Stochastic Ordering Inequalities in Parallel and Series Systems with Gumble Distributed Components

Abstract

The stochastic comparisons of parallel and series systems are worthy of study. In this article, we present some stochastic comparisons of parallel and series systems having independent components from Gumble distribution which is also known as an extreme value type-I distribution with two parameters (one location and one shape). This study only deals with the location parameter. Here, we first put a condition for the likelihood ratio ordering of the parallel systems and second, we use the concept of vector majorization technique to compare the systems by the reversed failure rate ordering, the failure rate ordering, the dispersive ordering, and the less uncertainty ordering with respect to the location parameter. AMS 2020 subject classifications: 62G30, 60E15, 60K10