A New Approach to Maintenance Optimisation of Repairable Parallel Systems Subject to Hidden Failures

Maintenance policies are developed for decision-making about repair and maintenance of deteriorating parallel systems consisting identical components whose failures are detected only by inspections. Inspections at periodic times reveal the true state of components and preventive and corrective maintenance actions are carried out in response to the observed components state. The decision process is driven by the excursion of a state process regulated through an age reduction model. The modelling approach allows a wide class of models to be considered. Assuming a threshold-type policy, the article aims at minimising the long-run average maintenance cost per unit time by determining appropriate inspection intervals and a maintenance threshold. Using the renewal-reward theorem, the expected cost per cycle and expected cycle length emerge as solutions of equations, and a recursive scheme is devised to solve them. We illustrate the procedure for the case when the components' lifetime conforms to the Weibull distribution. Furthermore, a sensitivity analysis is performed to examine the effect of model's parameters. The unified structure developed allows different scenarios to be explored.