Estimating parameters of intensity function and maintenance effect for repairable unit

A data-analytic procedure for successive inter-failure times (IFT) of repairable units is investigated. Specifically, a method of data analysis for the estimation of parameters of the failure process and the maintenance effect for repairable units is proposed. Malikʹs proportional age reduction (PAR) model for imperfect maintenance is utilized. The PAR model is reformulated in terms of the properties of non-homogeneous Poisson processes (NHPP) with piecewise continuous intensity function. The joint distribution of the IFTʹs is also derived. Two parametric families of intensity functions are considered, power-law and log-linear. Maximum likelihood method is employed to estimate the maintenance effect and the intensity function simultaneously. Two models are considered; one with effective corrective maintenance (CM) without preventive maintenance (PM) and the other with effective PM with minimal CM. Simulation results are presented to illustrate the accuracy of the estimation and the properties of the models. An application example for a set of failure and maintenance data of a central cooler in a nuclear power plant is also presented.