Misspecification analysis of two‐phase gamma‐Wiener degradation models

Abstract

AbstractA degradation model is used to analyze degradation data and product reliability. Owing to model uncertainty, the assumed degradation model may be improper, which can create a difference between the evaluated and actual product reliabilities. Thus, model misspecification analysis is essential. Recent studies on misspecification analysis have mainly considered single‐phase degradation models; two‐phase degradation models have not been investigated intensively. In this study, an approach to model misspecification analysis was developed for a two‐phase gamma‐Wiener process, where the change point was assumed to be known. The gamma and Wiener processes in a two‐phase degradation model may be incorrectly assumed, so five misspecified degradation models were considered: the two‐phase Wiener process, two‐phase gamma process, two‐phase Wiener‐gamma process, one‐phase Wiener process, and one‐phase gamma process. A Monte Carlo simulation was performed to examine the effects of model misspecification on the relative bias and relative variability. A case study was performed to examine the effects of model misspecification on the evaluated mean time to failure and median lifetime of a product for different sample sizes, termination time, and change points. The results clearly demonstrated the effects of model misspecification on the evaluated reliability of a product.