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Comparing the Effectiveness of Various Bayesian X̄ Control Charts

Author

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  • George Tagaras

    (Department of Mechanical Engineering, Aristoteles University of Thessaloniki, 54124 Thessaloniki, Greece)

  • Yiannis Nikolaidis

    (Department of Mechanical Engineering, Aristoteles University of Thessaloniki, 54124 Thessaloniki, Greece)

Abstract

In an attempt to improve the procedures for statistical process control many researchers have developed and proposed a variety of adaptive control charts in the last decade. The common characteristic of those charts is that one or more of the chart parameters (sampling interval, sample size,control limits) is allowed to change during operation, taking into account current sample information. Due to their flexibility, adaptive charts are more effective than their static counterparts but they are also more complex in terms of implementation. The purpose of this paper is to evaluate the economic performance of various adaptive control schemes to derive conclusions about their relative effectiveness. The analysis concentrates on Bayesian control charts used for monitoring the process mean in finite production runs. We present dynamic programming formulations and properties of the optimal solutions, which we then use to solve a number of numerical examples. The results from our comparative numerical study indicate that the chart parameter having the most positive impact on the economic performance by being adaptive is the sampling interval. It is therefore sufficient in most cases to use control charts with adaptive sampling intervals rather than other types of partially adaptive charts or the more complicated fully adaptive control charts.

Suggested Citation

  • George Tagaras & Yiannis Nikolaidis, 2002. "Comparing the Effectiveness of Various Bayesian X̄ Control Charts," Operations Research, INFORMS, vol. 50(5), pages 878-888, October.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:5:p:878-888
    DOI: 10.1287/opre.50.5.878.361
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    References listed on IDEAS

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    1. Joel M. Calabrese, 1995. "Bayesian Process Control for Attributes," Management Science, INFORMS, vol. 41(4), pages 637-645, April.
    2. W. K. Chiu, 1976. "Economic Design of np Charts for Processes Subject to a Multiplicity of Assignable Causes," Management Science, INFORMS, vol. 23(4), pages 404-411, December.
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    5. Tagaras, George, 1996. "Dynamic control charts for finite production runs," European Journal of Operational Research, Elsevier, vol. 91(1), pages 38-55, May.
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    Cited by:

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    2. Mahfuza Khatun & Michael B.C. Khoo & Sajal Saha & Philippe Castagliola, 2021. "A new distribution‐free adaptive sample size control chart for a finite production horizon and its application in monitoring fill volume of soft drink beverage bottles," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 37(1), pages 84-97, January.
    3. Michael Jong Kim & Viliam Makis, 2013. "Joint Optimization of Sampling and Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 61(3), pages 777-790, June.
    4. Kampitsis, Dimitris & Panagiotidou, Sofia, 2022. "A Bayesian condition-based maintenance and monitoring policy with variable sampling intervals," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    5. Viliam Makis, 2008. "Multivariate Bayesian Control Chart," Operations Research, INFORMS, vol. 56(2), pages 487-496, April.
    6. Asma Amdouni & Philippe Castagliola & Hassen Taleb & Giovanni Celano, 2017. "A variable sampling interval Shewhart control chart for monitoring the coefficient of variation in short production runs," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5521-5536, October.
    7. Shoshana Anily & Abraham Grosfeld-Nir, 2006. "An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand," Operations Research, INFORMS, vol. 54(2), pages 311-323, April.
    8. Jue Wang & Chi-Guhn Lee, 2015. "Multistate Bayesian Control Chart Over a Finite Horizon," Operations Research, INFORMS, vol. 63(4), pages 949-964, August.

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