Bayesian Approach for Estimating the Parameters of the Time-To-Failure Distribution and Its Percentiles Under Power Degradation Model

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 power degradation model for estimating the parameters of the time-to-failure distribution and its percentiles. Two different distributions are assumed for the degradation parameter of the model. 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 NASA turbofan Jet engine dataset and the results found are compared. In modeling the time-to-failure distribution, it is shown that based on the simulated data and real data, the Bayesian approach for the power degradation model with the skew-normal degradation parameter outperformed the Bayesian approach for the power degradation model with the log-logistic degradation parameter.