IDEAS home Printed from
   My bibliography  Save this article

On the average run lengths of quality control schemes using a Markov chain approach


  • Fu, James C.
  • Spiring, Fred A.
  • Xie, Hansheng


Control schemes such as cumulative sum (CUSUM), exponentially weighted moving average (EWMA) and Shewhart charts have found widespread application in improving the quality of manufactured goods and services. The run length and the average run length (ARL) have become traditional measures of a control scheme's performance. Determining the run length distribution and its average is frequently a difficult and tedious task. A simple unified method based on a finite Markov chain approach for finding the run length distribution and ARL of a control scheme is developed. In addition, the method yields the variance or standard deviation of the run length as a byproduct. Numerical results illustrating the results are given.

Suggested Citation

  • Fu, James C. & Spiring, Fred A. & Xie, Hansheng, 2002. "On the average run lengths of quality control schemes using a Markov chain approach," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 369-380, February.
  • Handle: RePEc:eee:stapro:v:56:y:2002:i:4:p:369-380

    Download full text from publisher

    File URL:
    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

    1. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
    2. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    3. Leybourne, Stephen J. & C. Mills, Terence & Newbold, Paul, 1998. "Spurious rejections by Dickey-Fuller tests in the presence of a break under the null," Journal of Econometrics, Elsevier, vol. 87(1), pages 191-203, August.
    4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    5. Stephen J. Leybourne And Paul Newbold, 2000. "Behaviour of the standard and symmetric Dickey-Fuller-type tests when there is a break under the null hypothesis," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 1-15.
    6. Montañés, Antonio & Reyes, Marcelo, 1999. "The asymptotic behaviour of the Dickey-Fuller tests under the crash hypothesis," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 81-89, March.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Lin, Yu-Chang & Chou, Chao-Yu, 2005. "On the design of variable sample size and sampling intervals charts under non-normality," International Journal of Production Economics, Elsevier, vol. 96(2), pages 249-261, May.
    2. Chakraborti, S. & Eryilmaz, S. & Human, S.W., 2009. "A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1054-1065, February.

    More about this item


    Access and download statistics


    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:stapro:v:56:y:2002:i:4:p:369-380. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.