Stochastic comparisons in systems with Frèchet distributed components

Comparing Lifetimes of Series and Parallel Systems with Heterogeneous Fréchet Components

“…Now, we discuss stochastic comparison of the lifetimes of parallel systems having independently Fréchet distributed components with respect to the reversed hazard rate order based on vector weak upper majorization of scale parameters but fixed location and shape parameters. The following result generalizes the result of Theorem 2 in Gupta et al [6].…”

“…Next, we generalize the corresponding results of Theorem 2, Theorem 3 and Theorem 4 in Gupta et al [6]. Specifically, let X 1 , .…”

“…The Fréchet distribution was introduced by Fréchet [1] as one of the extreme value distribution, and has been used in modeling and analysing several extreme events including accelerated life testing, earthquakes, wind speeds, and so on. A lot of studied results and various applications of the Fréchet distribution are presented in Broussard and Booth [2], Harlow [3], Kotz and Nadarajah [4], Xapson et al [5], Gupta et al [6], and so on.…”

“…Stochastic comparisons of parallel and series systems with heterogeneous components have been studied by many authors. For example, see Khaledi and Kochar [9,10], Genest et al [11], Balakrishnan and Zhao [12], Balakrishnan et al [13], and Gupta et al [6].…”

“…Gupta et al [6] have considered the stochastic comparisons between the lifetimes of parallel/series systems arising from independently distributed Fréchet components with respect to the usual stochastic order, the reversed hazard rate order and the hazard rate order based on location and scale parameters of the Fréchet distributed components.…”