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A dynamic programming approach to maintenance: Inspection models for a single machine under stochastic deterioration

Sanford Cohn, University of Massachusetts Amherst


Consider a single machine that produces N items each period. This machine which deteriorates over time needs occasional maintenance to restore it to its "new" condition. Our only indication that such deterioration has occurred is an increase in the incidence of defective items produced by the machine. The more periods that pass without maintenance, the higher the chances that the machine has deteriorated and will start producing more inferior items.^ We suppose that in the beginning of each period, the decision maker has three options: (1) To let the machine produce during that period without interfering with its production or inspecting it. (2) To inspect n items produced that period. If the inspected items are bad, maintenance is done at the end of the period on the machine to restore its "new" condition before the start of the next period. (3) To automatically do a maintenance on the machine at the start of the period without inspecting any of the items or doing any production.^ This choice must be made taking into account: (a) The machine deterioration rate, (b) The type of inspection that can be done and (c) The costs involved, e.g. inspection, maintenance, bad items produced, lost revenues, etc.^ Our thesis considers two different finite time horizon discounted dynamic programming models that can be used to optimally choose the correct option each period. The first model assumes that any inspection data obtained in a given period is only used in that period. The second model assumes that a single summary statistic of all past and present data is kept, and employed in making the decision.^ For both models, we proved the existence of a set of sufficient conditions based exclusively on input data that assure that the optimal policy has a special simple structure. In the first model, the optimal policy indicates that it is optimal to do nothing for the first few periods since the last maintenance, inspect before making a decision for the next few period, and if no maintenance is chosen in those periods, then automatically maintain in the following period. This structure is called a three tier policy.^ The second model's special structure says that for any given summary statistics, the optimal policy also has a three tier structure. In addition, for any given period, the optimal policy is to do nothing for the "best" summary statistics, inspect for the "next best" summary statistics and automatically maintain for the worst summary statistics. ^

Subject Area

Industrial engineering|Operations research

Recommended Citation

Cohn, Sanford, "A dynamic programming approach to maintenance: Inspection models for a single machine under stochastic deterioration" (1995). Doctoral Dissertations Available from Proquest. AAI9606498.