OPTIMAL MAINTENANCE POLICIES FOR MACHINES SUBJECT TO DETERIORATION AND RANDOM BREAK DOWN

Abstract

This dissertation develops mathematical models and derives optimal maintenance policies for machines,engaged in revenue earning processes, subject to physical deterior ation, random breakdowns and subsequent repairs. Maintenance policies are derived for a single machine and also for a group of identical machines. The earlier investigators have confined themselves in obtaining the PM policies which find little relevance to the needs of modern industrial systems. These policies require a non-stop maintenance throughout, or through a major part of the machine's useful life. Evidently, this is seldom feasible as it involves constant interference in the production continuity and necessitates extra expenditure on other items such as permanent repair crew, a large inventory throughout machine's operating life, etc. This practical difficulty is overcome by developing periodic PM policies. The second chapter of this work contains the development of the maintenance models for the derivation of the resultant periodic PM policies. By adopting these policies, the PM is executed for a short time causing no interference with the production continuity. The PM poli cies are derived for a single machine as well as for a group of identical machines. The work herein is extended and brought very close to -li the practical situation by deriving an optimal periodic PM policy for a machine having a constant rate of incomerate degradation despite restorative maintenance activity. The result of the derivation is then applied to a real life problem of a mining equipment where it is shown that the PM policy provided by this investigation is more purpose ful than that furnished by other researchers. Development of all models and the derivation of optimal periodic PM policies are followed by illustrative examples. Now, the derivation of the optimal periodic PM policies requires the down-time of the machine to be negligible in comparison to the unit of time used for computation of the income-rate which is the state variable in all these models. This assumption remains valid for most of the machines which are employed by either mass production processes or by public-service utilities. However, there are certain machines, for example a generating unit in a power plant, for which the downtime is quite appreciable and which require an increasing maintenance expenditure during their operating time. The maintenance analysis of such machines can better be performed by forming a discrete-time (and probabilistic) model as compared to the continuous time models of the second chapter. Therefore the semi-Markov decision process formulation is used in the next chapter of this work to develop amaintenance (during operation) and -111- repair/overhaul model. The machine maintenance and repair/ overhaul problem, under this technique, is formulated as a two-state semi-Markov process, i.e. the operating state and the repair or overhaul state. The machine is liable to fail during operation. It then makes a transition to the repair state. Otherwise, due to increasing maintenance cost, it becomes imperative to overhaul the machine even before its failure. At the end of the repair or overhaul, the machine becomes 'as good as new' and reverts back to the operating state. Thus this process also is periodic. Finally, two partial differential equation models of graduation degradation of the income-rate of a machine subject to deterioration are developed. The partial differential equation formulation of a physical system provides a much greater insight into overall behaviour of the system. In the field of maintenance engineering so far, however, no partial differential equation models exist or have been formulated. Therefore, the opportunity in this work is uti lized to develop these models so as to study the behaviour of a machine, with respect to maintenance, overtime and subject to a spatial variable (deterioration in the present case) and hence to derive optimal PM policy. The deterioration has been considered deterministic, as also stochastic thus broadening the scope of the models.