Non parametric hypothesis tests for comparing reliability functions

ABSTRACT

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 non parametric statistical methodology to compare two populations based on their mean residual life function and expected inactivity time function. We introduce some novel hypothesis testing procedures that involve both Cramér–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 behavior 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 discussed to demonstrate the practical utility of the tests.

KEYWORDS:

• Asymptotic distributions
• expected inactivity time function
• fixed-design local polynomial regression
• mean residual life function
• non parametric hypothesis testing.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62: Statistics