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Abstract
Deterioration problem is due to a decrease in engine performance the machine used constantly. Deterioration of the engine can cause production system problem. In this research, the development of optimization models taking into account the production and quality cost component in the multistage production system. All products will undergo inspection by sampling or census. Good product after sampling inspection will be delivered to the consumer, while the nonconforming product will be inspected prior to the census carried out rework. Dynamic programming used to optimize the decision-making process over the entire stage which was later named the optimal policy
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