_ X Q and R Q Charts: Robust Control Charts

When a process is first subjected to statistical quality control procedures, a typical approach is to collect 20-40 subgroups of observations and then to construct control charts such as X 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 be due to a special cause. In this paper, I present a new method of determining the control limits for X and R charts that results in easier detection of outliers and greater sensitivity to other forms of out-of-control behavior when outliers are present. The control limits for these XQ and RQ charts are determined from the average subgroup interquartile range. They are nearly as easy to construct as ordinary X and R charts. occasional observations from a subgroup and not on subgroups as a whole. These should be detected, investigated and the special cause eliminated if possible. Outliers also may be due simply to recording errors (perhaps indicating a quality problem in the data acquisition process). In either case, the presence of outliers tends to reduce the sensitivity of control charting procedures because the control limits become stretched so that the detection of the outliers themselves becomes less likely. Furthermore, these stretched control limits mean that other types of out-of-control behavior become more difficult to detect. These other forms of lack of control could, for example, include long-term oscillation or drift. The purpose of this paper is to present a method of determining the control limits of X and R charts that lessens the difficulties caused by the presence of outliers in the data used to establish the control limits. This method was investigated by simulation in a previous paper (Rocke, 1989), and was found to be superior in this respect to alternatives, including standard X and R charts. The present paper is intended to present the practical details of the construction of these charts including a table of the necessary constants. This new charting method will be appropriate when the following conditions are satisfied.