IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v131y2011i2p650-662.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(11)00067-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Zhang, Cai Wen & Xie, Min & Goh, Thong Ngee, 2008. "Economic design of cumulative count of conforming charts under inspection by samples," International Journal of Production Economics, Elsevier, vol. 111(1), pages 93-104, January.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Ou, Yanjing & Wu, Zhang & Tsung, Fugee, 2012. "A comparison study of effectiveness and robustness of control charts for monitoring process mean," International Journal of Production Economics, Elsevier, vol. 135(1), pages 479-490.
    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.

    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. Ou, Yanjing & Wu, Zhang & Goh, Thong Ngee, 2011. "A new SPRT chart for monitoring process mean and variance," International Journal of Production Economics, Elsevier, vol. 132(2), pages 303-314, August.
    2. Ou, Yanjing & Wu, Zhang & Tsung, Fugee, 2012. "A comparison study of effectiveness and robustness of control charts for monitoring process mean," International Journal of Production Economics, Elsevier, vol. 135(1), pages 479-490.
    3. Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2011. "Variable parameter and double sampling charts in the presence of correlation: The Markov chain approach," International Journal of Production Economics, Elsevier, vol. 130(2), pages 224-229, April.
    4. 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.
    5. Lee, Pei-Hsi, 2013. "Joint statistical design of X¯ and s charts with combined double sampling and variable sampling interval," European Journal of Operational Research, Elsevier, vol. 225(2), pages 285-297.
    6. L Bessegato & R Quinino & L L Ho & L Duczmal, 2011. "Variable interval sampling in economical designs for online process control of attributes with misclassification errors," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1365-1375, July.
    7. 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.
    8. 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.
    9. Khoo, Michael B.C. & Teoh, W.L. & Castagliola, Philippe & Lee, M.H., 2013. "Optimal designs of the double sampling X¯ chart with estimated parameters," International Journal of Production Economics, Elsevier, vol. 144(1), pages 345-357.
    10. Du, Shichang & Lv, Jun, 2013. "Minimal Euclidean distance chart based on support vector regression for monitoring mean shifts of auto-correlated processes," International Journal of Production Economics, Elsevier, vol. 141(1), pages 377-387.
    11. Franco, Bruno Chaves & Celano, Giovanni & Castagliola, Philippe & Costa, Antonio Fernando Branco, 2014. "Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies," International Journal of Production Economics, Elsevier, vol. 151(C), pages 121-130.
    12. Nduhura Munga, Justin & Dauzère-Pérès, Stéphane & Yugma, Claude & Vialletelle, Philippe, 2015. "A mathematical programming approach for optimizing control plans in semiconductor manufacturing," International Journal of Production Economics, Elsevier, vol. 160(C), pages 213-219.
    13. Imad Khan & Muhammad Noor-ul-Amin & Dost Muhammad Khan & Salman A. AlQahtani & Mostafa Dahshan & Umair Khalil, 2023. "Monitoring of Location Parameters with a Measurement Error under the Bayesian Approach Using Ranked-Based Sampling Designs with Applications in Industrial Engineering," Sustainability, MDPI, vol. 15(8), pages 1-18, April.
    14. Lei Yong Lee & Michael Boon Chong Khoo & Sin Yin Teh & Ming Ha Lee, 2015. "A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-18, May.
    15. Ho, Linda Lee & Aparisi, Francisco, 2016. "ATTRIVAR: Optimized control charts to monitor process mean with lower operational cost," International Journal of Production Economics, Elsevier, vol. 182(C), pages 472-483.
    16. Maravelakis, Petros E. & Castagliola, Philippe, 2009. "An EWMA chart for monitoring the process standard deviation when parameters are estimated," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2653-2664, May.
    17. Nasir Abbas & Muhammad Riaz & Shabbir Ahmad & Muhammad Abid & Babar Zaman, 2020. "On the Efficient Monitoring of Multivariate Processes with Unknown Parameters," Mathematics, MDPI, vol. 8(5), pages 1-32, May.
    18. Huynh, Linh & Hoang, Hien & Tran, Hung, 2020. "Does FDI enhance provincial productivity? A panel data analysis in Vietnam," MPRA Paper 117620, University Library of Munich, Germany, revised Aug 2021.
    19. Fabbri, Ricardo & Bastos, Ivan N. & Neto, Francisco D. Moura & Lopes, Francisco J.P. & Gonçalves, Wesley N. & Bruno, Odemir M., 2014. "Multi-q pattern classification of polarization curves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 332-339.
    20. Tomohiro, Ryosuke & Arizono, Ikuo & Takemoto, Yasuhiko, 2020. "Economic design of double sampling Cpm control chart for monitoring process capability," International Journal of Production Economics, Elsevier, vol. 221(C).

    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:eee:proeco:v:131:y:2011:i:2:p:650-662. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    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.