The control limits of the R chart are


the control limits become

which are tabulated for various values of n and are available in many SPC references and in the Table of Control Chart Constants in the Appendix.

The x chart

The estimator for the mean process level (centerline) is x. Since the estimate of the standard deviation of the mean process level a is a _ R

y/n d2y/n The control limits for an x chart based on R are

Example Consider the following data set where three measurements have been collected at each sampling time in Table 6.1. The first twenty samples are used to develop the monitoring charts and the last five samples are monitored by using these charts.

Data used in the development of the SPM charts by computing the mean and standard deviation and calculating the control limits are also plotted to check if any of these samples are out of control. If not, the charts are used as developed. If there are any out of control points, special causes for such behavior are investigated. If such causes are found, the corresponding data are excluded from the data set used for chart development and the chart limits are computed again. Since there are no data out of control for the first 20 samples, the charts are used as developed for monitoring the five "new" samples.

Table 6.1. A sample data set





St Dev

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