An improved self-starting cumulative count of conforming chart for monitoring high-quality processes under group inspection

The cumulative count of conforming (CCC) chart as a main statistical process control tool for monitoring high-quality processes has been widely studied. However, its applicability is limited to situations where units of product are inspected sequentially, or item by item. Motivated by real-life problems, this paper proposes an improved control charting technique for high-quality processes under group inspection. It integrates a self-starting feature and an approximately ARL- (average run length) unbiased design. The chart, named the CCCG chart, monitors the cumulative count of conforming samples until a non-conforming one is encountered. The ‘G’ in the subscript stands for ‘Group’. The self-starting feature caters to the need in practice to start monitoring a production process as soon as possible. The approximately ARL-unbiased design is developed to significantly improve the chart's sensitivity to process deterioration compared with the conventional design. The performance of the CCCG chart in phase I when the control limits are sequentially updated has been examined. Simulated data examples are presented to demonstrate the use and efficiency of the proposed technique. The CCCG chart is a natural generalisation of the traditional CCC chart and thus includes the latter as a special case.