Repairable system analysis in presence of covariates and random effects

This paper aims to model the failure pattern of repairable systems in presence of explained and unex-plained 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 distri-bution on the PLP parameters estimated from the data is used as an informative prior to make Bayes-ian 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.