Statistical process control (SPC) is a quality control method that enables the monitoring of processes using statistical methodologies. Nonparametric control charts, including the Tukey control chart (TCC), are a robust and effective instrument to assess a method since the actual distribution of the quality characteristic in question is indeterminate. The extended exponentially weighted moving average (EEWMA) control chart was employed to monitor the mean process because of its rapid detection of shifts. To maximize the benefits of both control charts, we developed a method known as EEWMA-TCC, which combines EEWMA with TCC. The efficacy of the proposed chart was evaluated under symmetrical distribution using various individual and aggregate performance metrics based on average run length (ARL) and percentage reduction in ARL (PDARL). Our findings indicated that the suggested chart outperforms control charts, including the TCC chart, the EWMA chart, the EEWMA chart, and the EWMA-TCC (mixed exponentially weighted moving average-Tukey) chart, in the quick identification of shifts. An application of the proposed designs in the crucial dimension of machined part data is demonstrated. The results indicated that they were consistent with the research findings. On the other hand, nonparametric control charts provide an alternate way to track the mean process.
Citation: Khanittha Talordphop, Yupaporn Areepong, Saowanit Sukparungsee. An empirical assessment of Tukey combined extended exponentially weighted moving average control chart[J]. AIMS Mathematics, 2025, 10(2): 3945-3960. doi: 10.3934/math.2025184
Statistical process control (SPC) is a quality control method that enables the monitoring of processes using statistical methodologies. Nonparametric control charts, including the Tukey control chart (TCC), are a robust and effective instrument to assess a method since the actual distribution of the quality characteristic in question is indeterminate. The extended exponentially weighted moving average (EEWMA) control chart was employed to monitor the mean process because of its rapid detection of shifts. To maximize the benefits of both control charts, we developed a method known as EEWMA-TCC, which combines EEWMA with TCC. The efficacy of the proposed chart was evaluated under symmetrical distribution using various individual and aggregate performance metrics based on average run length (ARL) and percentage reduction in ARL (PDARL). Our findings indicated that the suggested chart outperforms control charts, including the TCC chart, the EWMA chart, the EEWMA chart, and the EWMA-TCC (mixed exponentially weighted moving average-Tukey) chart, in the quick identification of shifts. An application of the proposed designs in the crucial dimension of machined part data is demonstrated. The results indicated that they were consistent with the research findings. On the other hand, nonparametric control charts provide an alternate way to track the mean process.
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Khanittha Talordphop, Yupaporn Areepong, Saowanit Sukparungsee. An empirical assessment of Tukey combined extended exponentially weighted moving average control chart[J]. AIMS Mathematics, 2025, 10(2): 3945-3960. doi: 10.3934/math.2025184
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