Mean residual life of coherent systems consisting of multiple types of dependent components

Eryılmaz, Serkan; Coolen, Frank P. A.; Coolen‐Maturi, Tahani

doi:10.1002/nav.21782

Cited by 28 publications

(12 citation statements)

References 25 publications

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“…Example 2.7. Consider the system depicted in Figure 1, given in Feng et al [2016] and Eryilmaz et al [2018b]. The system consists of six components in which components 1, 2, and 5 are of type one, and components 3, 4, and 6 are of type two.…”

Section: Proof See the Appendixmentioning

confidence: 99%

Optimal Redundancy Allocation in Coherent Systems with Heterogeneous Dependent Components

Kelkinnama¹,

Asadi²

2022

Preprint

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This paper is concerned with the optimal number of redundant allocation to n-component coherent systems consist of heterogeneous dependent components. We assume that the system is built of L groups of different components, L ≥ 1, where there are n i components in group i, andThe problem of interest is to allocate v i active redundant components to each component of type i, i = 1, . . . , L. To get the optimal values of v i , we propose two cost-based criteria. One of them is introduced based on the costs of renewing the failed components and the costs of refreshing the alive ones at the system failure time. The other criterion is proposed based on the costs of replacing the system at its failure time or at a predetermined time τ , whichever occurs first. The expressions for the proposed functions are derived using the mixture representation of the system reliability function based on the notion of survival signature. We assume that a given copula function models the dependency structure between the components. In the particular case that the system is a series-parallel structure, we provide the formulas for the proposed cost-based functions. The results are discussed numerically for some specific coherent systems.

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Section: Proof See the Appendixmentioning

confidence: 99%

Optimal Redundancy Allocation in Coherent Systems with Heterogeneous Dependent Components

Kelkinnama¹,

Asadi²

2022

Preprint

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“…, ω n 1 ,n 2 ) of (n 1 + 1) × (n 2 + 1) elements represents the minimal signature of the system (see e.g. [9]).…”

Section: Systems With Two Types Of Componentsmentioning

confidence: 99%

Computing minimal signature of coherent systems through matrix-geometric distributions

Eryılmaz

Tank

2021

J. Appl. Probab.

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Signatures are useful in analyzing and evaluating coherent systems. However, their computation is a challenging problem, especially for complex coherent structures. In most cases the reliability of a binary coherent system can be linked to a tail probability associated with a properly defined waiting time random variable in a sequence of binary trials. In this paper we present a method for computing the minimal signature of a binary coherent system. Our method is based on matrix-geometric distributions. First, a proper matrix-geometric random variable corresponding to the system structure is found. Second, its probability generating function is obtained. Finally, the companion representation for the distribution of matrix-geometric distribution is used to obtain a matrix-based expression for the minimal signature of the coherent system. The results are also extended to a system with two types of components.

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“…28 Eryilmaz et al 29 developed the survival signature-based marginal and joint reliability importance measures to optimise system design, as well as consider mean residual life of coherent systems with multiple types of dependent components in the article. 30 A survival signature based reliability analysis on complex systems with common cause failures has been proposed in this paper. The α-factor model distinct between the total failure rate of a component and the common cause failures modelled by α-factor parameters, which can be got through experts' judgement of the system or the past data on the system.…”

Section: Introductionmentioning

confidence: 99%

Survival Signature-based Reliability Approach for Complex Systems Susceptible to Common Cause Failures

Geng

2019

Int. J. Rel. Qual. Saf. Eng.

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The importance of reliability to complex systems cannot be disputed as they are the backbones of our society. In practice, the common cause failures may have severe reverse function on complex systems’ overall stability. Survival Signature opens a new way to perform reliability analysis on systems with multiple component types. This paper under takes a research on survival signature-based reliability analysis on complex systems susceptible to Common Cause Failures. To be specific, it proposes the standard [Formula: see text]-factor model and general [Formula: see text]-factor model to combine with the survival signature. In practical applications, the [Formula: see text]-factor estimator of the system might not be defined completely due to limited data, or knowledge which requires to take imprecision into account. Some numerical cases are presented to show the applicability of the methods for complex systems. In addition, this paper may attract people’s attention on the conception of Design for Reliability.

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Mean residual life of coherent systems consisting of multiple types of dependent components

Cited by 28 publications

References 25 publications

Optimal Redundancy Allocation in Coherent Systems with Heterogeneous Dependent Components

Optimal Redundancy Allocation in Coherent Systems with Heterogeneous Dependent Components

Computing minimal signature of coherent systems through matrix-geometric distributions

Survival Signature-based Reliability Approach for Complex Systems Susceptible to Common Cause Failures

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