Comparing Lifetimes of Series and Parallel Systems with Heterogeneous Fréchet Components

Symmetry

Longxiang Fang¹  Yanqin Wang¹ 

[1] Department of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China;

关键词: Fréchet distribution;    usual stochastic order;    reversed hazard rate order;    likelihood ratio order;    series system;    parallel system;   

DOI  :  10.3390/sym9010010

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown