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Improved Ordering Results for Fail-Safe Systems with Exponential Components

Author

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  • N. Balakrishnan
  • Abedin Haidari
  • Ghobad Barmalzan

Abstract

Let X2: n and Y2: m be the second order statistics from n independent exponential variables with hazards λ1, …, λn, and an independent exponential sample of size m with hazard change to λ, respectively. When m ⩾ n, we obtain necessary and sufficient conditions for comparing X2: n and Y2: m in mean residual life, dispersive, hazard rate, and likelihood ratio orderings based on some inequalities between λi’s and λ. The established results show how one can compare an (n − 1)-out-of-n system consisting of heterogeneous components with exponential lifetimes with any (m − 1)-out-of-m system consisting of homogeneous components with exponential lifetimes.

Suggested Citation

  • N. Balakrishnan & Abedin Haidari & Ghobad Barmalzan, 2015. "Improved Ordering Results for Fail-Safe Systems with Exponential Components," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(10), pages 2010-2023, May.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:10:p:2010-2023
    DOI: 10.1080/03610926.2012.755204
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    Cited by:

    1. Jiandong Zhang & Rongfang Yan & Yiying Zhang, 2023. "Reliability analysis of fail-safe systems with heterogeneous and dependent components subject to random shocks," Journal of Risk and Reliability, , vol. 237(6), pages 1073-1087, December.

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