A Bayesian approach for reliability estimation for non-homogeneous and interval-censored failure data

Abstract

Reliability estimation is paramount to predicting costs, planning maintenance actions, and estimating system availability in high-risk industries such as aerospace, aeronautics, and Oil and Gas (O&G). However, a shortage of historical data is very common because of restrictions related to manufacturer rights, costs, or collecting the data. In this context, generic datasets serve as prior information to model failure distributions. A popular approach to dealing with non-homogeneous generic data assumes that the failure rate is constant, which is not true in many cases. In this paper, we propose a Bayesian approach to consider non-constant failure rates using the Weibull distribution. Here, we account for the uncertainty on the Weibull parameters by modeling the population variability via Empirical Bayes. In addition, the challenge is to consider the generic dataset to provide interval-censored failure data. To obtain the posterior distribution after incorporating specific data on the equipment of interest, the Bayesian model also considers the likelihood of complete failure and censored data. As there is no family of conjugate distributions, the posterior estimate is sampled through the Markov Chain Monte Carlo method. The model was tested using simulated data as an application example.