Modelling of dependence between critical failure and preventive maintenance: The repair alert model

Abstract

We consider the competing risks problem for a repairable unit which at each sojourn may be subject to either a critical failure, or a preventive maintenance (PM) action, where the latter will prevent the failure. It is reasonable to expect a dependence between the failure mechanism and the PM regime. The paper presents a new model, called the repair alert model, for handling such cases. This model is a special case of random signs censoring, which was introduced by Roger Cooke [1993. The total time on test statistic and age-dependent censoring. Statist. Probab. Lett., 18, 307–312]. The pleasant feature of random signs censoring is that the marginal distribution of the failure time is identifiable. The repair alert model introduces the so-called repair alert function, which characterizes the “alertness” of the maintenance crew, and which is shown to be uniquely identifiable from field data. Statistical estimation is considered both nonparametrically and parametrically.