The figure below is an example of the X-R chart for this bowling example. The top part of the figure is the X chart. Each weekly average bowling score (i.e., the average of the three individual games) is plotted. The overall average (Xdbar = X double bar) has been calculated and plotted as a solid line. Xdbar is the average of all the subgroup averages. Upper and lower control limits have also been calculated and plotted. The X chart is in statistical control. The lower part of the figure is the range (R) chart. The range is plotted for each week. The average range and control limits have been calculated and plotted. The range is also in statistical control.
What does it mean when the X-R chart is in statistical control? It means that the subgroup average is consistent over time and the variation within a subgroup is consistent over time. We can predict what the process will do in the near future. In the bowling example, this means that you can predict what the average of your three games on any given night will be. Your average will be between about 158 and 208 with a long term average of about 183. You can also predict what your range in bowling scores will be on any given night. The range can be anywhere from 0 to about 62 with an average range of about 24. As long as the process stays in control (your bowling), the results will continue to the same.
a. Always consider variation first. If the R chart is out of control, the control limits on the X chart are not valid since you do not have a good estimate of . All tests for statistical control apply to the X chart. Points beyond the limits, number of runs and length of runs tests apply to the R chart. 2b1af7f3a8