effects of inspection errors on economically design of ccc-r control chart

Ccc-r chart extended approach of ccc charts, is a technique applied when nonconforming items are rarely observed. however, it is usually assumed that the inspection process is perfect in the implementation control charts imperfect inspections may have a significant impact on the performance of the control chart and setting the control limits. this paper first investigates the effect of inspection errors on the formulation of ccc-r chart, then an economic model is presented in the presence of inspection errors to design control chart so that the average cost per item minimized. the r parameter in the chart is optimized with respect to the economic objective function, modified consumer risk, and modified producer risk.