Stochastic comparisons of series, parallel and [formula omitted]-out-of-[formula omitted] systems with heterogeneous bathtub failure rate type components

Abstract

In this paper, we explore stochastic comparisons of order statistics arising from a two parameter distribution with bathtub shaped failure rate. We obtain detailed results in the contexts of the usual stochastic order, the hazard rate order, the reversed hazard rate order and the likelihood ratio order for series, parallel and k-out-of-n systems. Results involving multivariate chain majorization are also established.