Economic-Statistical Design of a Control Chart for High Yield Processes When the Inspection is Imperfect

CCC-r control chart is a monitoring technique for high yield processes. It is based on the analysis of the number of inspected items until observing a specific number of defective items.  One of the assumptions in implementing CCC-r chart that has a significant effect on the design of the control chart is that the inspection is perfect. However, in reality, due to the multiple reasons, the inspection is exposed to errors. In this paper, we study the economic-statistical design of CCC-r charts when the inspection is imperfect. Minimization of the average cost per produced item is considered as the objective function. The economic objective function, modified consumer risk, and modified producer risk are simultaneously considered, and then the optimal value of r parameter is selected.