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The joint reliability signature of order statistics

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  • Leila Mohammadi

Abstract

In this article, we investigate the joint reliability signature of a number of k-out-of-n systems. We assume to have n components with independent and identically distributed lifetimes. Each system is composed of all of the components and fails upon the failure of the k-th component, for some k≤n . Given an ordering of the failure times, we determine a formula for the joint reliability signature, which is a high-dimensional matrix. Furthermore, we prove a relationship between the joint reliability signature and the order of the failure times and obtain the number of essentially different joint reliability signatures as a function of the number of systems. Moreover, we demonstrate how the joint reliability signature of several k-out-of-n systems is related to their joint signature. A computer program is presented to calculate the joint reliability signature and joint signature, for all permutations of the failure times together.

Suggested Citation

  • Leila Mohammadi, 2019. "The joint reliability signature of order statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(19), pages 4730-4747, October.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:19:p:4730-4747
    DOI: 10.1080/03610926.2018.1473596
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    Cited by:

    1. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2024. "Joint reliability of linear consecutive k-type systems with shared components in a zigzag structure," Reliability Engineering and System Safety, Elsevier, vol. 241(C).

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