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# Robust Control Charts

Summary: When a process is first submitted to statistical quality control, a standard procedure is to collect 20-40 subgroups of about five units each and then to construct control charts, such as X-bar charts and R charts, with limits determined by the data. These control charts are then used to detect problems in control such as outliers or excess variability in subgroup means that may have a special cause. In this article, the robustness of these charting procedures is investigated. If the number of false alarms when the process is in control is held constant, the most sensitive procedures for detecting the out-of-control state are those that plot a subgroup statistic that is sensitive to outliers (e.g., mean or range) but determine the control limits in the resistant fashion. Ordinary charting procedures, such as the standard X-bar and R charts, perform less well, and the worst performance is turned in by procedures in which the subgroup statistics are themselves resistant (e.g., median charts). To illustrate the point that robustness depends not only on resistance of the statistical tools to outliers but also on the purpose of the analysis, robust cumulative sum charts are briefly discussed. When outliers may be present, unlike X-bar and R charts, an overall better performance is obtained when a resistant subgroup statistic like the trimmed mean is used.

**Topics:**Statistical Process Control (SPC)**Keywords:**X-bar control charts,Outliers,Cumulative sum control chart (CUSUM),R (range) chart**Author:**Rocke, David M.**Journal:**Technometrics