Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

Zhang, Zhengcheng

doi:10.1017/s0021900200007129

Cited by 14 publications

(13 citation statements)

References 27 publications

(29 reference statements)

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“…However, representations ( demonstrated in Example 5.1 of [22]. Related work on system signatures includes [4], [5], [9], [10], [11], [14], [15], [20], [29], and [30]. Few representation results have been obtained in the literature for coherent systems with heterogeneous components.…”

Section: )mentioning

confidence: 99%

Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

Navarro

Samaniego

2011

J. Appl. Probab.

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Signature-based representations of the reliability functions of coherent systems with independent and identically distributed component lifetimes have proven very useful in studying the ageing characteristics of such systems and in comparing the performance of different systems under varied criteria. In this paper we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of systems with homogeneous and heterogeneous components.

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Section: )mentioning

confidence: 99%

Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

Navarro

Samaniego

2011

J. Appl. Probab.

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“…The conditional probability Pr(T = T(i)|T ∈ A) means that the ith failure in the repairable system causes the failure of the system under the partial information A about the system lifetime. Recently, some properties of the conditional probability Pr(T = X i∶n |T ∈ A), where X i∶n is the ith order statistic of the component lifetimes, have been obtained for different forms of A; see [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Mixture representation for the residual lifetime of a repairable system

Chahkandi

Ahmadi

2017

Appl Stoch Models Bus & Ind

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In this paper, we consider a repairable system in which two types of failures can occur on each failure. One is a minor failure that can be corrected with minimal repair, whereas the other type is a catastrophic failure that destroys the system. The total number of failures until the catastrophic failure is a positive random variable with a given probability vector. It is assumed that there is some partial information about the failure status of the system, and then various properties of the conditional probability of the system failure are studied. Mixture representations of the reliability function for the system in terms of the reliability function of the residual lifetimes of record values are obtained. Some stochastic properties of the conditional probabilities and the residual lifetimes of two systems are finally discussed.failures by minimal repairs, and by system lifetime, we mean the time until a catastrophic failure in the system. The aging properties of the system, under the condition that the system can be repaired (N − 1) times and the Nth failure destroys the system, has been studied in [16]. In this paper, we consider the situation when one may have some partial information about the system lifetime, i.e., the time until the catastrophic failure, and we are then interested in finding the dynamic

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“…For more details about signatures, readers can refer to Boland [6], Navarro, Ruiz and Sandoval ( [19], [20]), Navarro et al [22], Samaniego ([24], [25]), and Zhang [31]. The residual lifetime of a coherent system is an important concept in reliability theory and survival analysis.…”

Section: Introductionmentioning

confidence: 99%

The Residual Lifetime of Surviving Components From Failed Coherent Systems

Zhang

Meeker

2014

IEEE Trans. Rel.

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In this paper, we consider the residual lifetimes of surviving components of a failed coherent system with n independent and identically distributed components, given that before time t1 (t1 > 0), exactly r (r < n) components have failed and, at time t2 (t2 > t1) the system just failed. Some aging properties and preservation results of the residual lives of the surviving components of such systems are obtained. Also some examples and applications are given. Abstract-In this paper, we consider the residual lifetimes of surviving components of a failed coherent system with n independent and identically distributed components, given that before time t1 (t1 > 0), exactly r (r < n) components have failed and, at time t2 (t2 > t1) the system just failed. Some aging properties and preservation results of the residual lives of the surviving components of such systems are obtained. Also some examples and applications are given. Index Terms-Order

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Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

Cited by 14 publications

References 27 publications

Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

Mixture representation for the residual lifetime of a repairable system

The Residual Lifetime of Surviving Components From Failed Coherent Systems

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