Estimation of reliability with semi-parametric modeling of degradation

In many real life scenarios, stress accumulates over time and the system fails as soon as the accumulated stress or degradation equals or exceeds a critical threshold. For some devices, it is possible to obtain measurements of degradation over time, and these measurements may contain useful information about product reliability. In this paper, we propose a semi-parametric random effect (frailty) model for degradation path, and a method of estimating this path as well as the reliability. Consistency of the estimator under general conditions is established. Simulation results show superiority of the performance of the proposed method over a parametric competitor. The method is illustrated through the analysis of a real data set.