IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4671-d1281773.html
   My bibliography  Save this article

A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes

Author

Listed:
  • Eftychia Mamzeridou

    (Department of Statistics & Actuarial-Financial Mathematics, University of the Aegean, 83200 Samos, Greece)

  • Athanasios C. Rakitzis

    (Department of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, Greece)

Abstract

In this work, a control chart with multiple runs rules is proposed and studied in the case of monitoring inflated processes. Usually, Shewhart-type control charts for attributes do not have a lower control limit, especially when the in-control process mean level is very low, such as in the case of processes with a low number of defects per inspected unit. Therefore, it is not possible to detect a decrease in the process mean level. A common solution to this problem is to apply a runs rule on the lower side of the chart. Motivated by this approach, we suggest a Shewhart-type chart, supplemented with two runs rules; one is used for detecting decreases in process mean level, and the other is used for improving the chart’s sensitivity in the detection of small and moderate increasing shifts in the process mean level. Using the Markov chain method, we examine the performance of various schemes in terms of the average run length and the expected average run length. Two illustrative examples for the use of the proposed schemes in practice are also discussed. The numerical results show that the considered schemes can detect efficiently various shifts in process parameters in either direction.

Suggested Citation

  • Eftychia Mamzeridou & Athanasios C. Rakitzis, 2023. "A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes," Mathematics, MDPI, vol. 11(22), pages 1-16, November.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4671-:d:1281773
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4671/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/22/4671/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maria Melkersson & Dan-Olof Rooth, 2000. "Modeling female fertility using inflated count data models," Journal of Population Economics, Springer;European Society for Population Economics, vol. 13(2), pages 189-203.
    2. Mukherjee, Amitava & Sen, Rudra, 2018. "Optimal design of Shewhart–Lepage type schemes and its application in monitoring service quality," European Journal of Operational Research, Elsevier, vol. 266(1), pages 147-167.
    3. C. Fu, James & Shmueli, Galit & Chang, Y. M., 2003. "A unified Markov chain approach for computing the run length distribution in control charts with simple or compound rules," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 457-466, December.
    4. Tee Chin Chang & Fah Fatt Gan, 2007. "Modified Shewhart Charts for High Yield Processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(7), pages 857-877.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Song, Zhi & Mukherjee, Amitava & Zhang, Jiujun, 2021. "Some robust approaches based on copula for monitoring bivariate processes and component-wise assessment," European Journal of Operational Research, Elsevier, vol. 289(1), pages 177-196.
    2. Markos V. Koutras & Sotirios Bersimis & Demetrios L. Antzoulakos, 2006. "Improving the Performance of the Chi-square Control Chart via Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 409-426, September.
    3. Muhammad Riaz & Muhammad Abid & Hafiz Zafar Nazir & Saddam Akber Abbasi, 2019. "An enhanced nonparametric EWMA sign control chart using sequential mechanism," PLOS ONE, Public Library of Science, vol. 14(11), pages 1-15, November.
    4. Massimiliano Bratti & Alfonso Miranda, 2010. "Endogenous Treatment Effects for Count Data Models with Sample Selection or Endogenous Participation," DoQSS Working Papers 10-05, Quantitative Social Science - UCL Social Research Institute, University College London, revised 10 Dec 2010.
    5. Alison L. Booth & Hiau Joo Kee, 2009. "Intergenerational Transmission of Fertility Patterns," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(2), pages 183-208, April.
    6. Hossein Kavand & Marcel Voia, 2018. "Estimation of Health Care Demand and its Implication on Income Effects of Individuals," Springer Proceedings in Business and Economics, in: William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), Productivity and Inequality, pages 275-304, Springer.
    7. Guido Heineck, 2006. "The relationship between religion and fertility: Evidence from Austria," Papers on Economics of Religion 06/01, Department of Economic Theory and Economic History of the University of Granada..
    8. Echávarri Aguinaga, Rebeca, 2009. "Education and the dynamics of family decisions," DFAEII Working Papers 1988-088X, University of the Basque Country - Department of Foundations of Economic Analysis II.
    9. Thomas Baudin, 2015. "Religion and fertility: The French connection," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(13), pages 397-420.
    10. Yung-Ming Chang & Tung-Lung Wu, 2011. "On Average Run Lengths of Control Charts for Autocorrelated Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 419-431, June.
    11. George Hondroyiannis, 2010. "Fertility Determinants and Economic Uncertainty: An Assessment Using European Panel Data," Journal of Family and Economic Issues, Springer, vol. 31(1), pages 33-50, March.
    12. Alfonso Miranda, 2008. "Planned fertility and family background: a quantile regression for counts analysis," Journal of Population Economics, Springer;European Society for Population Economics, vol. 21(1), pages 67-81, January.
    13. Massimiliano Bratti & Alfonso Miranda, 2011. "Endogenous treatment effects for count data models with endogenous participation or sample selection," Health Economics, John Wiley & Sons, Ltd., vol. 20(9), pages 1090-1109, September.
    14. Kate J. Li & Duncan K. H. Fong & Susan H. Xu, 2011. "Managing Trade-in Programs Based on Product Characteristics and Customer Heterogeneity in Business-to-Business Markets," Manufacturing & Service Operations Management, INFORMS, vol. 13(1), pages 108-123, October.
    15. Yamaguchi, Hikaru & Murakami, Hidetoshi, 2023. "The multi-aspect tests in the presence of ties," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    16. Parra Álvarez, Juan Carlos & Misas A., Martha & López-Enciso, Enrique Antonio, 2011. "Heterogeneidad en la fijación de precios en Colombia : análisis de sus determinantes a partir de modelos de conteo," Chapters, in: López Enciso, Enrique & Ramírez Giraldo, María Teresa (ed.), Formación de precios y salarios en Colombia T.1, volume 1, chapter 8, pages 251-293, Banco de la Republica de Colombia.
    17. Yu-Fei Hsieh & Tung-Lung Wu, 2013. "Recursive equations in finite Markov chain imbedding," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 513-527, June.
    18. Veronica Amarante, 2017. "Inequality and Household Size: A Microsimulation for Uruguay," International Journal of Microsimulation, International Microsimulation Association, vol. 10(1), pages 73-105.
    19. Yaguang Wu & Qingan Qiu, 2022. "Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks," Mathematics, MDPI, vol. 10(15), pages 1-18, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4671-:d:1281773. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.