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The Pearson Residual‐Based Control Charts for Monitoring Overdispersed Count Sequences.

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Title: The Pearson Residual‐Based Control Charts for Monitoring Overdispersed Count Sequences.
Authors: Mou, Zhengcheng1 (AUTHOR), Chiang, Jyun‐You2 (AUTHOR), Tsai, Tzong‐Ru3 (AUTHOR) tzongru@gms.tku.edu.tw, Liu, Guojun1 (AUTHOR)
Source: Quality & Reliability Engineering International. Feb2026, Vol. 42 Issue 1, p461-477. 17p.
Subjects: Quality control charts, Log-linear models, Pearson correlation (Statistics), Scientific observation
Abstract: Most existing control charts are designed for positively autocorrelated count data and seldom address the issue of overdispersion. The log‐linear Poisson autoregression model (LLPAM) can capture overdispersion in count data, accommodate both positive and negative autocorrelations, and incorporate real‐valued covariates. This makes it a more flexible alternative to the standard Poisson model. However, Shewhart‐type charts applied to LLPAM often exhibit inflated false alarm rates and reduced sensitivity to parameter shifts under moderate temporal dependence. To address these limitations, we propose two monitoring schemes based on Pearson residuals (PRs): a Shewhart‐type chart and an exponentially weighted moving average (EWMA) chart. Both methods allow simultaneous monitoring of LLPAM parameters under positive or negative autocorrelation. Simulation studies show that the proposed PR‐based charts consistently outperform the observation‐based Shewhart chart in terms of average run length (ARL), standard deviation of run length (SDRL), median run length (MDRL), and relative mean index (RMI), while maintaining false alarm rates close to nominal levels. An application to Escherichia coli infection data from North Rhine–Westphalia further demonstrates the practical utility of the proposed control charts. [ABSTRACT FROM AUTHOR]
Copyright of Quality & Reliability Engineering International is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: <searchLink fieldCode="DE" term="%22Quality+control+charts%22">Quality control charts</searchLink><br /><searchLink fieldCode="DE" term="%22Log-linear+models%22">Log-linear models</searchLink><br /><searchLink fieldCode="DE" term="%22Pearson+correlation+%28Statistics%29%22">Pearson correlation (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+observation%22">Scientific observation</searchLink>
– Name: Abstract
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  Data: Most existing control charts are designed for positively autocorrelated count data and seldom address the issue of overdispersion. The log‐linear Poisson autoregression model (LLPAM) can capture overdispersion in count data, accommodate both positive and negative autocorrelations, and incorporate real‐valued covariates. This makes it a more flexible alternative to the standard Poisson model. However, Shewhart‐type charts applied to LLPAM often exhibit inflated false alarm rates and reduced sensitivity to parameter shifts under moderate temporal dependence. To address these limitations, we propose two monitoring schemes based on Pearson residuals (PRs): a Shewhart‐type chart and an exponentially weighted moving average (EWMA) chart. Both methods allow simultaneous monitoring of LLPAM parameters under positive or negative autocorrelation. Simulation studies show that the proposed PR‐based charts consistently outperform the observation‐based Shewhart chart in terms of average run length (ARL), standard deviation of run length (SDRL), median run length (MDRL), and relative mean index (RMI), while maintaining false alarm rates close to nominal levels. An application to Escherichia coli infection data from North Rhine–Westphalia further demonstrates the practical utility of the proposed control charts. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Quality & Reliability Engineering International is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/qre.70094
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      – Code: eng
        Text: English
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        PageCount: 17
        StartPage: 461
    Subjects:
      – SubjectFull: Quality control charts
        Type: general
      – SubjectFull: Log-linear models
        Type: general
      – SubjectFull: Pearson correlation (Statistics)
        Type: general
      – SubjectFull: Scientific observation
        Type: general
    Titles:
      – TitleFull: The Pearson Residual‐Based Control Charts for Monitoring Overdispersed Count Sequences.
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            NameFull: Mou, Zhengcheng
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            NameFull: Chiang, Jyun‐You
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            NameFull: Tsai, Tzong‐Ru
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            – D: 01
              M: 02
              Text: Feb2026
              Type: published
              Y: 2026
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