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

Abstract

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 CCC_G 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 CCC_G 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 CCC_G chart is a natural generalisation of the traditional CCC chart and thus includes the latter as a special case.

Keywords:

• ARL-unbiased
• control chart
• cumulative conformance count
• high-quality process
• self-starting

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions that have resulted in an improved article. This work is supported by the National Natural Science Foundation of China under Grant No. 71102158.