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What are the best sample sizes for the Xbar and CUSUM charts?

Author

Listed:
  • Wu, Zhang
  • Yang, Mei
  • Khoo, Michael B.C.
  • Castagliola, Philippe

Abstract

The and CUSUM control charts are used most widely for monitoring the mean of a quality characteristic x. This article studies the sample sizes and nCUSUM of these two charts in the domain of statistical design. However, the study takes the important sampling inspection cost (including the variable and fixed cost components) into consideration. The chart performance will be measured by a weighted average ATS (Average Time to Signal). There are two interesting findings based on the results of this study: (1) The chart becomes more statistically effective for detecting mean shifts when the fixed sampling cost cannot be neglected and/or when the mean shift range is small. If and nCUSUM are set as 4 and 1, respectively, based on some conventional wisdom, the simple chart often outperforms the more complicated CUSUM chart from an overall viewpoint. (2) Under all circumstances, the overall statistical performance of both charts can be improved, or significantly improved, by the optimization design. The optimal values of and nCUSUM depend on the ratio between the fixed and variable sampling costs, the range of the mean shift, and the in-control Average Time to Signal. For the general cases, the best sample sizes are or 4, and nCUSUM=2 or 3.

Suggested Citation

  • Wu, Zhang & Yang, Mei & Khoo, Michael B.C. & Castagliola, Philippe, 2011. "What are the best sample sizes for the Xbar and CUSUM charts?," International Journal of Production Economics, Elsevier, vol. 131(2), pages 650-662, June.
    • Handle: RePEc:eee:proeco:v:131:y:2011:i:2:p:650-662
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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. Ho, Linda Lee & Trindade, Anderson Laécio Galindo, 2009. "Economic design of an X chart for short-run production," International Journal of Production Economics, Elsevier, vol. 120(2), pages 613-624, August.
    3. De Magalhães, M.S. & Costa, A.F.B. & Moura Neto, F.D., 2009. "A hierarchy of adaptive control charts," International Journal of Production Economics, Elsevier, vol. 119(2), pages 271-283, June.
    4. Torng, Chau-Chen & Lee, Pei-Hsi & Liao, Nai-Yi, 2009. "An economic-statistical design of double sampling control chart," International Journal of Production Economics, Elsevier, vol. 120(2), pages 495-500, August.
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    6. Wu, Zhang & Yang, Mei & Jiang, Wei & Khoo, Michael B.C., 2008. "Optimization designs of the combined Shewhart-CUSUM control charts," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 496-506, December.
    7. Zhang Wu & Jianxin Jiao & Mei Yang & Ying Liu & Zhaojun Wang, 2009. "An enhanced adaptive CUSUM control chart," IISE Transactions, Taylor & Francis Journals, vol. 41(7), pages 642-653.
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    Cited by:

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    2. Lim, S.L. & Khoo, Michael B.C. & Teoh, W.L. & Xie, M., 2015. "Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated," International Journal of Production Economics, Elsevier, vol. 166(C), pages 20-35.
    3. Xiao, Xiao & Jiang, Wei & Luo, Jianwen, 2019. "Combining process and product information for quality improvement," International Journal of Production Economics, Elsevier, vol. 207(C), pages 130-143.
    4. Iziy Azamsadat & Sadeghpour Gildeh Bahram & Monabbati Ehsan, 2017. "Comparison Between the Economic-Statistical Design of Double and Triple Sampling X¯\bar{X} Control Charts," Stochastics and Quality Control, De Gruyter, vol. 32(1), pages 49-61, June.

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