Figure - available from: Annals of Operations Research
This content is subject to copyright. Terms and conditions apply.
Source publication
A network with multi-state (stochastic) elements (arcs or nodes) is commonly called a stochastic flow network. It is important to measure the system reliability of a stochastic flow network from the perspective of operations management. In the real world, the system reliability of a stochastic flow network can vary over time. Hence, a critical issu...
Similar publications
The distribution laws’ composition of the permanent, long-term temporary, snow and wind loads acting on the structure of buildings and structures is estimated. The following load distribution laws are respectively adopted: normal, logarithmically normal, Gumbel and Weibull. The calculation of the four main central statistical moments was carried ou...
Citations
... In existing studies, reliability evaluation is mainly performed based on failure data or simulation. The evaluation method based on failure data is the earliest and most commonly used at present [1][2][3]. Failure data refer to the record data generated during development, testing, or use, including the failure mode, failure type, cause of failure, impact on production and occurrence time, etc., which describe the key features of fault events. According to research experiences, the time between the failures or service life of electromechanical equipment such as computer numerical control (CNC) machine tools is subject to certain probability distribution types. ...
... Based on the above definition, this paper proposes a reliability fuzzy-evaluation method based on failure-state characterization. It mainly includes the following three contributions: (1) The failure-grade fuzzy-evaluation method is proposed to characterize the failure state considering fault severity, failure maintenance time and expense; (2) The modified adaptive small-sample-expansion method is proposed based on error judgement and correlation coefficient judgement for the time between failures and the failure-grade evaluation index, respectively, aiming to solve the problem of a small sample size; and (3) A novel reliability-evaluation model is established to more accurately estimate the reliability level of equipment by considering the failure grade and membership degree. The remainder of this paper is organized as follows: Section 2 presents the reliability-evaluation scheme considering multiple states of failure, which is proposed based on the traditional Weibull-distribution-based reliability modeling framework; Section 3 presents the failure-grade fuzzy-evaluation method and an example analysis; Section 4 outlines the modified adaptive small-sample-expansion method and an example analysis; Section 5 presents the novel reliability-evaluation model and an example analysis; and Section 6 offers the main conclusions and future recommendations based on this work. ...
... i and x * i are the ith value for the time between failures and the corresponding failure-grade index in the original data from smallest to largest; (4) For the data optimization of the time between failures, taking the original data t O and the newborn data in each iteration t n as failure data, respectively, the Weibull distribution functions can be determined as F O (t) and F N (t) according to Equation (2). Then, the largest error between two distribution curves can be calculated by ...
For complex equipment, it is easy to over-evaluate the impact of failure on production by estimating the reliability level only through failure probability. To remedy this problem, this paper proposes a statistical evaluation method based on fuzzy failure data considering the multi-state characteristics of equipment failures. In this method, the new reliability-evaluation scheme is firstly presented based on the traditional statistical analysis method using the Weibull distribution function. For this scheme, the failure-grade index is defined, and a fuzzy-evaluation method is also proposed by comprehensively considering failure severity, failure maintenance, time, and cost; this is then combined with the time between failures to characterize the failure state. Based on the fuzzy failure data, an improved adaptive-failure small-sample-expansion method is proposed based on the classical bootstrap method and the deviation judgment between distributions of the original and newborn samples. Finally, a novel reliability-evaluation model, related to the failure grade and its membership degree, is established to quantify the reliability level of equipment more realistically. Example cases for three methods of the scheme (the failure-grade fuzzy-evaluation method, the sample-expansion method, and the reliability-evaluation modeling method) are presented, respectively, to validate the effectiveness and significance of the proposed reliability-evaluation technology.
... Let the random variable denoted by Xk (where k=1, 2,….) represents the time interval between two consecutive software failure represented by (k −1) -th and k -th big data accession, so the function Zk(x) for the hazard rate in the phase of operation at any point of time x is given [19] by: ...
... However, a practical network consists of components (nodes or arcs) whose capacities are multistate. Because of failure, maintenance, etc., the components' capacities are uncertain and a network with multistate capacities is called a stochastic flow network (SFN) (Chang 2019;Chang and Lin 2015;Forghani-elahabad and Mahdavi-Amiri 2016a, b;Levitin and Lisnianski 2001;Lin et al. 2013Lin et al. , 2016Nguyen 2020;Ramirez-Marquez and Coit 2007). Hence, the quickest path for an SFN should be the multistate capacity of each component; further, the QPP should be extended to evaluate the system reliability, which is the probability of a given amount of data received at a sink successfully through multiple disjoint minimal paths (MPs) under a time constraint (Lin 2011a, b, c, d) in an SFN. ...
... Time and budget are two important factors in an SFN. In several studies (Chang 2019;Chang andLin 2015, 2016;Lin 2010a, b, c, d;Lin et al. 2013Lin et al. , 2016, researchers developed the system reliability evaluation for the SFN under time or budget constraint. To enhance system reliability for a computer network, Lin (2011c, d) proposed an algorithm to evaluate network reliability with spare routing. ...
... Time and budget are two important factors in an SFN. In several studies (Chang 2019;Chang andLin 2015, 2016;Lin 2010a, b, c, d;Lin et al. 2013Lin et al. , 2016, researchers developed the system reliability evaluation for the SFN under time or budget constraint. To enhance system reliability for a computer network, Lin (2011c, d) proposed an algorithm to evaluate network reliability with spare routing. ...
