Simulating Natural Variations of Samples and Basic Patterns in S2 Control Chart

Document Type : Research Paper

Authors

1 Professor of Industrial Engineering, Department of Industrial Engineering, AmirKabir University of Technology, Tehran, Iran.

2 M.A. in Industrial Engineering, Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran.

10.22084/ier.2025.29453.2169

Abstract

Since 1990 up to now, numerous papers with various problem-solving have been presented to recognize and analyze the basic patterns in process control charts. These papers have commonly utilized the simulated samples for testing, evaluating and training their proposed models. Most papers have studied the behaviour of the runs of consecutive samples in mean or individual measurement control charts, and have not simultaneously interpreted the patterns in variability and mean control charts. On the other hand, few papers which have monitored simultaneously the patterns in variability and mean control charts, have not selected the generalized method based on statistical reasoning to simulate samples in variability control chart. The presentation of a simulation method of samples in variability control chart and also, emphasizing simultaneous monitor of successive samples behaviour in mean and variability control charts, are the aims of current work. In this way, we recommend applying S2 control chart to monitor process variability. Unfortunately, little attention has been given to the usage of this chart in quality control references; while samples are unbiased in S2 chart and therefore its accuracy is high. To reach these goals, the statistical distribution function of samples in S2 chart is known. Then, the generating functions of the basic patterns in variable quality characteristics control charts and also numerical parameters corresponding to the patterns will be described. Moreover, the disadvantages of the samples simulation method in previous papers will be explained and based on the proposed simulations in this study, solutions will be presented.

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Main Subjects

References

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Journal of Industrial Engineering Research in Production Systems
Volume 13, Issue 26
September 2025
Pages 5-17

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