Bayesian analysis for the transformed exponential dispersion process with random effects

• Published in: Reliability engineering & system safety 2022-01, Vol.217, p.108104, Article 108104
• Main Authors: Duan, Fengjun, Wang, Guanjun
• Format: Article
• Language: English
• Subjects: Age; Age- and state-dependent degradation; Algorithms; Approximation; Approximation method; Bayesian analysis; Bayesian MCMC; Dispersion; Gallium arsenide lasers; Heterogeneity; Lasers; Mathematical models; Mean; Performance degradation; Random effect; Reliability engineering; Reliability evaluation; Service life assessment; Transformed exponential dispersion process; Variance
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2021.108104

The basic exponential-dispersion (ED) process can be used to describe many degradation phenomena, but its degradation increments are only age-dependent, which limits its application especially for the phenomena with state-dependent degradation increments. This paper proposes a transformed ED (TED) process degradation model with both age- and state-dependent increments, which is an extended model including the basic ED process model as a special case. The mean and variance functions of the TED process are derived, and the variance-to-mean ratio of the TED process is no longer a constant. Besides, the random effect is introduced into the TED degradation process model to describe the heterogeneity among different units. For the TED process with and without random effects, the Bayesian MCMC algorithm is applied to estimate the model parameters. Further, an approximation method based on moment generating function is used to evaluate the lifetime and remaining useful life (RUL) distribution of products based on the fixed effect and random effect TED process models. Finally, a numerical example of GaAs laser is used to illustrate the effectiveness of the proposed models and methods. The results show that the proposed TED process has better performance for this degradation data set compared with existing process models. •An age- and state-dependent degradation model (TED process model) is proposed.•The random effect is introduced into the proposed TED process model.•The mean, variance and first hitting time of the TED process are derived.•The Bayesian method is used to conduct the statistical inference for TED process.