Semiparametric Estimation of Gamma Processes for Deteriorating Products

Gamma processes and their variants are natural choices for degradation modeling of many products. Motivated by practical needs, this paper investigates semiparametric inference of the simple gamma process model and the random effect variant. Maximum likelihood estimates (MLEs) are obtained through the EM algorithm, while the confidence intervals are constructed via the bootstrap method. The simulation study reveals that estimations based on the full likelihood method are more efficient than the pseudo likelihood method. In addition, a score test is developed to examine existence of the random effect under the semiparametric scenario. A comparison study using a fatigue crack growth dataset shows that performance of the semiparametric estimations is comparable to the parametric counterpart. The developed methods are then applied to a tire tread wear problem where the wear level of each tire is measured only once.