Parametric Estimation in a Recurrent Competing Risks Model

A resource-efficient approach to making inferences about the distributional properties of the failure times in a competing risks setting is presented. Efficiency is gained by observing recurrences of the competing risks over a random monitoring period. The resulting model is called the recurrent competing risks model (RCRM) and is coupled with two repair strategies whenever the system fails. Maximum likelihood estimators of the parameters of the marginal distribution functions associated with each of the competing risks and also of the system lifetime distribution function are presented. Estimators are derived under perfect and partial repair strategies. Consistency and asymptotic properties of the estimators are obtained. The estimation methods are applied to a data set of failures for cars under warranty. Simulation studies are used to ascertain the small sample properties and the efficiency gains of the resulting estimators.