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.
Single-Subgroup Performance Measures and Diagnostic Procedures for X-Bar Control Charts
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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