Optimal preventive and corrective maintenance for equipment with Erlangian life‐time distribution

We consider the case of important systems located on operational sites far away from logistic support forces, either because the operational site is in an inhospitality place, or because it is not profitable to maintain a dedicated team on the operational site. Due to the importance of the systems, some service level agreement has been signed, including conditional financial clauses. To take into account such a situation, a preventive maintenance is realised according to projected calendars. This paper shows that, given that the life‐times of equipments are supposed to be Erlang‐k distributed, it is optimal to realise a preventive maintenance, as long as the ratio of the two intervention costs Cp/Cc is lower than the ratio (k − 1) /k; Cp being the cost of a preventive maintenance intervention and Cc being the cost of a curative maintenance intervention (because of excessive delay, there is a significant penalty associated with each curative maintenance intervention). The methodology to compute the optimal value of the period T^* and the corresponding optimal cost per time unit are presented, for a given value of the ratio Cp/Cc.