An EM‐based likelihood inference for degradation data analysis using gamma process

Abstract

The gamma process is widely used for the lifetime estimation of highly reliable products that degrade over time. Typically, incomplete likelihood is used to estimate the model parameters and the reliability estimates for the first passage time distribution of the gamma process; however, it (i.e., pseudo method) does not consider interval censoring and right censoring information of the degradation data. In this work, the expectation‐maximization algorithm‐based method (EM method) is developed for the estimation of the gamma process model parameters and the reliability estimates incorporating interval censoring and right censoring. The asymptotic variance–covariance matrix and the asymptotic confidence intervals for the parameters are constructed, and then a comparison between the pseudo method and the EM method is made. Monte Carlo simulation studies and real‐life data applications are conducted in order to illustrate the performance of the proposed EM method over the pseudo method.