Application of a semi-Markov model and a simulated annealing algorithm for the selection of an optimal maintenance policy M. STOPCZYK, B. SAKOWICZ, G.J. ANDERS, Fellow IEEE Department of Microelectronics and Computer Science, Technical University of Lodz, al. Politechniki 11, 90-924 Lodz, POLAND, e-mail: stopczyk@dmcs.pl Abstract—This paper describes maintenance policy model based on semi-Markov processes. Optimal policy is found by means of multiobjective optimization and modified simulated annealing algorithm with a Tabu List. The procedure is demonstrated on a practical example involving finding an optimal maintenance policy for a devices that is subjected to frequent minimal repairs and occasionally to a major overhaul. I. INTRODUCTION The ability to optimally choose maintenance policy of a device (planning inspections and repairs) is very important for every enterprise. Knowing the deterioration stage of equipment (or even better – the remaining lifetime) the person responsible for a device can make a decision concerning further exploitation, repair of individual elements or replacement with new ones. Unfortunately, estimation of remaining life is a very difficult task. The common solution is to hire an expert who in a subjective way defines the level of the deterioration and suggests further work. Due to the fact that wrong expertise can be very easily verified (mainly when the device fails) it is a common practice to recommend the replacement or major overhaul of most components (lots of them unnecessary), which results in an increased utilization costs of the equipment. An obvious conclusion from the above reasoning is that in order to avoid unnecessary additional costs one should use other techniques that enable estimation of the remaining lifetime. Remaining lifetime of a device depends to a large extent on two factors – frequency of making inspections (technical surveys) and quality of repairs (for given part of device only most crucial and necessary repairs can be made or complete overhaul can be provided). Defining both, times when the inspections should be performed and which components should be repaired, are difficult tasks. One should remember that when inspection takes place, the equipment is temporarily unavailable (that results in additional costs). As a result, utilization costs can be overestimated due to the fact that inspections are made too frequently [1]. This paper proposes a new mathematical model for the selection of an optimal maintenance policy. The original model proposed in [2] presented the method of calculation of the remaining life of the equipment. This paper defines several possible optimization procedures to find out the best maintenance policy and demonstrates an implementation of the simulating annealing algorithm for this purpose. In order to speedup the calculation process, it is proposed to include some elements of a Tabu search optimization procedure in the simulating annealing approach. The whole procedure is illustrated on a practical numerical example. The paper is organized as follows. The maintenance model is reviewed in Sections II and III. The optimization problem is defined in Sections IV to VII followed by a numerical example in Section VIII. Concluding remarks are given at the end of the paper. II. PROPOSED MODEL In most cases for every device one can distinguish four states of deterioration: (like)new (D1) minor deterioration (D2) major deterioration (D3) failure (F) The proposed analytical approach to the problem assumes that if left without any control or supervision, device will reach every state and end up in failure. To avoid this situation periodically inspections should be made and necessary repairs should be performed. After a repair the device can move to a “better” deterioration state. Inspections can be made when device is in states D1, D2 or D3. After reaching state F, only general repair can be performed and we will assume that it will cause the device to be in the D1 state again. In the proposed model inspections are marked with letters I1, I2 and I3.