A delay-time model for repairable machinery: Maximum likelihood estimation of optimum inspection intervals

A delay-time model is presented for a complex repairable system in which defects arise according to a nonhomogeneous Poisson process. The focus of this paper is not on the resulting probabilistic model itself, but on the estimation of the model parameters and their errors from records of failure times and number of defects found at inspections of a machine which has been operated for some time under some (usually suboptimal) inspection regime. The likelihood function of the observed failure and inspection data is derived, and a general approach for estimating the optimum inspection interval is discussed. An example relating to the maintenance of medical equipment is used to illustrate the techniques described in the paper.