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Run-length distribution for variance control charts with runs rules using finite Markov chain imbedding
Journal of the Korean Data & Information Science Society 2019;30:919-31
Published online July 31, 2019;
© 2019 Korean Data and Information Science Society.

Hyeonggyu Kim1 · Gyo-Young Cho2

12Department of Statistics, Kyungpook National University
Correspondence to: Professor, Department of Statistics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu, 41566, Korea. E-mail:
Received June 25, 2019; Revised July 9, 2019; Accepted July 11, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
We propose a method for obtaining run-length distribution for Shewhart control charts with supplementary runs rules. We use Markov chain imbedding for obtaining the run length distribution. The method has several advantages. It is easy and fast to calculate and can be applied to other areas such as reliability with these advantages. In addition, accurate and clear distribution can be obtained. In this paper, we calculate probabilities of the run length according to the changes of the variances through S2 control charts with supplementary runs rules. When the variance increases, the average run length (ARL) decreases rapidly. Also, when the degree of freedom increases, the ARL decreases.
Keywords : Markov chain imbedding, probability distribution, quartiles, run length, variance.