Comparing Residual Lives and Inactivity Times by Transform Stochastic Orders

Comparison of residual lives and inactivity times is an important topic in reliability. In this framework, our purpose is twofold. First, we interpret a family of stochastic orders, known in the literature as transform stochastic orderings, in terms of stochastic comparisons among residual lives and inactivity times at quantiles. Second, we introduce a new stochastic order that occupies an intermediate position between two of these transform orderings, namely the convex order and the star order. As an application, we introduce a new aging class intermediate between the aging classes increasing hazard rate and increasing hazard rate average and show its usefulness.