Abstract
A single extreme point that plots outside of the 3σ control limits for the Shewhart charts indicate one possible out-of-control signal for the presence of assignable causes. Assignable causes can also cause unusual variation within the control limits. Runs rules have been used widely to detect patterns in successive observations. Excellent discussions about runs rules can be found in Nelson (Nelson, L. S. (1984). The Shewhart control chart—tests for special causes. Journal of Quality Technology 16:237–239.), Champ and Woodall (Champ, C. W., Woodall, W. H. (1987). Exact results for Shewhart control charts with supplementary runs rules. Technometrics 29:393–399.), Klein (Klein, M. (2000). Two alternatives to the Shewhart [Xbar] control chart. Journal of Quality Technology 32:427–431.), and Khoo (Khoo, B. C. Michael. (2003). Design of runs rules schemes. Quality Engineering 16, (27–43)). In this article, enhanced rules for the Hotelling's χ 2 chart will be suggested to increase the chart's sensitivity.
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