A1323
Title: Statistical inference for lifetimes of one-shot devices with gamma frailty components
Authors: Ping Shing Ben Chan - The Chinese University of Hong Kong (Hong Kong) [presenting]
Abstract: The inferential procedure for the lifetimes of one-shot devices with $M$ components is studied. Assuming the component's lifetimes are exponentially distributed and the dependency among component lifetimes is governed by a frailty parameter which is assumed to be gamma distributed. The unconditional distribution of the component lifetimes will be derived. First, the time-censored samples are considered. An EM algorithm is proposed to find the maximum likelihood estimators of the unknown parameters. The algorithm is very easy to implement. The estimates of the variance-covariance of the estimators based on the missing information principle are also given. Then the results are extended to one-shot device data. The EM algorithm for the time-censored data has been modified to tackle the one-shot device data. A simulation study will then be conducted to examine the performance of the proposed algorithm. The estimators' biases and mean square errors under various settings will be presented. The coverage probabilities and average lengths of the confidence intervals constructed based on the asymptotic distribution of the estimators will also be given. Finally, an example is presented to illustrate the method of inference developed in the article.
