Although Shewhart control charts have had a tremendous impact on quality improvement, the inability to precisely measure chart performance has limited their role, and subsequently overall effectiveness in the control of manufacturing processes. Measures of performance in terms of operational characteristics (OC) are defined on two distinct levels: (a) single-subgroup level, which examines the probability of a rule violation at any given subgroup (b) multiple-subgroup level, which considers the probability of one or more rule violations throughout process monitoring. Single-subgroup performance measures for X-bar charts that employ four rules are formulated. These measures are exact expressions of operational characteristics, except for the numerical approximation to the integral of the normal distribution. Applications of these models to simulated data demonstrate their accuracy in predicting chart performance. In addition, a diagnostic methodology is described which utilizes the derived performance measures to predict the mean of a shifted distribution. The proposed diagnostic procedure is illustrated in validation and application examples.
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May 1994
This article was originally published in
Journal of Engineering for Industry
Research Papers
Single-Subgroup Performance Measures and Diagnostic Procedures for X-Bar Control Charts
G. E. Rahn,
G. E. Rahn
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680
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S. G. Kapoor,
S. G. Kapoor
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
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R. E. DeVor
R. E. DeVor
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
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G. E. Rahn
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680
S. G. Kapoor
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
R. E. DeVor
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
J. Eng. Ind. May 1994, 116(2): 216-224
Published Online: May 1, 1994
Article history
Received:
September 1, 1991
Revised:
February 1, 1993
Online:
April 8, 2008
Citation
Rahn, G. E., Kapoor, S. G., and DeVor, R. E. (May 1, 1994). "Single-Subgroup Performance Measures and Diagnostic Procedures for X-Bar Control Charts." ASME. J. Eng. Ind. May 1994; 116(2): 216–224. https://doi.org/10.1115/1.2901933
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