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We develop transition probabilities for the various states of the infinite horizon problem and a solution algorithm for finding the best policy in polynomial time by finding a control limit on the sampling policy. We formulate a partially observable, discrete-time Markov decision process in order to obtain the near-optimal combined preventive maintenance/statistical process control policy that minimizes the costs associated with maintenance, sampling, and poor quality. In this paper, we extend the initial preliminary investigation of this idea of using an chart in conjunction with an age-replacement preventive maintenance policy.
Not until recently has the proposal been made to integrate these two fields and utilize the relationship between quality and equipment performance to improve the productivity of a manufacturing process. The economic design of control charts and the optimization of preventive maintenance policies have separately received a tremendous amount of attention in the quality and reliability literature over the years in an attempt to reduce the costs associated with operating manufacturing processes.
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