Reliability Estimation for Products Subjected to Two-Stage Degradation Tests Based on a Gamma Convolution

Degradation models have received much attention in the area of reliability estimation, mostly because it is possible to obtain robust information about the lifetime of highly reliable products and systems. However, in the last years, multivariate models have received more attention. This is because the quality of many products is a function of various environmental conditions, and the effect of these conditions over a performance characteristic can cause a failure of the product, either marginally or jointly. A gamma process is considered in this study to marginally model the degradation of a performance characteristic through two degradation test phases performed sequentially. The degradation increments obtained during the first test and the second test are modeled jointly considering the convolution of two marginal gamma processes. In this way, it is possible to obtain a robust model to get reliability estimates considering the effect of two serial degradation test, which can consider multiple covariates. This modeling is illustrated with crack propagation data and important results are presented.