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Economic-Statistical Performance of Auxiliary Information-Based Maximum EWMA Charts for Monitoring Manufacturing Processes

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  • Jen-Hsiang Chen

    (Department of Information Management, Shih Chien University Kaohsiung Campus, 200 University Road, Neimen District, Kaohsiung City 84550, Taiwan)

  • Shin-Li Lu

    (Department of Industrial Management and Enterprise Information, Aletheia University, 32 Chen-Li Street, Tamsui District, New Taipei City 25103, Taiwan)

Abstract

An auxiliary information-based maximum exponentially weighted moving average chart, namely, the AIB-MaxEWMA chart, is superior to the existing MaxEWMA chart in detecting small process mean and/or variability shifts. To date, AIB-MaxEWMA chart was designed based on the statistical perspective, which ignores the cost of process monitoring. The economic-statistical performance of the AIB-MaxEWMA chart for monitoring process shifts is investigated. The Monte Carlo simulation was conducted to determine the optimal decision variables, such as sample size, sampling interval, control limit constant, and smoothing constant, by minimizing the expected cost function under the statistical constraints. Numerical simulations indicate that when an auxiliary variable is highly related to the study variable, AIB-MaxEWMA charts not only have better statistical performance, but also have lower expected costs than MaxEWMA charts. Sensitivity analyses also show that a larger expected time to sample an auxiliary variable results in larger optimal expected costs and lower optimal sample size and sampling interval. The relationship between optimal decision variables and minimal costs is valuable for reference by researchers or process engineers.

Suggested Citation

  • Jen-Hsiang Chen & Shin-Li Lu, 2022. "Economic-Statistical Performance of Auxiliary Information-Based Maximum EWMA Charts for Monitoring Manufacturing Processes," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2320-:d:854465
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    References listed on IDEAS

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    1. Serel, Dogan A. & Moskowitz, Herbert, 2008. "Joint economic design of EWMA control charts for mean and variance," European Journal of Operational Research, Elsevier, vol. 184(1), pages 157-168, January.
    2. 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.
    3. Nasir Abbas & Muhammad Riaz & Ronald J. M. M. Does, 2014. "An EWMA-Type Control Chart for Monitoring the Process Mean Using Auxiliary Information," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(16), pages 3485-3498, August.
    4. Muhammad Riaz, 2008. "Monitoring process mean level using auxiliary information," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(4), pages 458-481, November.
    5. Muhammad Riaz & Ronald Does, 2009. "A process variability control chart," Computational Statistics, Springer, vol. 24(2), pages 345-368, May.
    6. Shin-Li Lu, 2019. "Economic-statistical design of EWMA-semicircle charts under the Taguchi loss function," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 13(4), pages 489-506.
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