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A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    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.
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