~ W ~ . = - , .-,-,Vr,.~tr.~uq ELSEVIER European Journal of Operational Research 99 (1997) 565-583 EUROPEAN JOURNAL OF OPERATIONAL RESEARCH Preventive maintenance in a 1 out of n system: The uptime, downtime and costs M.A.J. Smith a'b'*, R. Dekker a a Erasmus University Rotterdam, Econometric Institute, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands b TNO Physics and Electronic Laboratory, The Hague, The Netherlands Abstract In repairable systems with redundancy, failed units can be replaced by spare units in order to reduce the system downtime. The failed units are sent to a repair shop or manufacturer for corrective maintenance and subsequently are returned for re-use. In this paper we consider a 1 out of n system with cold standby and we assume that repaired units are "as good as new". When a unit has an increasing failure rate it can be advantageous to perform preventive maintenance in order to return it to its "as good as new" state, because preventive maintenance will take less time and tends to be cheaper. In the model we present we use age-replacement; a machine is taken out for preventive maintenance and replaced by a standby one if its age has reached a certain value, Tpm. In this paper we derive an approximation scheme to compute the expected uptime, the expected downtime and the expected costs per time unit of the system, given the total number of units and the age-replacement value, Tpm. Consequently the number of units and the value Tpm can be determined for maximum long-term economy. © 1997 Elsevier Science B.V. Keywords: Reliability; Maintenance; Replacement; Optimisation I. Introduction A 1 out of n system with cold standby is a system that consists of n units of which one has to operate. When the operating machine fails, one of the other (n - 1) machines is put into operation. Cold standby means that the redundant machines cannot fail while they are waiting. One encounters this type of system often in situations where a high reliability is necessary. This is the case for example in the process industry, power generating companies and with airline companies. Here we see large systems that consist of serial and parallel chains of subsystems, with expensive units like turbines, motors, pumps etc. The failure of a subsystem can cause an expensive downtime of the whole system. In order to reduce the downtime redundancy is necessary. Note that the idea of a 1 out of n system is also applicable to replaceable components or exchangeables. * Corresponding author. 0377-2217/97/$17.00 (~) 1997 Elsevier Science B.V. All fights reserved. PII S0377-2217(96) 00321-9