
equipment failure or reducing it to the acceptable level. First,
determining the basic types of maintenance mode and their
influence on the risk of equipment failure is the premise of
decision-making on maintenance mode [1-4]. Now, the logical
judgment in decision-making on maintenance mode is mainly
applied in the reliability-based maintenance analysis, but it
does not cover all risk factors and places much emphasis on
economy in the analysis, so it is not suitable for the decision-
making on task-based maintenance mode. Hence, failure risk
and its factors (failure probability, consequence, detectability
and maintenance difficulty) are taken as the decision-making
indicators to create the logical judgment diagram for the risks
of decision-making on maintenance mode of equipment
components within task cycle. If any maintenance mode
cannot be judged through the logical judgment diagram for
risks, it is necessary to analyze the features of the maintenance
mode and take the safety, task and economic risks as the
decision-making indicators. Maintenance mode[5,6] involves a
multiple attribute choice, so the decision-making indicators are
interconnected with each other. The evaluation features fuzzy
language, so the fuzzy theory is utilized with analytic network
process to build a decision-making model for risks of
equipment maintenance mode based on fuzzy analytic network
process, so as to select the optimal maintenance mode.
II. INFLUENCE OF MAINTENANCE MODE ON FAILURE RISK
Based on the features of equipment maintenance guarantee
within task cycle, the maintenance modes for equipment
components within task cycle include post-event maintenance,
state-based maintenance, preventive periodic maintenance,
preventive periodic replacement and improvement
maintenance. Through the analysis on measurement in the
evaluation of failure risk, the main indicators of failure risk
evaluation include probability of failure occurrence,
detectability of failure and influence degree of consequences
[7]. Among them, the influence degree of failure consequences
involves the influence degree of safety, task and economic
consequences. Hence, the failure risks can be classified into
safety, task and economic risks based on the influence of
failure consequences. Above all, the failure risk evaluation
indicator system of equipment within task cycle as presented
in Fig. 1.
FIGURE I. FAILURE RISK EVALUATION INDICATOR SYSTEM OF EQUIPMENT
WITHIN TASK CYCLE
The decision-making on maintenance mode for risks aims to
select a maintenance mode reasonably for avoiding the risk of
equipment failure or reducing it to the acceptable level. Therefore,
it is necessary to analyze the influence of each maintenance mode
on avoiding or lowering equipment failure risk.
Failure Risk Evaluation Indicators of
Complex Equipment within Task Cycle
Safety Risks Task Risks Economic Risks
Probability of failure
occurrence
Detectability of failure
Safety consequences of
failure
Probability of failure
occurrence
Detectability of failure
Safety consequences of
failure
Probability of failure
occurrence
Detectability of failure
Safety consequences of
failure
2016 International Conference on Mechatronics, Control and Automation Engineering (MCAE 2016)
© 2016. The authors – Published by Atlantis Press
0086

