Optimal production, maintenance, and warranty strategies for item sold with rebate combination warranty

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In this paper, a decision model is developed for an imperfect production system in which the demand for a product is assumed to be influenced by the warranty period offered to the customer. The production process may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time at which point non-conforming items are produced. To assess the state of the production process, periodic inspections are carried out during each production run. At the time of inspection, if the process is found to be in the ‘out-of-control’ state then restoration is done; otherwise, preventive maintenance is performed. The proposed model is formulated under a general process shift distribution and a rebate combination warranty. The expected cost per unit item is taken as the criterion for optimality. Some analytical results of the model are derived with restrictions. The optimal decisions (i.e. the optimal number of inspections, the optimal production time, and the optimal warranty period offered to the customer) are obtained numerically and the sensitivity of some model parameters is examined in a numerical example.