Model Mis-Specification Analyses of Weibull and Gamma Models Based on One-Shot Device Test Data

Model mis-specification is of great importance in reliability assessment. Different choices of probability models for fitting data may result in substantially different inferential results on some lifetime characteristics of interest. Gamma and Weibull models have been used extensively for modeling lifetime data. Hence, accelerated life models have been developed recently for one-shot device test data under both these models for making inference on mean lifetime as well as the reliability at use level. However, model mis-specification analyses between these two models have not been studied in this context. Here, we examine the effect of model mis-specification between gamma and Weibull models on the likelihood estimation and the inference on the mean lifetime and the reliability at some mission times based on one-shot device test data. Moreover, a distance-based test statistic and the Akaike information criterion as specification tests are studied for the purpose of model validation. A simulation study is carried out to evaluate the bias and coverage probabilities of confidence intervals under model mis-specification. The obtained results reveal that the effect of model mis-specification is negligible only when the sample size is small and when the accelerated and use levels are close, and that the use of specification test is quite important for an accurate reliability assessment.