Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Statistical Design of X Control Chart with Improved 2-of-3 Main and Supplementary Runs Rules

개선된 3 중 2 주 및 보조 런 규칙을 가진 X관리도의 통계적 설계

  • Received : 2012.08.23
  • Accepted : 2012.10.15
  • Published : 2012.12.31
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Abstract

Purpose: This paper introduces new 2-of-3 main and supplementary runs rules to increase the performance of the classical $\bar{X}$ control chart for detecting small process shifts. Methods: The proposed runs rules are compared with other competitive runs rules by numerical experiments. Nonlinear optimization problem to minimize the out-of-control ARL at a specified shift of process mean for determining action and warning limits at a time is formulated and a procedure to find two limits is illustrated with a numerical example. Results: The proposed 2-of-3 main and supplementary runs rules demonstrate an improved performance over other runs rules in detecting a sudden shift of process mean by simultaneous changes of mean and standard deviation. Conclusion: To increase the performance in the detection of small to moderate shifts, the proposed runs rules will be used with $\bar{X}$ control charts.

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References

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