Industrial equipment reliability estimation: A Bayesian Weibull regression model with covariate selection

•A three-state continuous-time semi-Markov process with Weibull-distributed transition times is used for degradation modeling.•Transition times are influenced by a set of covariates, whose number is reduced by a two-step selection procedure.•A Markov-Chain Monte Carlo algorithm is developed for sampling from the posterior distribution.•The developed model enables estimating reliability and time-dependent state probabilities, depending on the operating conditions. A three-state continuous-time semi-Markov process is used to model the degradation of an industrial equipment. The transition times are assumed Weibull-distributed and influenced by a set of covariates. A Weibull Regression Model is developed within the Bayesian probability framework, to account for the influence of these covariates and estimate the model parameters with the related uncertainty, on the basis of few data and expert judgment. The number of covariates is reduced by a two-step selection procedure derived from the condition monitoring engineering practice. The developed model enables estimating reliability and time-dependent state probabilities for a component degrading in given operational and ambient conditions, represented by a vector of covariates. The model is illustrated by way of a real case study concerning the degradation process affecting diaphragm valves used in the biopharmaceutical industry.