In the recent trends, production plants in the automobile industries all over the world are facing a lot of challenges to achieve better productivity and customer satisfaction due to increasing the passenger’s necessity and demand for transportation. In this direction, the belt, tyre, and tube manufacturing plants act as vital roles in the day-to-day life of the automobile industries. Tyre production plant comprises five major units, namely, raw material selection, preparation, tyre components, finishing, and inspection. The main purpose of this research is to implement the new method to predict the most critical subsystems in the tyre manufacturing system of the rubber industry. As mathematically, any one maintenance parameter among reliability, availability, maintainability, and dependability (RAMD) parameters is evaluated to identify the critical subsystems and their effect on the effectiveness of the tyre production system. In this research, the effect of variation in maintenance indices, RAMD, is measured to identify the critical subsystem of the tyre production system based on the mathematical modeling Markov birth-death approach (MBDA), and the equations of the subsystems are derived by using the Chapman–Kolmogorov method. Besides, it also calculates the performance of certain maintenance parameters concerning time such as mean time between failures (MTBF), mean time to repair (MTTR), and dependability ratio for each subsystem of the tyre production system. Finally, RAMD analysis of the tyre production systems has been executed for predicting the most critical subsystem by changing the rates of failure and repair of individual subsystems with the utilization of MATLAB software. RAMD analysis reveals that the subsystem bias cutting is most critical with the minimum availability of 0.8387, dependability 5.19, dependability ratio 0.8701, and maximum MTTR 38.46 hours of the subsystem. In this implementation of the proposed method, a real-time case study of the industrial repairable system of tyre manufacturing system has been taken for evaluating RAMD indices of the production plant of rubber industry cited in the southern region of Tamil Nadu, India.