TABLE I. ANALYSIS ON INFLUENCE OF MAINTENANCE MODES ON EQUIPMENT FAILURE RISK
No. Maintenance
Mode Time Probability of
Occurrence Severity of
Consequence Detectability Failure
Risk Applicable
1 Post-event
maintenance After failure
occurs No influence No influence No influence No
influence
Equipment maintenance for failure with
less severe consequences and low risk
level
2 Periodic
maintenance At fixed
intervals Reduce No influence No influence Reduce
Equipment maintenance for failure with
common probability of occurrence
&severity of consequences and moderate
risk level
3 Periodic
replacement Within fixed
periods Reduce
considerably No influence No influence Reduce
Equipment maintenance for failure with
common probability of occurrence and
severity of consequences and moderate
risk level, but high maintenance cost
4 State-based
maintenance
condition of
sensor and
monitoring &
diagnosis
technology
Reduce
considerably No influence Increase Reduce
Equipment maintenance for failure with
high frequency of occurrence, high
severity of consequences, high risk level,
and high maintenance cost
5 Improvement
maintenance
Preparation
period for
task
Reduce
considerably Reduce
considerably Increase
considerably Reduce
considerably
Equipment maintenance for failure with
very high frequency of occurrence or
unbearable consequences, and very high
risk level
III. DECISION-MAKING IDEA FOR RISKS OF MAINTENANCE
MODE OF EQUIPMENT COMPONENTS WITHIN TASK CYCLE
The decision-making idea for risks of maintenance mode
of equipment components within task cycle is as follows: first,
analyze the influence of maintenance mode on the risk of
equipment failure, and employ the logical judgment method to
decide the maintenance mode; second, employ the fuzzy
analytic network process to decide the maintenance mode for
components if their maintenance mode cannot be determined
through logical judgment. The specific idea is shown in Fig. 2.
FIGURE II. LOGICAL JUDGMENT DIAGRAM FOR DECISION-MAKING RISKS OF
MAINTENANCE MODE OF EQUIPMENT COMPONENTS WITHIN TASK CYCLE
The logical judgment is simple to implement, and able to
gain the correct conclusion within a short period. Based on the
analysis of the influence of maintenance mode on equipment
failure risk in Table 1, the logical judgment diagram for
decision-making risks of maintenance mode of equipment
components within task cycle is designed by referring to the
reliability-based logical judgment diagram with an aim to
decide the selection of maintenance mode.
Analytic network process matches with the thinking habits
of human while making a decision, and effectively deals with
the issue involving no structure or semi-structure, so it is one
of the commonest methods in the field of multiple attribute
decision-making. If the maintenance mode of any component
cannot be judged through logical judgment, it can take safety,
task and economic risks as the decision-making indicators, so
it is a typical multiple attribute decision-making issue.
Decision-making indicators are interconnected with each other,
and the evaluation features fuzzy language. Hence, fuzzy
theory is combined with analytic network process to build a
decision-making model for maintenance mode risks of
equipment components within task cycle.
IV. RISK MODEL FOR MAINTENANCE MODE OF EQUIPMENT
COMPONENTS WITHIN TASK CYCLE
A. Risk Model for Maintenance Mode of Equipment
Components within Task Cycle Based on Logical Judgment
The logical judgment diagram for decision-making risks of
maintenance mode of equipment components within task cycle
is employed to make a judgment. For components with low
failure risk, post-event maintenance is implemented. For
components with high probability of failure occurrence,
improvement maintenance is implemented. For components
with high severity of failure, improvement maintenance is
implemented. For high difficulty of failure detection,
improvement maintenance is implemented. The maintenance
for other components will be further judged.
Start
Yes
Safety
Task
Whether failure risk is
Wh
et
h
er
f
a
il
ure
f
requency
exceeds the acceptable range
D
ec
i
s
i
on-ma
ki
ng
on maintenance
mode
No
N
o
No
Wh
et
h
er t
h
e sever
i
ty o
f
failure consequences
exceeds the acceptable range
W
h
et
h
er t
h
e
diffi
cu
l
ty o
f
failure detection exceeds the
acce
p
table level
Economic
Periodic
maintenance
Periodic
replaceme
State-based
maintenance
Post-event
maintenance
Improvement
maintenance
Improvement
maintenance
Improvement
maintenance
Objective
Criterion
Alternative
Yes
Yes
Yes
No
2016 International Conference on Mechatronics, Control and Automation Engineering (MCAE 2016)
© 2016. The authors – Published by Atlantis Press
0087

B. Risk Model for Maintenance Mode of Equipment
Components within Task Cycle Based on Fuzzy Analytic
Network Process
If the maintenance mode of any component cannot be
determined through logical judgment, we take the safety, task
and economic risks as the decision-making criteria, take three
maintenance modes including preventive periodic maintenance,
preventive periodic replacement and state-based maintenance
as the alternatives, and take the optimal maintenance mode as
the decision-making objective, so as to build a risk model for
maintenance mode of equipment components within task cycle
based on fuzzy analytic network process. To be specific, it
contains 7 steps as follows:
1) Construct the fuzzy superiority matrix of maintenance
mode based on risk evaluation indicators:Through the
pairwise comparison of preventive periodic maintenance,
preventive periodic replacement and state-based maintenance
based on decision-making indicators, the superiority matrix of
each maintenance mode is obtained, i.e.

