Bayesian estimation of time to failure distributions based on skew normal degradation model : an application to GaAs laser degradation data

Abstract

In this paper, the Bayesian method which involves informative and weakly informative priors are considered to estimate the parameters and percentiles of the time to failure distribution. The parameters of the time to failure distribution and its percentiles are determined based on linear degradation model where the degradation parameter is assumed to follow the skew normal distribution. For the prior distributions, location and scale parameters of the skew normal distribution is assumed to follow the uniform distribution while the shape parameter is assumed to follow gamma distribution. Two gamma priors are considered, either informative or weakly informative prior, depending on the assumed values of the hyper parameters. The performance of the method under the different prior assumptions is compared using a simulation study based on Markov Chain Monte Carlo method as well as a real data application. It is found that the parameter estimation based on informative prior is more precise as opposed to the weakly informative prior, especially in the case of small sample size. In addition, the skew normal degradation model is compared to the log-logistic degradation model through a simulation study and a real application of GaAs laser data. When modeling the percentiles of the time to failure distribution, results found based on the skew normal distribution is generally found to be more precise, particularly for the higher percentile values.