Maintenance Models for Stochastically Failing Equipment.
STANFORD UNIV CALIF DEPT OF STATISTICS
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Two maintenance models are developed for machines subject to two distinct modes of failure. In the single machine model, the equipment is inspected at discrete time intervals and classified according to its deterioration, positive states representing deterioration towards one mode of failure and negative states towards the other. Transition among states of deterioration is governed by a Markov chain. At each inspection there is the option of replacing the machine at a cost dependent upon the state of the equipment. If no replacement is made, an operating cost, also state dependent, is charged. Sufficient conditions on the Markov chain and the replacement and operating costs are developed which guarantee that the optimal maintenance policy minimizing total discounted and long run average costs is a control limit replacement rule replace the machine if and only if its state is higher than a designated positive state or lower than a designated negative state. Characterization of the optimal policy allows for efficient computation through linear programming. A parametric linear programming analysis indicates how the policy varies with different costs. Modified author abstract
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems