Hybrid intensity models for repairable systems

In recent years, several authors have proposed mathematical models for complex repairable systems, extending the common assumptions of minimal repairs and renewals. These models all have weaknesses but we believe that modifications of existing models offer flexible analyses with realistic physical interpretations, enabling us to model the effects of replacements, repairs, preventive maintenance and inspections. These modifications correspond with specific types of superposed renewal processes and bear some resemblance to proportional intensities models, both described by Cox in 1962 and 1972, respectively. We discuss the properties and interpretations of these variants, explaining why we consider them particularly suited to modelling the effects of typical maintenance interventions. Finally, we illustrate an application of these models to repairable systems of five oil pumps, for which maintenance data were recently published, and demonstrate comparable performance with improved robustness.