Reliability Research of<i>k</i>-out-of-<i>n</i>: G Supply Chain System Based on Copula

Jia, Xujie; Cui, Lirong

doi:10.1080/03610926.2012.707736

Cited by 21 publications

(14 citation statements)

References 17 publications

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“…There are different kinds of copulas, such as t copula, Clayton copula, and so on. The popular methods to get the appropriate copula and parameters of a copula are statistics analysis and simulation techniques Reliability and safety indexes for a safety‐critical unit …”

Section: Reliability and Safety Indexes For Scsmentioning

confidence: 99%

“…Eryilmaz analyzed the reliability of coherent systems and weighted‐k‐out‐of‐n systems based on the Copula method. Navarro and Spizzichino, Noh et al, Jia, Zhang, and Navarro and Durante also studied correlated input variables using the Copula. Copula shows the dependent structure of random variables and can capture nonlinear dependence.…”

Section: Introductionmentioning

confidence: 99%

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Copula‐based reliability and safety analysis of safety‐critical systems with dependent failures

Jia

Xing

2018

Quality & Reliability Eng

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A safety-critical system (SCS) is a system whose failure could result in a certain serious consequence, such as loss of life and significant damage to property or environment. Examples of SCSs abound in real-world applications, such as medical instruments, emergency shutdown systems, and fire/gas detection systems. An SCS can assume 1 of 3 states: working, safe failure, and dangerous (or unsafe) failure. To analyze reliability and safety of SCSs accurately, we build multi-state models of an SCS and its constituent units. The dependent relationships (nonlinear correlation) of different parts within a safety-critical unit as well as across the units are modeled using the Copula method. Formulas computing reliability and safety indexes of a safety-critical unit and of safety-critical series or parallel systems are derived. Numerical examples are provided to demonstrate the application of the proposed methodology.

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Section: Reliability and Safety Indexes For Scsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Copula‐based reliability and safety analysis of safety‐critical systems with dependent failures

Jia

Xing

2018

Quality & Reliability Eng

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“…17 Nevertheless, choosing an appropriate copula function is application dependent, and it requires collecting the corresponding data from experiments and/or fields. 20,23 In the context of binary-state systems, the dependency among components is characterized by a joint lifetime distribution, which can be constructed by a copula function. In the context of MSSs, there are, however, more than two states for both components and systems.…”

Section: Multi-state K-out-of-n Systemsmentioning

confidence: 99%

“…tg, are s-dependent and can be calculated in the same manner as equation (16). Hence, the probability P pd j (t) that the partially dependent multistate k-out-of-n system is residing at state j or above can be evaluated by equations (16) and (18)- (20).…”

Section: Reliability Assessment Of Dependent K-outof-n Systemsmentioning

confidence: 99%

A copula-based reliability modeling for nonrepairable multi-state k-out-of-n systems with dependent components

Liu

Chen

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part O:

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As k-out-of-n systems have widespread applications in engineering practices, their reliability modeling and evaluation are a great concern of reliability community. However, most reported works on k-out-of-n reliability modeling and evaluation are based on the premise that all the components are s-independent. Such simplified treatment may not be realistic as components in a system often suffer the same working or environmental conditions and/or interact with one another, resulting in dependency between their failure processes. To characterize such dependency in reliability modeling and evaluation, a copula-based reliability modeling for dependent multi-state k-out-of-n systems is developed in this work using copula functions and minimal paths of system states. The state probability and reliability functions of dependent multistate k-out-of-n systems with identical components, nonidentical components, and partially dependent components are formulated. Two illustrative examples and a port oil transportation system are presented to demonstrate the implementation of the proposed method, and a sensitivity analysis is also conducted to examine how sensitive the reliability measures are with respect to the degree of dependency.

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“…A detailed review of copulas can be found in Nelsen [1]. Some works on copula based reliability analysis are in [2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Multivariate copula based dynamic reliability modeling with application to weighted-k-out-of-n systems of dependent components

Eryılmaz

2014

Structural Safety

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Reliability Research ofk-out-of-n: G Supply Chain System Based on Copula

Cited by 21 publications

References 17 publications

Copula‐based reliability and safety analysis of safety‐critical systems with dependent failures

Copula‐based reliability and safety analysis of safety‐critical systems with dependent failures

A copula-based reliability modeling for nonrepairable multi-state k-out-of-n systems with dependent components

Multivariate copula based dynamic reliability modeling with application to weighted-k-out-of-n systems of dependent components

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