Bayesian approach for estimating the parameters and percentiles of the time-to-failure distribution based on general degradation models

Abstract

The degradation models are often applied on the degradation data for studying time-to-failure distribution. In this study, the Bayesian approach is applied on the three different types of degradation models, which are linear, exponential and power degradation models, for estimating the parameters of the time-to-failure distribution and its percentiles. Two different distributions are assumed for the degradation parameter of the models. The degradation parameter is firstly assumed to follow the skew-normal distribution with three jointly independently distributed parameters such that the gamma prior is assumed for the shape parameter, while the scale and the location parameters are assumed uniform. The second distribution assumed for the degradation parameter is the log-logistic distribution with two jointly independent random parameters where the shape parameter is assumed gamma, while the scale parameter is assumed uniform. Based on the Gibbs sampling method carried out under the JAGS platform, the models considered are applied on the simulated data and the real data, and the results found are compared in terms of point estimate, biasness, standard deviation and deviance information criteria. In the Bayesian degradation modelling based on all the models studied, it is found that modelling involving the skew-normal degradation parameter outperformed modelling involving the log-logistic parameter based on smaller values of standard deviation and deviance information criteria.