33
()
S
i
Sj
Fx

,

33
()
T
i
Tj
Fx

 and

33
()
C
i
Cj
Fx

. The corresponding relations in the
conversion of fuzzy language and fuzzy numbers are presented
in Table 2.
TABLE II. CONVERSION OF FUZZY NUMBERS FOR MAINTENANCE MODE
SUPERIORITY BASED ON RISK EVALUATION INDICATORS
No. Fuzzy Language Triangular Fuzzy
1 Equally superior (1,1,1)
2 Basically equally superior (1/2,1,3/2)
3 Slightly superior (1,3/2,2)
4 Superior (3/2,2,5/2)
5 Much superior (2,5/2,3)
6 Very much superior (5/2,3,7/2)

12 12 12 13 13 13
21 23 23 2 3
31 31 31 32 32 32
33 21 21
(1,1,1) ( , , ) ( , , )
( ) ( , , ) (1,1,1) ( , , )
( , , ) ( , , ) (1,1,1)
ij
xyz xyz
F x xyz xyz
xyz xyz








 (1)
2) Construct a fuzzy weight matrix of risk evaluation
indicators:Through asking the experts about the importance of
safety risk, task risk and economic risk through pairwise
comparison, the weight matrix of risk evaluation indicators is
obtained, i.e.

33
()
P
W
PW ij
Fx

. The corresponding relations in the
conversion of fuzzy language and fuzzy numbers are as
presented in Table 2.
3) Construct a fuzzy relational matrix of risk evaluation
indicators for maintenance mode:By comparing the relations
among safety, task and economic risks of maintenance mode
pairwise, the modified weight matrix of risk evaluation
indicators for maintenance mode is obtained, i.e.

33
()
TC
TC
ij
Fx

,

33
()
EC
E
C
ij
Fx

 and

33
()
CC
CC
ij
Fx

. The corresponding relations
in the conversion of fuzzy language and fuzzy numbers are
presented in Table 3.
TABLE III. TABLE 3 CONVERSION OF FUZZY NUMBERS FOR MODIFIED
WEIGHTS OF RISK EVALUATION INDICATORS
No. Fuzzy Language Triangular Fuzzy
1 Absolutely Superior (5/2,3,7/2)
2 Extremely Superior (3/2,2,5/2)
3 Much Superior (1,3/2,2)
4 Slightly Superior (1/2,1,3/2)
5 Superior (1/2,2/3,1)
6 Not Much Superior (2/5,1/2,2/3)
7 Not Superior (2/7,1/3,2/5)
4) Convert fuzzy superiority matrix into numerical
superiority matrix:
The following calculation is employed to convert fuzzy
superiority matrix into numerical superiority matrix:
3
1
(1,2,3,)
(1,2,3,)
ij
i
kj
k
Djji
Pjjk

  


  



(2)
1
333
111
(, , )
iiii ij kj
jkj
xx




  



 (3)
()sup[min((),())]
ij i j
yx
Pxy

   
   (4)
(1,2, 3)
(1,2,3,)min()
ij ij
jij
Pjji D


    

 
, 1,2,...,in

(5)
1,
,,,1,2,3,
()
()( )
0,
ij
ji
ijji
ij ii jj
jji
D
others

  
 



 
 
 




(6)
5) Construct an un-weighted super-matrix:
Based on the calculation of analytic network process, the un-
weighted super-matrix is obtained as follows:
12
21 22 23
00
000





   






(7)
In which, 12

is a 33

matrix representing the weight of
maintenance mode relative to risk evaluation indicators. 21

is a 33

matrix representing the weight of risk evaluation
indicator relative to maintenance mode. 22
 is a 33

matrix
representing the mutual influence of risk evaluation indicators.
23

represents the weight of risk evaluation indicator relative
to objective.
2016 International Conference on Mechatronics, Control and Automation Engineering (MCAE 2016)
© 2016. The authors – Published by Atlantis Press
0088

6) Construct a weighted super-matrix:
The eigenvector of each superiority matrix is calculated and
normalized to obtain the weighted super-matrix:
12
21 22 23
00
000
W
WW W W





