Nonparametric tests for comparing reliability functions

In reliability and related disciplines comparing reliability functions of two (or more) aging processes is a crucial step in the process of determining reliability and understanding an aging process.The aim of this paper is to propose a nonparametric statistical methodology to compare two populations based on their MRL and EIT functions. We introduce some novel hypothesis testing procedures that involve both Cram´er-von Mises and Kolmogorov-Smirnov type test statistics and their decision rules are constructed based on the asymptotic distributions of these test statistics and bootstrapping method. We study the practical behaviour of the proposed testing procedures extensively through simulations. The results reveal that the proposed hypothesis testing procedures perform efficiently in identifying small and large differences. Two real life examples are discussedto demonstrate the practical utility of the tests.