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The increasing need and demand for automobiles has put production facilities in the automotive industries across the globe under a lot of pressure to increase productivity and customer satisfaction. Critical researches and reviews on the raw materials and extraction of manufacturing facilities play crucial roles in the day-to-day operations of the automotive industries in this direction. The selection of raw materials, preparation of product components, finishing, and inspection are the five main units that make up a production plant. The main goal of this study is to evaluate the four stages to control manufacturing process. The stages are Planning, Routing, Scheduling and Dispatching. The effectiveness of the of the stages in manufacturing systems is determined mathematically by evaluating each maintenance parameter using Gumbel Hougaard Family Copula method based on the mathematical modeling Markov birth–death approach (MBDA), and the equations of the system are derived by using the Chapman–Kolmogorov approaches. Besides, it also calculates the performance of certain maintenance parameters concerning time such as mean time to failures (MTTF), profit analysis and sensitivity analyses with the utilization of MAPLE software.
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