2021 Volume 6 Issue 1 Pages 1-10
Products or systems degrade over time. Degradation over time is often modeled by stochastic processes to account for inherent randomness. Based on the assumption of additive accumulation of degradation, a family of degradation stochastic processes based on the Lévy process (the Wiener, gamma and inverse Gaussian (IG) processes are members of this family of processes) has been well studied in the literature. Recently, degradation stochastic model based on the generalized inverse Gaussian distribution was provided. This model is a generalization of the prominent existing degradation models in a sense, under the mild conditions. In this study, we propose a stochastic degradation model based on the Birnbaum-Saunders (BS) distribution. The BS distribution can be obtained as an approximation of an IG distribution. The BS distribution is proposed as the fatigue failure life distribution based on a physical consideration. The maximum likelihood estimation of the proposed model is also developed. Four case applications are performed to demonstrate the advantages of the proposed model, based on the well-known real degradation data sets of the GaAs laser devices and crack sizes of three kinds of specimens, and also a simulation study is conducted.
