A parameter-free adaptive EWMA chart with variable sample sizes and variable sampling intervals for the process mean. (English) Zbl 07572887
Summary: In this article, a parameter-free adaptive EWMA (AE) chart, which adopts the variable sample size (VSS), variable sampling interval (VSI) or both (VSSVSI) features, is developed to monitor the mean of a normal process. The simulation method is employed to compute the run-length profiles of the proposed VSS, VSI and VSSVSI based AE charts. The extra quadratic loss and integral relative average run-length/time-to-signal measures are used as a performance criterion in order to evaluate the sensitivities of the control charts. The run-length evaluation shows that the proposed VSS, VSI and VSSVSI based AE charts surpass the VSS, VSI and VSSVSI based EWMA charts, respectively, in detecting small mean shifts but the latter prevails in detecting moderate to large mean shifts. The proposed charts also outperform their fixed sampling rate based AE counterparts. An example is given to compare the implementation of the existing and proposed charts.
Keywords:
average run-length; control chart; EQL and IRARL; Monte Carlo simulation; process mean; statistical process controlReferences:
| [1] | Montgomery, DC., Introduction to statistical quality control (2009), New York: Wiley, New York · Zbl 1274.62015 |
| [2] | Reynolds, MR, Optimal variable sampling interval control charts, Seq Anal, 8, 4, 361-379 (1989) · Zbl 0712.62098 |
| [3] | Reynolds, MR; Amin, RW; Arnold, JC., CUSUM charts with variable sampling intervals, Technometrics, 32, 4, 371-384 (1990) · Zbl 0725.62092 |
| [4] | Luo, Y.; Li, Z.; Wang, Z., Adaptive CUSUM control chart with variable sampling intervals, Comput Stat Data Anal, 53, 7, 2693-2701 (2009) · Zbl 1453.62146 |
| [5] | Epprecht, EK; Simoes, BFT; Mendes, FCT., A variable sampling interval EWMA chart for attributes, Int J Adv Manuf Technol, 49, 1-4, 281-292 (2010) |
| [6] | Tang, A.; Castagliola, P.; Sun, J., An adaptive exponentially weighted moving average chart for the mean with variable sampling intervals, Qual Reliab Eng Int, 33, 8, 2023-2034 (2017) |
| [7] | Haq, A., Weighted adaptive multivariate CUSUM charts with variable sampling intervals, J Stat Comput Simul, 89, 3, 478-491 (2019) · Zbl 07193734 |
| [8] | Ayyoub, HN; Khoo, MBC; Saha, S., Variable sampling interval EWMA chart for multivariate coefficient of variation, Comm Statist Theory Methods, 1-22 (2020) |
| [9] | Haq, A.; Akhtar, S., Auxiliary information based maximum EWMA and DEWMA charts with variable sampling intervals for process mean and variance, Comm Statist Theory Methods, 1-22 (2020) |
| [10] | Katebi, M.; Khoo, MBC., Optimal economic statistical design of combined double sampling and variable sampling interval multivariate \(####\) control charts, J Stat Comput Simul, 91, 10, 2094-2115 (2021) · Zbl 07497068 |
| [11] | Annadi, HP; Keats, JB; Runger, GC, An adaptive sample size CUSUM control chart, Int J Prod Res, 33, 6, 1605-1616 (1995) · Zbl 0917.90157 |
| [12] | Zhou, W.; Lian, Z., Optimum design of a new VSS-NP chart with adjusting sampling inspection, Int J Prod Econ, 129, 1, 8-13 (2011) |
| [13] | Hu, X.; Castagliola, P.; Sun, J., The performance of variable sample size \(####\) chart with measurement errors, Qual Reliab Eng Int, 32, 3, 969-983 (2016) |
