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Stochastic manufacturing system with process deterioration and machine breakdown

This paper presents a realistic manufacturing inventory model with process deterioration and machine breakdown. In economic manufacturing quantity model, process usually starts with ‘in-control’ state and produces items of good quality. After some random point of time, process may deteriorate and shift to ‘out-of-control’ state due to occurrence of assignable cause. From that point, process produces some percentage of non-conforming items. Further process deterioration after machine shift may result in machine breakdown at any random time during the production period. If machine breakdown occurs during the production period, then corrective (emergency) repair is performed immediately otherwise preventive (regular) repair is performed at the end of production period. The proposed model is formulated assuming that the time required for production facility shifting from ‘in-control’ state to ‘out-of-control’ state, time when machine breaks down, corrective and preventive repairing time and demand of items follows probability distribution. We have derived analytically the optimal production time which minimises the total expected production cost annually for machine breakdown and no machine breakdown cases. The solution procedure is illustrated with the help of numerical examples for different probability distributions. Sensitivity of the optimal solution with respect to different parameters are also analysed.