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Process monitoring using inflated beta regression control chart

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  • Luiz M A Lima-Filho
  • Tarciana Liberal Pereira
  • Tatiene C Souza
  • Fábio M Bayer

Abstract

This paper provides a general framework for controlling quality characteristics related to control variables and limited to the intervals (0, 1], [0, 1), or [0, 1]. The proposed control chart is based on the inflated beta regression model considering a reparametrization of the inflated beta distribution indexed by the response mean, which is useful for modeling fractions and proportions. The contribution of the paper is twofold. First, we extend the inflated beta regression model by allowing a regression structure for the precision parameter. We also present closed-form expressions for the score vector and Fisher’s information matrix. Second, based on the proposed regression model, we introduce a new model-based control chart. The control limits are obtained considering the estimates of the inflated beta regression model parameters. We conduct a Monte Carlo simulation study to evaluate the performance of the proposed regression model estimators, and the performance of the proposed control chart is evaluated in terms of run length distribution. Finally, we present and discuss an empirical application to show the applicability of the proposed regression control chart.

Suggested Citation

  • Luiz M A Lima-Filho & Tarciana Liberal Pereira & Tatiene C Souza & Fábio M Bayer, 2020. "Process monitoring using inflated beta regression control chart," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-20, July.
    • Handle: RePEc:plo:pone00:0236756
    DOI: 10.1371/journal.pone.0236756
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    References listed on IDEAS

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    3. Christian Paroissin & Laura Penalva & Agnès Pétrau & Ghislain Verdier, 2016. "New control chart for monitoring and classification of environmental data," Environmetrics, John Wiley & Sons, Ltd., vol. 27(3), pages 182-193, May.
    4. Huwang, Longcheen & Huang, Chun-Jung & Wang, Yi-Hua Tina, 2010. "New EWMA control charts for monitoring process dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2328-2342, October.
    5. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    6. Teyarachakul, Sunantha & Chand, Suresh & Tang, Jen, 2007. "Estimating the limits for statistical process control charts: A direct method improving upon the bootstrap," European Journal of Operational Research, Elsevier, vol. 178(2), pages 472-481, April.
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    8. Diego Ramos Canterle & Fábio Mariano Bayer, 2019. "Variable dispersion beta regressions with parametric link functions," Statistical Papers, Springer, vol. 60(5), pages 1541-1567, October.
    9. Cook, Douglas O. & Kieschnick, Robert & McCullough, B.D., 2008. "Regression analysis of proportions in finance with self selection," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 860-867, December.
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    12. de Sousa, Maria da Conceição Sampaio & Cribari-Neto, Francisco & Stosic, Borko D., 2005. "Explaining DEA Technical Efficiency Scores in an Outlier Corrected Environment: The Case of Public Services in Brazilian Municipalities," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 25(2), November.
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    1. Tokelo Irene Letshedi & Jean-Claude Malela-Majika & Sandile Charles Shongwe, 2022. "New extended distribution-free homogenously weighted monitoring schemes for monitoring abrupt shifts in the location parameter," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-25, January.

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