| [14] | Hassani, Z.; Amiri, A.; Castagliola, P., Variable sample size of exponentially weighted moving average chart with measurement errors, Sci Iran, 28, 4, 2386-2399 (2021) |
| [15] | Prabhu, SS; Montgomery, DC; Runger, GC., A combined adaptive sample size and sampling interval \(####\) control scheme, J Qual Technol, 26, 3, 164-176 (1994) |
| [16] | Costa, AFB., \(####\) chart with variable sample size and sampling intervals, J Qual Technol, 29, 2, 197-204 (1997) |
| [17] | Reynolds, MR; Arnold, JC., EWMA control charts with variable sample sizes and variable sampling intervals, IIE Trans, 33, 6, 511-530 (2001) |
| [18] | Arnold, JC; Reynolds, MR, CUSUM control charts with variable sample sizes and sampling intervals, J Qual Technol, 33, 1, 66-81 (2001) |
| [19] | Mahadik, SB., \(####\) charts with variable sample size, sampling interval, and warning limits, Qual Reliab Eng Int, 29, 4, 535-544 (2013) |
| [20] | Zhou, M., Variable sample size and variable sampling interval Shewhart control chart with estimated parameters, Oper Res, 17, 1, 17-37 (2017) |
| [21] | Saha, S.; Khoo, MBC; Lee, MH, A variable sample size and sampling interval control chart for monitoring the process mean using auxiliary information, Qual Technol Quant Manag, 16, 4, 389-406 (2019) |
| [22] | Khoo, MBC; See, MY; Chong, NL, An improved variable sample size and sampling interval s control chart, Qual Reliab Eng Int, 35, 1, 392-404 (2019) |
| [23] | Shojaie, M.; Imani, DM., Development of U control chart by variable sample size and sampling interval to improve the statistical properties, Eng Rep, 3, 6 (2021) |
| [24] | Capizzi, G.; Masarotto, G., An adaptive exponentially weighted moving average control chart, Technometrics, 45, 3, 199-207 (2003) |
| [25] | Haq, A.; Gulzar, R.; Khoo, MBC., An efficient adaptive EWMA control chart for monitoring the process mean, Qual Reliab Eng Int, 34, 4, 563-571 (2018) |
| [26] | Jiang, W.; Shu, L.; Apley, DW., Adaptive CUSUM procedures with EWMA-based shift estimators, IIE Trans, 40, 10, 992-1003 (2008) |
| [27] | Dai, Y.; Luo, Y.; Li, Z., A new adaptive CUSUM control chart for detecting the multivariate process mean, Qual Reliab Eng Int, 27, 7, 877-884 (2011) |
| [28] | Su, Y.; Shu, L.; Tsui, KL., Adaptive EWMA procedures for monitoring processes subject to linear drifts, Comput Stat Data Anal, 55, 10, 2819-2829 (2011) |
| [29] | Saleh, NA; Mahmoud, MA; Abdel-Salam, ASG., The performance of the adaptive exponentially weighted moving average control chart with estimated parameters, Qual Reliab Eng Int, 29, 4, 595-606 (2013) |
| [30] | Huang, W.; Shu, L.; Su, Y., An accurate evaluation of adaptive exponentially weighted moving average schemes, IIE Trans, 46, 5, 457-469 (2014) |
| [31] | Aly, AA; Mahmoud, MA; Hamed, R., The performance of the multivariate adaptive exponentially weighted moving average control chart with estimated parameters, Qual Reliab Eng Int, 32, 3, 957-967 (2016) |
| [32] | Tang, A.; Castagliola, P.; Sun, J., The effect of measurement errors on the adaptive EWMA chart, Qual Reliab Eng Int, 34, 4, 609-630 (2018) |
| [33] | Tang, A.; Castagliola, P.; Sun, J., Optimal design of the adaptive EWMA chart for the mean based on median run length and expected median run length, Qual Technol Quant Manag, 16, 4, 439-458 (2019) |
| [34] | Haq, A.; Khoo, MBC., A parameter-free adaptive EWMA mean chart, Qual Technol Quant Manag, 17, 5, 528-543 (2020) |
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