The optimal preventive-maintenance schedule for a production system consisting of N identical parallel production units is investigated. The lifetimes of the units are IFR-distributed, i.e. with an increasing failure rate, and are supposed to be statistically independent. The relevant costs are due to production losses, which are increasing and convex in the number of units that are out of operation simultaneously. Actual maintenance costs (either preventive or corrective) are supposed to be negligible as compared with the costs due to these production losses. First we consider the apparently trivial case of geometric (discrete-time) or exponential (continuous-time) lifetime distributions for the units. In this situation, preventive maintenance cannot improve the condition of a unit. Hence, apparently the only relevant policy is to do corrective maintenance on failed units. However, the analysis reveals that this conclusion is not correct. It turns out that taking non-failed units out of operation deliberately can be better than restricting to corrective maintenance only. We first show that, in the case of geometrically distributed lifetimes and unit repair times, the optimal preventive-maintenance policy is characterized by a single control limit K. Whenever the number of working units is less than or equal to K, no units are taken out of operation, while i – K units are set apart whenever i (> K) units are operational. Next we consider the case with exponentially distributed lifetimes and repair times. Moreover, we assume that the repair capacity is limited, in the sense that only s (⩽ N) units can be under repair simultaneously. We show that, also in this case, it can be optimal to take a working unit out of operation until the next decision epoch (which is either a failure epoch or a repair completion epoch). It is shown that the optimal policy has a weak monotonicity property: the number of units which remain in operation increases with the number of available units. However, it is not necessarily true that, under the optimal policy, the number of units in standby position increases with the number of available units. Numerical examples are presented which illustrate that, for a wide range of parameter values, the easiest policy (only perform corrective maintenance on failed units) performs rather well as compared with the overall optimal policy. Finally we consider the possible extension to the practically more interesting case of non-exponential lifetime distributions. In particular, we assume that the lifetimes are composed of two non-identical exponential phases. A unit in its first lifephase is called ‘good’, while a unit in its second phase is called ‘doubtful’. In this situation, one has the option to put a good or doubtful unit in standby position until the next decision epoch or to perform preventive maintenance on a doubtful unit. The latter brings a unit back from the doubtful into the good state. An indication is given of the problems that arise in generalizing the results obtained for the exponential case.