(8)
In which, 12
W is the eigenvector of 12
, 21
W is the
eigenvector of 21
, and 22
W is the eigenvector of 22
.
7) Construct an extreme super-matrix:The calculation of
power method is employed to obtain the extreme super-matrix.
In the extreme super-matrix, the maintenance mode with the
highest weight is the optimal maintenance mode.
V. CASE ANALYSIS
Taking the fuel injector of fuel system in a diesel engine as
an example, a model is built. The Delphi method is utilized to
obtain the comparison matrix of maintenance mode based on
decision-making indictors, the comparison matrix of decision-
making indicators in terms of weight, and the superiority of
risk evaluation indicators for each maintenance mode, through
asking experts for opinions. results are shown in Table 4-10:
TABLE IV. SUPERIORITY OF MAINTENANCE MODE BY TAKING SAFETY RISK
INDICATORS AS CRITERION
TABLE V. SUPERIORITY OF MAINTENANCE MODE BY TAKING TASK RISK
INDICATORS AS CRITERION
Task
Strategy CM TBM OCM Superiority
TBC （1, 1, 1） (2/5, 1/2, 2/3） (1/2, 2/3, 1) 0.0512
TBR (1/2,2/3, 1) （1, 1, 1） (1, 3/2, 2） 0.6091
CBM (1, 3/2, 2） （3/2, 2, 5/2） （1, 1, 1） 0.3397
TABLE VI. SUPERIORITY OF MAINTENANCE MODE BY TAKING ECONOMIC
RISK INDICATORS AS CRITERION
Economic
Strategy CM TBM OCM Superiority
TBC （1, 1, 1） （2/5, 1/2, 2/3） （2/5, 1/2, 2/3）0.2161
TBR （3/2, 2, 5/2） （1, 1, 1） （3/2, 2, 5/2）0.6046
CBM （2/3, 1, 2） （1/2, 1, 3/2） （1, 1, 1） 0.1793
TABLE VII. SUPERIORITY OF RISK EVALUATION INDICATORS
TABLE VIII. SUPERIORITY OF PERIODICAL MAINTENANCE MODE UNDER
DIFFERENT CRITERIA
TBC
Criterion Safety Task Economic Superiority
Safety （1, 1, 1） (2/3, 1, 2) (1/2, 1, 3/2）0.312
Task (2/7, 1/3, 2/5) （1, 1, 1） (2/7, 1/3, 2/5) 0.337
Economic (5/2, 3, 7/2）(5/2,3, 7/2) （1, 1, 1） 0.351
TABLE IX. SUPERIORITY OF PERIODICAL REPLACEMENT MODE UNDER
DIFFERENT CRITERIA
TBR
Criterion Safety Task Economic Superiority
Safety （1, 1, 1） (1/2, 1, 3/2) （1, 3/2, 2）0.398
Task (2/7, 1/3, 2/5) （1, 1, 1） (5/2, 3, 7/2) 0.425
Economic (1/2, 2/3, 1) （2/3, 1, 2） （1, 1, 1） 0.177
TABLE X. SUPERIORITY OF STATE-BASED MAINTENANCE MODE UNDER
DIFFERENT CRITERIA
OBM
Criterion Safety Task Economic Superiority
Safety （1, 1, 1） (2/5, 1/2, 2/3) (2/3, 1, 2) 0.507
Task (1/2, 1, 3/2） （1, 1, 1） (1/2, 2/3, 1) 0.302
Economic （1, 3/2, 2）(3/2, 2, 5/2) （1, 1, 1） 0.191
The un-weighted super-matrix is calculated as presented in Table 11.
TABLE XI. UN-WEIGHTED SUPER-MATRIX OF DECISION-MAKING ON MAINTENANCE MODE
Un-weighted Super-matrix Strate
gy
Criterion Objective
TBC TBM OBM Safety Availability Cost
Strategy TBC 0.0000 0.0000 0.0000 0.3120 0.3370 0.3510 0.0000
TBM 0.0000 0.0000 0.0000 0.3980 0.4250 0.1770 0.0000
OBM 0.0000 0.0000 0.0000 0. 5070 0.3020 0. 1910 0.0000
Criterion Safet
y
0.2916 0.3884 0.3200 0.0000 0.5000 0.5000 0.4722
Availabilit
y
0.0512 0.6091 0.3397 0.5000 0.0000 0.5000 0.4289
Cost 0.2161 0.6046 0.1793 0.5000 0.5000 0.0000 0.0989
Ob
j
ective 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Safety
Strategy CM TBM OCM Superiority
TBC (1, 1, 1) (2/3, 1, 2) (1/2, 2/3, 1) 0.2916
TBR (2/3, 1, 2) (1, 1, 1) (1/2, 1, 3/2) 0.3884
CBM (1, 3/2, 2) (1/2, 1, 3/2) (1, 1, 1) 0.3200
Decision-
making
Objective
Criterion Safety Task Economic Superiority
Safety （1, 1, 1） (3/2, 2, 5/2) (1/2, 1, 3/2）0.4722
Task （1/2, 1, 3/2） （1, 1, 1） (2/5,1/2,2/3）0.4289
Economic (2/5, 1/2, 2/3） (3/2, 2, 5/2) （1, 1, 1） 0.0989
2016 International Conference on Mechatronics, Control and Automation Engineering (MCAE 2016)
© 2016. The authors – Published by Atlantis Press
0089

