Scheduling preventive maintenance of oil pumps using generalised proportional intensities models

Percy and Alkali presented generalizations of the proportional intensities model introduced by Cox. They identified several features of these models that are particularly relevant for modelling complex repairable systems subject to preventive maintenance (PM). These include the baseline intensity, scaling factors and explanatory variables. We investigate these aspects in detail and apply the models to five sets of reliability data collected from the main pumps at oil refineries. We use likelihood methods to estimate the model parameters and compare how well the models fit the data. Our analyses suggest that a log-linear baseline intensity function performs well and that an exponential deterministic scaling function is useful for corrective maintenance. The inclusion of explanatory variables to represent the quality of last maintenance and time since last maintenance also proves to be beneficial. We develop algorithms for simulating the reliability behaviour of a complex repairable system into the future, in order to schedule appropriate maintenance activities, identifying special cases that simplify the algebra. Applying these methods to the oil pump data, we derive recommendations for PM plans and demonstrate that adopting this strategy can lead to substantial savings.