Improved Ordering Results for Fail-Safe Systems with Exponential Components

N. Balakrishnan, Abedin Haidari and Ghobad Barmalzan

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 10, 2010-2023

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.

Date: 2015
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DOI: 10.1080/03610926.2012.755204

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