A modelling approach to optimal imperfect maintenance of repairable equipment with multiple failure modes

Most of the existing works on optimal imperfect maintenance activities of a repairable equipment with independent components consider a single model for equipment behaviour. In addition, it is assumed that all the components of the equipment share the same model and the same maintenance intervals and that effectiveness of maintenance is known. In this paper we take a different approach. In order to formalize the uncertainty on the occurrence of failures and on the effect of maintenance activities, we consider, for each component, a class of candidate models. These models are obtained by combining failure rate models with imperfect maintenance models. The best model, that might be different for the different components, is then selected. All the parameters are assumed to be unknown and are jointly estimated via maximum likelihood. Model selection is performed, separately for each component, using standard selection criteria that take the problem of over-parametrization into account. The selected models are used to derive the cost per time unit and the average reliability of the equipment, the objective functions of a Multi-Objective Optimization Problem with maintenance intervals of each single component as decision variables. The proposed procedure is illustrated using a real data example.