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This article presents a study with the aim of optimizing a production system, consisting of a machine that produces a single type of parts, that degrades over time. This degradation affects the availability of the deployed machine and increases the defective rate of the manufactured products. The machine is subject to random failures and repairs. It has a defective rate which increases with its degradation. An overhaul of the machine allows to reduce this defective rate and bring it back to its initial condition. The objective of this study is to find a joint policy for production, maintenance and quality control, in order to increase the availability of the machine, improve the quality of the manufactured products and minimize the total cost of production. To achieve this goal, we formulated the research problem and used a stochastic dynamic programming approach to develop the Hamilton-Jacobi-Bellman (HJB) type optimum conditions. Then, we simulated a practical hybrid application to optimize the production of a Router class R CNC cutting machine that transforms polypropylene sheets in a Quebec (Canada) company specialized in the production of fire pumps. The obtained results allowed us to propose a critical threshold production policy, corrective and preventive maintenance strategies, and a sampling type of quality control to the company. Finally, we performed a sensitivity analysis to ensure the validation of the proposed policies. [ABSTRACT FROM AUTHOR]