Sequential Bayesian inference for Weibull distribution parameters with initial hyperparameter optimization for system reliability estimation

In this study, we investigated the sequential Bayesian inference of the Weibull distribution parameters of the components of a system the remaining useful life of which can be estimated using lifetime estimation or survival function of certain types of components. Failure observations are collected sequentially and analyzed as censored data. Here, we propose a sequential Bayesian inference with optimized prior distribution (SBOPD) to provide an effective way to estimate the parameters of the Weibull distribution of the components. In this framework, the Bayesian inference of the parameters of the Weibull distribution is updated by a certain number of new failure observations. Two measures are used to estimate more accurately and effectively in the preliminary stages of the system life cycle; the posterior distribution of the previous update is used as the prior information of the new update, and the initial prior distribution is optimized using prior knowledge of the parameters. With optimized hyperparameters for the initial prior distribution, parameter estimation with SBOPD provided a better estimate at the preliminary stages of the system life than conventional methods.