Détermination de la périodicité optimale pour le remplacement préventif

Abstract

The complexity of the phenomena of failures leads us to seek means of improving the strategies and the policies of maintenance to make it possible the equipment to adequately fulfill the functions for which they were conceived. The theory of reliability in engineering plays a very important part in the maintenance of such equipment. Thus, the mathematical methods of preventive maintenance were developed mainly in the field of research in order to generate programs of effective preventive maintenance. The most important problem in the mathematical methods of maintenance is to conceive maintenance planned with two options of maintenance: preventive replacement and corrective replacement. In the case of the preventive replacement, the system or apparatus is replaced by new before it breaks down. Whereas, in the case of a corrective replacement it is the unit or the failing part which is replaced. The determination of the optimal periodicity for the replacement of machine elements, components, modules or subsets always poses an economic problem and of profitability, especially when the installations are similar or the machines are identical. This economic problem can be solved by the knowledge of the operational reliability and the determination of the most advantageous moment to carry out this operation of preventive replacement. The optimal periodicity for the preventive replacement can be obtained according to two mathematical models: the model of replacement per block and the model of replacement based on the age. Each model can give place to several alternatives. In this work we studied analytically and numerically two simplified models of preventive replacement namely: the replacement by block, i.e. we supposed that between two preventive replacements, it can break down only one there, that is the case more running in practice; The replacement based on the age, i.e. the age of each part is known and one changes the part as soon as its age reaches this value. The principle consists in calculating the average total costs by part and unit of time, to seek its minimum and to take the period corresponding to this minimum like optimal period to carry out the preventive maintenance. This cost is composed of the cost of preventive maintenance and that of the balanced corrective maintenance of the probability of vi failures. An analytical study carried out in the case of a law of Weibull, made it possible to solve the resulting differential equations under certain mathematical conditions. Then these equations are solved numerically for the various parameters of this problem which are the maintenance costs ratio, the shape parameter and the scale parameter. The results obtained were analyzed and discussed; their applications to cases real can provide to the service maintenance a key element to choose the most suitable period to carry out the preventive maintenance at the minimum cost.