Residual‐based CUSUM beta regression control chart for monitoring double‐bounded processes

This paper proposes a control chart useful for detecting small shifts in the mean of a double‐bounded process, such as fractions and proportions, in the presence of control variables. For this purpose, we consider the cumulative sum (CUSUM) control chart applied to different residuals of the beta re...

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Bibliographic Details
Published inQuality and reliability engineering international Vol. 38; no. 6; pp. 3252 - 3269
Main Authors Rauber, Cristine, Lima‐Filho, Luiz M. A., Bayer, Fábio M.
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 01.10.2022
Subjects
beta regression
control chart
Control charts
cumulative sum
CUSUM charts
Regression models
residuals
run length
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Summary:This paper proposes a control chart useful for detecting small shifts in the mean of a double‐bounded process, such as fractions and proportions, in the presence of control variables. For this purpose, we consider the cumulative sum (CUSUM) control chart applied to different residuals of the beta regression model. We conduct an extensive Monte Carlo simulation study to evaluate and compare the performance of the proposed control chart with two other control charts in the literature in terms of run length analysis. The numerical results show that the proposed control chart is more sensitive to detect changes in the process than its competitors and that the quantile residual is the most suitable residual to be used in our proposal. Finally, based on the quantile residual, we present and discuss applications to real and simulated data to show the applicability of the proposed control chart.
ISSN:0748-8017
1099-1638
DOI:10.1002/qre.3140