Misspecification analysis of two-phase gamma-Wiener degradation models.

A 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.