Generalized proportional intensities models for repairable systems

Based upon the non-homogeneous Poisson process as recommended by Ascher & Feingold (1984), we investigate suitable models for describing the inter-failure times of complex repairable systems. Specifically, we modify and develop the proportional intensities model (PIM) introduced by Cox (1972b) for this purpose. We illustrate the suitability of these models on hypothetical data taken from the first of these two books. Having identified potential benefits from this approach, we extend the PIM to introduce a new class of generalized proportional intensities models (GPIM), which allow for the inclusion of preventive maintenance (PM) and predictor variables. We discuss the properties and variations of GPIM and comment on similarities and differences between these and other proposed models for complex repairable systems. We also demonstrate the application of simple GPIM to a published data set that was collected from the petroleum industry, using the programming language Fortran and the mathematical software Mathcad. Finally, we consider how the analysis can be improved and extended for scheduling PM actions in practice.