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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

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    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.

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