Finite sample behaviour of the Hollander-Proschan goodness of fit with reliability and maintenance data

Abstract

In maintenance and reliability everyday practices the data samples which are often made available are multiply censored, i.e. the times to failure are randomly mixed with incomplete lifetimes. This fact adds complexity when sound decisions are required to be made in identifying failure mechanisms, evaluating maintenance practices and/or manufacturing methods. Hollander & Proschan have derided a Goodness of Fit (GOF) test statistic which has a number of advantages, i.e. can accommodate multiply censored data, can be employed irrespective of the failure and censoring distributions, and finally is indeed an omnibus and straightforward method to compute. Although the test statistic has received attention in the literature of reliability and maintenance applications over the last two decades, only a limited investigation has been carried out in terms of its finite sample behavior. This paper investigates the usefulness of this particular GOF method within the reliability and maintenance context and provides a literature review of alternative approaches. Furthermore, the finite sample properties are investigated through extensive Monte Carlo Simulations, with the Weibull distribution when parameters are estimated from the data and a wide range of censoring percentages.