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International Society of Science and Applied Technologies |
| An Enhanced Cumulative Quantity Control Chart Based on Asymmetric Runs Rules | ||||
| Author |
Pei Wen Chen
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| Abstract | The cumulative quantity control (CQC) chart is a statistical process control tool designed for monitoring highquality processes, particularly those with very low defect rates. Unlike traditional control charts that track defect counts or proportions over fixed sample sizes, the CQC chart accumulates production quantities until a defective item is observed. This approach allows for more efficient monitoring in processes where defect rates are rare. Its applications extend beyond manufacturing, such as microchip production, circuit board assembly, and other precision manufacturing processes with extremely low defect rates. In non-manufacturing sectors, it tracks the occurrence of errors in transaction processing or monitors defective drug batches. Improving the sensitivity of control charts remains a key focus in statistical process control research. Most existing studies concentrate rely on symmetric runs rules which apply identical decision criteria to both sides of the control limits. However, symmetric rules do not offer balanced detection performance for the CQC chart due to the asymmetric nature of the statistics. This imbalance can result in improved detection on one side while severely limiting the effectiveness on the other. In this study, a one-sided m-of-k rule is applied to establish the lower control limit of the CQC chart, while retaining the original upper control limit. A Markov chain model is developed to assess the effectiveness of control charts incorporating various runs rules. The results demonstrate that the one-sided m-of-k rule scheme not only overcomes the limitations of current methods for monitoring high-yield production, but also enhances sensitivity in detecting increases in the defect rate.
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| Keywords | CQC chart, runs rules, high-yield, Markov chain | |||
| Article #: RQD2025-72 | ||||
Proceedings of 30th ISSAT International Conference on Reliability & Quality in Design |