Optimal control limits for cumulative count of conforming charts in the presence of inspection errors

The control chart based on cumulative count of conforming (CCC) items between the occurrence of two non-conforming ones, or the CCC chart, has been shown to be very useful for monitoring high-quality processes. However, as in the implementation of other Shewhart-type control charts, it is usuallly assumed that the inspection is free of error. This assumption may not be valid and this may have a significant impact on the interpretation of the control chart and the setting of control limits. This paper first investigates the effect of inspection errors and discusses the setting of control limits in such cases. Even if inspection errors are considered, the average time to alarm increases in the beginning when the process deteriorates. Since this is undesirable, the control limits in the presence of inspection errors should be set so as to maximize the average run length when the process is at the normal level. A procedure is presented for solving this problem.