A degradation model for products with failure-free life

For highly reliable products that degrade over time, it is not uncommon to observe an initial period during which no failure occurs. In this paper, a degradation model that gives rise to a first passage time distribution with failure-free life is proposed as a more plausible model compared to many common models. We call it Beta process as its increments are approximated by three-parameter Beta distributions. We start with a discrete time process as a degradation process is commonly measured at regular time intervals. We derive a closed-form first passage time distribution under a constant failure threshold. Closed-form maximum likelihood (ML)-type estimators are developed for the parameters of the Beta process. Then, the discrete time process is extended to the case of a continuous time process. Comprehensive simulations and case studies show that the Beta processes outperform many common degradation processes in reliability estimation.