2022 年 7 巻 3 号 p. 102-112
Products or systems degrade over time. Degradation over time is frequently modeled by stochastic processes to account for inherent randomness. Based on the assumption of additive accumulation of degradation, a family of degradation processes based on the Lévy processes has been well studied in the literature. Recently, a stochastic degradation model based on the generalized inverse Gaussian (GIG) distribution shows good performance in the empirical evaluation studies based on some well-known real datasets. The likelihood function of this model can be seen a generalization of the likelihood function of the existing degradation processes including the Wiener, gamma, inverse Gaussian (IG) processes, which belong to Lévy process. However, it is not clear that which stochastic models are the best for modeling the degradation phenomena although the numerous papers have appeared in decades.
In this paper, we consider more flexible degradation stochastic model than the prominent models. Specifically, we propose new stochastic degradation models based on the powered inverse Gaussian (PIG) distribution, which can be seen a generalization of the IG distribution, and the powered generalized inverse Gaussian (PGIG) distribution. The likelihood function of this model can be seen a generalization of the likelihood function of GIG degradation model. The performances of the proposed models are assessed by comparing the proposed models with the prominent models, based on some well-known real datasets. The results of the evaluation show that the proposed models perform better than existing models. And a simulation study is conducted.
