Lifetime Inference of Skew-Wiener Linear Degradation Models

Abstract

Degradation models are widely used to assess the lifetime information of highly reliable products which possess quality characteristics whose degradation over time can be related to reliability. The performance of a degradation model depends strongly on the appropriateness of the model describing a product’s degradation path. Conventionally, mixed (or random) effects formulation is one well-known approach in literature. However, normality (symmetry) of random effects is a routine assumption in degradation models, but it may be unrealistic, obscuring important features of unit-to-unit variations. In this paper, motivated by laser data, we relax this assumption by assuming that the random effects density is skew-normal to provide flexibility in capturing a broad range of non-normal and asymmetric behavior. Based on the extended degradation model, we first derive an implicit expression of a product’s lifetime distribution, including density, distribution functions and its corresponding mean-time-to-failure (MTTF). Furthermore, whether the degradation model is correctly specified or not, the valid confidence intervals of the product’s MTTF and qth quantile can be established by using an observed information-based approach. Finally, the laser degradation data is used to illustrate the proposed model. Key words and phrases: Degradation model; Wiener process; Skew-normal; First passage time; Information matrix. ?