Article
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A New EWMA Control Chart for Monitoring Multinomial Proportions
Version 1
: Received: 6 June 2023 / Approved: 6 June 2023 / Online: 6 June 2023 (07:45:37 CEST)
A peer-reviewed article of this Preprint also exists.
Gan, S.; Yang, S.-F.; Chen, L.-P. A New EWMA Control Chart for Monitoring Multinomial Proportions. Sustainability 2023, 15, 11797. Gan, S.; Yang, S.-F.; Chen, L.-P. A New EWMA Control Chart for Monitoring Multinomial Proportions. Sustainability 2023, 15, 11797.
Abstract
Control charts have been widely used for monitoring process quality in manufacturing and play an important role in triggering a signal in time when detecting a change in process quality. Many control charts in literature assume that the in-control distribution of the univariate or multivariate process data is continuous and not categorical. This research develops two exponentially weighted moving average (EWMA) proportion control charts for monitoring a process with multinomial proportions when considering both large and small sample sizes. For a large sample size , the charting statistic depends on the well-known Pearson χ2 statistic, and the control limit of the EWMA proportion chart is determined by an asymptotical chi-square distribution. For a small sample size, we derive the exact mean and variance of the Pearson χ2 statistic. Hence, the exact EWMA proportion chart is determined. The proportion chart can also be applied to monitor the distribution-free continuous multivariate process as long as each categorical proportion associated with specification limits of each quality variable is known or estimated. Lastly, we investigate the detection performance of the proposed EWMA proportion chart by numerical analyses. Real data analysis demonstrates the beneficial application of the proposed EWMA proportion charts.
Keywords
Control chart; Multinomial distribution; specification limits; Pearson χ^(2 )statistic
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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