Statistical modeling and reliability analysis of multiple repairable systems with dependent failure times under perfect repair

In repairable systems, a fundamental aspect to be considered is to predict the reliability of the systems under study. Establishing reliability models for multiple repairable systems, however, is still a challenging problem when considering the dependency or unobserved heterogeneity of component failures. This paper focuses on a special repair assumption, called perfect repair, for repairable systems with dependent failures, where only the failed component is restored to as good as new condition. A frailty model is proposed to capture the statistical dependency and unobserved heterogeneity. The classical inferential method for estimating parameters and the reliability predictors will be shown for models in repairable systems under the assumption of perfect repair. An extensive simulation study is conducted under different scenarios to verify the suitability of the model and the asymptotic consistency and efficiency properties of the maximum likelihood estimators. The proposed methodology can be especially useful for industries that operate with repairable systems subjected to the replacement of parts after failures and to non-quantifiable factors that can interfere with the failure times of these parts. We illustrate the practical relevance of the proposed model on two real data sets. The first deals with a set of 9 sugarcane harvesters, observed during a fixed period of time, whose cutting blades failed several times in this interval. The other deals with a set of 5 dump trucks whose diesel engines also had recurring failures during the observation period. Parametric inference is carried out under the power-law process model that has found significant attention in industrial applications. •Unquantifiable factors can interfere with the failure intensity function of systems.•Dependence between failure times of systems must be considered.•Shared frailty model for multiple repairable systems subjected to perfect repairs.•Capture the unobserved heterogeneity between systems and their failure times.•Ability to predict the reliability of a repairable system after a perfect repair.