Statistical Design of X Control Chart with Improved 2-of-3 Main and Supplementary Runs Rules

Abstract Purpose: This paper introduces new 2-of-3 main and supplementary runs rules to increase the performance of the classical  control chart for detecting small process shifts.Methods: The proposed runs rules are compared with other competitive r uns rules by numerical experiments. Nonlinear optimization problem to minimize the out-of-control A RL at a specified shift of process mean for determining action and warning limits at a time is formulated a nd a procedure to find two limits is illustrated with a numerical example.Results: The proposed 2-of-3 main and supplementary runs rules demonst rate 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  control charts.Key Words：Action limit, Average Run Length, Runs Rule, Warning limit,  Control Chart † ● Received 23 August 2012, revised 15 October 2012, accepted 15 October 2012* Corresponding Author(skseo@dau.ac.kr)ⓒ 2012, The Korean Society for Quality ManagementThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits u nrestricted non-Commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.※ 이 논문은 동아대학교 교내연구비 지원에 의하여 연구되었음.