Stochastic order relations among parallel systems from Weibull distributions. (English) Zbl 06441354

Torrado, Nuria; Kochar, Subhash C.

J. Appl. Probab. 52, No. 1, 102-116 (2015).

Summary: Let \(X_{\lambda_{1}}, X_{\lambda_{2}},\ldots, X_{\lambda_{n}}\) be independent Weibull random variables with \(X_{\lambda_{i}} \sim W(\alpha, \lambda_{i})\), where \(\lambda_{i} > 0\) for \(i = 1,\ldots, n\). Let \(X_{n:n}^{\lambda}\) denote the lifetime of the parallel system formed from \(X_{\lambda_{1}}, X_{\lambda_{2}}, \ldots, X_{\lambda_{n}}\). We investigate the effect of the changes in the scale parameters \((\lambda_{1}, \ldots, \lambda_{n})\) on the magnitude of \(X_{n:n}^{\lambda}\) according to reverse hazard rate and likelihood ratio orderings.

MSC:

62G30	Order statistics; empirical distribution functions
60E15	Inequalities; stochastic orderings
60K10	Applications of renewal theory (reliability, demand theory, etc.)

Keywords:

likelihood ratio order; reverse hazard rate order; majorization; order statistics; multiple-outlier model