A stochastic flow network composed of multistate arcs can be utilized to describe several practical systems such as computer networks, where transmission time taken for sending data to a sink is an important index. Determining a path with minimum transmission time is known as the quickest path problem (QPP). All algorithms addressing the QPP assume that the determined minimal paths (MPs) are disjoint. Further, for the general case of intersectional MPs, if a congestion phenomenon occurs during the transmission process, these algorithms will lead to an incorrect outcome. Moreover, in practical scenarios, as a budget limit is considered, spare routing is applied to consolidate the system. The objective is to develop an algorithm based on Monte Carlo simulations (MCSs) for evaluating the system reliability while considering the congestion phenomenon. The system reliability is the probability that a specific amount of data can be transmitted successfully through multiple MPs under both time and budget constraints. Furthermore, spare routing to increase the system reliability is established in advance to specify the main and spare MPs. Experiments validate the evaluation of system reliability based on MCSs. The credibility and efficiency of the proposed algorithm are also discussed.
... But, the methods for collecting data have been beyond the focus of this paper, and as the existing literature (Lin et al., 2013(Lin et al., , 2014, we assume that the information on spoilage rate is known in advance. Furthermore, we refer the readers to the work by Chang (2019) for the big data architecture to deal with parameter estimation in network reliability analysis. Vector R (r 1 , r 2 ,…, r m ) is named the spoilage pattern vector. ...
The fundamental mission of a distribution network is to satisfy the customer demand by providing sufficient delivery capacity. However, the capacity of a distribution network is practically stochastic because of unexpected events, and moreover, the commodities may rot or be spoilt during delivery owing to inclement weather, traffic accidents, collisions, and so on, such that the intact commodity flow may not meet market demand. This paper focuses on the reliability of a multi-state distribution network (MSDN) with cost and spoilage characteristics, defined as the probability that the MSDN is able to distribute a sufficient quantity of goods to meet the market demand under delivery spoilage and budget limit considerations. A specific spoilage rate associated with each route is adopted to characterize the perishability of commodity flows, and the critical routes whose spoilage rate change has the biggest impact on network reliability are identified with the use of sensitivity analysis method. Apart from delivery cost, the cost involved with the disposal of spoilt goods is also incorporated into the reliability indicator. A minimal paths based algorithm is presented to calculate network reliability, together with an example to illustrate the procedure. A real fruit distribution network is accordingly discussed to demonstrate the utility of the algorithm and the managerial implication of network reliability.
An electrical power network (EPN) is a critical infrastructure that provides electricity to private homes, industry, and defense and security organizations. The performance measures of EPNs include reliability, voltage stability, power quality, and economic indices. Reliability indices, which measure the frequency and duration of power outages experienced by customers, are critical performance measures of EPNs. Previous studies have examined the use of reliability indices to assess the performance of power generators in EPNs or the EPN with a single power generator, a single electricity region, and multistate transmission facilities. This paper further considers multiple multistate facilities and electricity regions and stochastic capacity for power plants and electrical substations in power supply reliability assessment. We propose a solution procedure based on a capacitated-flow network model for power supply reliability assessment, considering the line loss rates, which refer to the amount of power dissipated in an electrical conductor during transmission and distribution. A real case study is considered to illustrate that the proposed methodology can assist system engineers in designing and operating EPN reliably.
Multistate flow networks (MFNs) and their reliability problem have been studied extensively. However, most of the research on MFN reliability assumes that flow into and out of any arc is equal. In practical applications, flow may experience loss during transmission such that flow into and out of an arc may not be equal. Thus, this article concentrates on the reliability of an MFN with flow loss effect, defined as the probability that the sink node can receive a flow of at least
d
units when the flow experiences loss without replenishment during transmission. Using minimal paths, a simple method is put forth to compute this reliability index, and the solution procedure is illustrated via a simple network example. Finally, computational experiments are provided to investigate the impact of flow loss on network reliability.
A two-terminal multi-state network (TMSN) is a network (system) with multi-state subsystems (arcs and nodes) and two terminals (source and sink nodes). In a TMSN, system reliability is a widely applied performance indicator of demand satisfaction. To assess system reliability, previous studies relied on knowing the upper bounds (d-MCs) or lower bounds (d-MPs) for specified demand d and a given capacity probability distribution. Accordingly, a novel minimal cut (MC)-based simulation approach is proposed, which does not rely on knowing the d-MCs and capacity probability distribution. An algorithm based on Monte Carlo simulation with demand confirmation via MCs is developed to estimate system reliability. In addition, an extension with a time attribute is examined to investigate the reliability degradation with time. Additional case studies, including a real-life instance of the Taiwan Academic Network, are analyzed to validate the scalability and applicability of the proposed approaches.
To evaluate the performance of engineering systems, this study acts as a bridge between the theories of classical and capacitated-flow network reliabilities and helps integrate them. Unlike existing works, in which a deterministic probability distribution was used for arcs in a network, in this study, the time-dependent reliability function is applied for components in arcs. In particular, the proposed model applies an arbitrary reliability function to evaluate reliability. In arc-level reliability analysis, the components in an arc are characterized by a reliability function, and such components comprise a capacitated-flow arc. Therefore, a certain number of components can be derived from the probability distribution of the capacity provided by an arc. In system-level reliability analysis, an algorithm is used to generate the minimal component vectors (MCV) for the given demand and time constraints. The system reliability can be calculated in terms of the MCVs using the derived capacity probability distribution. Based on the reliability analysis, a maintenance issue with two policies is discussed. Examples, including a large-scale case study of the Taiwan Academic Network, are discussed to validate the correctness, applicability, and scalability of the proposed model.
