Cumulative conformance count chart with variable sampling intervals and control limits

The cumulative conformance count (CCC) chart has been used for monitoring processes with very low fraction of nonconforming items. Typically, the items produced from the process were examined using 100% inspection for generating the CCC chart. However, this would be costly when taking the inspection cost and time into consideration and thus limit its application. Instead of inspecting the items one by one, this study takes sample from them, and regards the time between two successive samples as the sampling interval. In order to increase the sensitivity of the CCC chart to process change, the sampling interval and control limits are allowed to vary in this study. The average time to signal process change of the modified CCC chart (called the variable sampling interval and control limit (VSI/VCL) CCC chart) is derived by the Markov chain approach and taken as the performance measure to evaluate its statistical efficiency. With some minor changes, this chart can be reduced to the VSI CCC chart, the VCL CCC chart, and the standard CCC chart. In addition, comparisons among them are made and discussed. Copyright (C) 2010 John Wiley & Sons, Ltd.