The calculation results of weighted super-matrix are presented in Table 12.
TABLE XII. WEIGHTED SUPER-MATRIX OF DECISION-MAKING ON MAINTENANCE MODE
weighted
Super-matrix Strategy Criterion
Objective
TBC TBM OBM Safety Availability Cost
Strategy
TBC 0.0000 0.0000 0.0000 0.1348 0.04755 0.07245 0.0000
TBM 0.0000 0.0000 0.0000 0.1857 0.27078 0.31705 0.0000
OBM 0.0000 0.0000 0.0000 0.1776 0.16264 0.11440 0.0000
Criterion
Safety 0.0000 0.3481 0.2523 0.0000 0.25000 0.25000 0.4722
Availability 0.0000 0.6720 0.2581 0.2500 0.00000 0.25000 0.4289
Cost 1.0000 0.0000 0.5107 0.2500 0.25000 0.00000 0.0989
Objective 0.0000 0.0000 0.0000 0.0000 0.00000 0.00000 0.0000
The extreme super-matrix is constructed as presented in Table 13.
TABLE XIII. EXTREME SUPER-MATRIX OF DECISION-MAKING ON MAINTENANCE MODE
Extreme Super-matrix Strategy Criterion
Objective
TBC TBM OBM Safety Availability Cost
Strategy
TBC 0.0576 0.0576 0.0576 0.0576 0.0576 0.0576 0.0576
TBM 0.1636 0.1636 0.1636 0.1636 0.1636 0.1636 0.1636
OBM 0.1013 0.1013 0.1013 0.1013 0.1013 0.1013 0.1013
Criterion
Safety 0.2042 0.2042 0.2042 0.2042 0.2042 0.2042 0.2042
Availability 0.2318 0.2318 0.2318 0.2318 0.2318 0.2318 0.2318
Cost 0.2415 0.2415 0.2415 0.2415 0.2415 0.2415 0.2415
Objective 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Based on the calculation results in Table 13, it is obvious
that fuel injector has the largest superiority through periodic
replacement, i.e. 0.1636 0.507
0.0576 0.1636 0.1013 
 , so the optimal
maintenance mode of fuel injector is periodic replacement.
VI. SUMMARY
This paper analyzes the basic types of maintenance
mode for equipment components within task cycle, and the
influence of maintenance modes on the risk of equipment
failure. By taking the failure risk and its factors as the
decision-making indicators, the logical judgment method is
utilized to create the logical judgment diagram for decision-
making risks of maintenance mode for equipment components
within task cycle. Based on the applicability of each
maintenance mode, the equipment applicable to post-event
maintenance mode and improvement maintenance mode are
selected. If any maintenance mode cannot be judged through
logical judgment diagram, safety, task and economic risks are
taken as the decision-making indicators, and fuzzy theory is
combined with analytic network process to build a decision-
making model for the risks of maintenance mode for
equipment based on fuzzy analytic network process, and
provide the method for deciding the optimal maintenance
mode. This achievement will provide the support for decision-
making in the preparation of equipment maintenance plan
before execution of task, and help select the optimal
maintenance mode to lower the failure risk and improve the
task completion rate of equipment.
ACKNOWLEDGMENT
This work was supported by National Natural Science
Foundation of China (71401171), PLA General Armament
Department Pre-research Fund (9140A19030214JB11273),
Military Universities 2110 Projects Phase III (4142D4557).
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2016 International Conference on Mechatronics, Control and Automation Engineering (MCAE 2016)
© 2016. The authors – Published by Atlantis Press
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