Comparing Lifetimes of Series and Parallel Systems with Heterogeneous Fréchet Components

Abstract

Abstract:In this paper, we discuss stochastic comparisons of lifetimes of series and parallel systems with heterogeneous Fréchet components in terms of the usual stochastic order, reversed hazard rate order and likelihood ratio order. The partial results established here extend some well-known results in the literature of Gupta et al. Specifically, first, we generalize the result of Theorem 2 from the usual stochastic order to the reversed hazard rate order. Second, we generalize the result of Theorem 3 from the reversed hazard rate order to the likelihood ratio order. Last, we generalize the result of Theorem 4 from the hazard rate order to the likelihood ratio order when shape parameter 0 < α ≤ 1.

Stochastic comparisons of series and parallel systems with independent heterogeneous Gumbel and truncated Gumbel components

“…Also the extended version of Weibull distribution has been studied for these systems by Fang and Zhang (2015), Fang and Balakrishnan (2016), Barmalzan et al (2017, 2019) and Balakrishnan et al (2018b). Stochastic comparisons of the series and parallel systems with Frèchet components have been also studied by Gupta et al (2015) and Fang and Wang (2017).…”

Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components

“…Further, they obtained sufficient conditions for the hazard rate ordering of the smallest order statistics. For some recent references on the problems related to stochastic comparisons, we refer to [14], [5], [11], [20] and the references therein.…”