Nonparametric estimation and bootstrap confidence intervals for the optimal maintenance time of a repairable system

Consider a repairable system operating under a maintenance strategy that calls for complete preventive repair actions at pre-scheduled times and minimal repair actions whenever a failure occurs. Under minimal repair, the failures are assumed to follow a nonhomogeneous Poisson process with an increasing intensity function. This paper departs from the usual power-law-process parametric approach by using the constrained nonparametric maximum likelihood estimate of the intensity function to estimate the optimum preventive maintenance policy. Several strategies to bootstrap the failure times and construct confidence intervals for the optimal maintenance periodicity are presented and discussed. The methodology is applied to a real data set concerning the failure histories of a set of power transformers.