Title: Kullback-Leibler goodness-of-fit tests for exponential simple step-stress accelerated life testing models
Authors: Anastasia Gaponik - RWTH Aachen University, Institute of Statistics (Germany) [presenting]
Maria Kateri - RWTH Aachen University (Germany)
Abstract: Step-stress accelerated life testing (SSALT) experiments are used for assessing the reliability of products in reasonable time. Under a SSALT model, the test units are exposed to stress levels that increase at intermediate time points. For the SSALT model specification, which influences the associated statistical inference procedures, there are three core assumptions to make: the underlying lifetime distributions for each stress level, the model for the joint cumulative distribution function, and the link model that connects the respective lifetime to the stress. To ensure accurate results of reliability prediction, a justification for the chosen assumptions is required. We focus on testing the validity of the first assumption. It is common practice to assume exponential distributed lifetimes for the units under test. In spite of the rich bibliography on goodness-of-fit testing of exponentiality, the literature on goodness-of-fit tests for exponential SSALT models is restricted. We consider a simple SSALT model (i.e. consisting of two stress levels) under the cumulative exposure model and investigate tests based on the Kullback-Leibler information, comparing different entropy estimators. Moreover, via Monte Carlo simulations, the Kullback-Leibler test statistics are compared in terms of power to several common nonparametric goodness-of-fit tests against Weibull and Gamma distributed alternatives.