Assessing device reliability based on scheduled discrete degradation measurements

Degradation measurements are increasingly important in reliability studies because few failures are observed during the short time of many experiments. In this article, we assess device reliability from discrete degradation processes under scheduled inspections. In some particular situations, since the degradation quantities of the device characteristic are only observed specifically at the scheduled time points, the exact occurrence time and the corresponding damage amount of each degradation event are not recorded. For this sort of situation, there are plenty of examples such as the amount of shock damages of the database in a computer system, the amount of fatigues of the shock absorber for a car, and the amount of growth of a metal crack on an aircraft.A discrete degradation model, a non-homogeneous compound Poisson (NHCP) model, is considered. We derive the first passage time distribution (FPTD) and construct the likelihood function for the estimations of model parameters under the scheduled inspections. Due to the importance of assessing a model’s adequacy, we conduct a flexible procedure of goodness-of-fit (GOF) test for the assumed model. To illustrate the process of methodology and inference, a simulation study is conducted under several cases of sample size and inspection schedule, where the cumulative failure rate of the occurrence of events is assumed to follow an exponential growth model and an exponential distribution is used to describe the degradation increments. Based on a tolerance quantity of the variation in lifetime estimation, the simulation study is useful in choosing sample size and inspection schedule for planning the degradation tests.