Repairable system analysis in presence of covariates and random effects

• We describe the failure process of buses powertrain system subject to heterogeneity.
• Heterogeneity due to different service types is explained by a covariate.
• Random effect is modeled through a joint pdf on failure process parameters.
• The powertrain reliability under new future operating conditions is estimated.

This paper aims to model the failure pattern of repairable systems in presence of explained and unexplained heterogeneity. The failure pattern of each system is described by a Power Law Process. Part of the heterogeneity among the patterns is explained through the use of a covariate, and the residual unexplained heterogeneity (random effects) is modeled via a joint probability distribution on the PLP parameters. The proposed approach is applied to a real set of failure time data of powertrain systems mounted on 33 buses employed in urban and suburban routes. Moreover, the joint probability distribution on the PLP parameters estimated from the data is used as an informative prior to make Bayesian inference on the future failure process of a generic system belonging to the same population and employed in an urban or suburban route under randomly chosen working conditions.