Estimation of Time to Hard Failure Distributions Using a Three-Stage Method

Degradation analysis is a tool for assessing the lifetime distribution in reliability analysis. The lifetime of a product, in degradation analysis, is defined as the time when the value of a chosen degradation characteristic reaches a predetermined threshold. This kind of failure is called a soft failure, in contrast with a hard failure which means that the product is not functioning at any positive performance level. In this article, we introduce the idea of considering the threshold for the degradation characteristic as random. The difference between the time to soft failure and hard failure is then modeled. We modify Lu & Meeker's two-stage method, and a new approach named the three-stage method is developed. We apply both the two- and three-stage methods to a simulation study. From the simulation study, we conclude that when the time to soft failure is very different from the time to hard failure, the three-stage method leads to a better performance than the two-stage method. Fatigue-crack growth data are analysed at the end.