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Design and efficiency of the variance component model control chart
Journal of the Korean Data & Information Science Society 2017;28:981-99
Published online September 30, 2017
© 2017 Korean Data & Information Science Society.

Chan Yang Cho1 · Changsoon Park2

12Department of Statistics, Chung-Ang University
Correspondence to: Changsoon Park
Professor, Department of Applied Statistics, Chung-Ang University, 84, Heukseok-ro, Dongjak-gu, Seoul 06974, Korea. E-mail:
Received July 5, 2017; Revised August 22, 2017; Accepted August 31, 2017.
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.
In the standard control chart assuming a simple random model, we estimate the process variance without considering the between-sample variance. If the between-sample exists in the process, the process variance is under-estimated. When the process variance is under-estimated, the narrower control limits result in the excessive false alarm rate although the sensitivity of the control chart is improved. In this paper, using the variance component model to incorporate the between-sample variance, we set the control limits using both the within- and between-sample variances, and evaluate the efficiency of the control chart in terms of the average run length (ARL). Considering the most widely used control chart types such as X, EWMA and CUSUM control charts, we compared the differences between two cases, Case I and Case II, where the between-sample variance is ignored and considered, respectively. We also considered the two cases when the process parameters are given and estimated. The results showed that the false alarm rate of Case I increased sharply as the between-sample variance increases, while that of Case II remains the same regardless of the size of the between-sample variance, as expected.
Keywords : Average run length, between-sample variance, false alarm rate, simple random model, within-sample variance