Chapter One Inference for one-shot devices with Weibull component lifetimes under gamma frailty model

Frailty models are used to incorporate random effects for immeasurable heterogeneity. It is a popular model used in reliability and survival analyses. In some applied problems, immeasurable heterogeneity would result in biased and/or inefficient inferential results. Despite that, little is known about the impact of misspecifying the time-constant baseline hazard in the analysis of parametric shared frailty models for one-shot devices. This study discusses how the shared frailty model with a Weibull component lifetime distribution fits one-shot device test data with multiple failure modes. We develop an efficient expectation-maximization algorithm for determining the maximum likelihood estimates of model parameters. We compare the model with Weibull lifetime distribution with exponential lifetime distribution. We finally apply the proposed model to two real-life datasets involving modified Class-H failure mode data and mice tumor toxicological data.