An economic-statistical model for production and maintenance planning under adaptive non-central chi-square control chart

Most of the inventory control models assume that quality defect never happens, which means production process is perfect. However, in real manufacturing processes, the production process starts its operation in the in-control state; but after a period of time, shifts to the out-of-control state because of occurrence of some disturbances. In this paper, in order to approach the model to real manufacturing conditions, a process is considered in which quality defect and machine deterioration may occur. Since the adaptive control charts detect the occurrence of assignable cause quicker than the traditional control charts, an adaptive non-central chi-square control chart is designed, which monitors the process mean and variance, simultaneously. In addition, to reduce the failure rate of the machine, two types of maintenance policies consisting of reactive and preventive are planned. Then, the particle swarm optimization algorithm is employed to minimize the overall cost per cycle involving inventory cost, quality loss cost, inspection cost and maintenance cost subject to statistical quality constraints. Finally, to demonstrate the effectiveness of the suggested approach, two comparative studies are presented. The first one confirms that integration of production planning, maintenance policy and statistical process monitoring leads to a significant increase in the cost savings. The second one indicates superiority of the developed adaptive control chart in comparison with the control chart with the fixed parameters.