X-R charts should be used when you have taken data frequently. As long as the process stays in control (your bowling), the results will continue to the same. The range can be anywhere from 0 to about 62 with an average range of about 24. You can also predict what your range in bowling scores will be on any given night. Your average will be between about 158 and 208 with a long term average of about 183. In the bowling example, this means that you can predict what the average of your three games on any given night will be. We can predict what the process will do in the near future. 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. The range is also in statistical control. The average range and control limits have been calculated and plotted. The lower part of the figure is the range (R) chart. Upper and lower control limits have also been calculated and plotted. Xdbar is the average of all the subgroup averages. The overall average (Xdbar = X double bar) has been calculated and plotted as a solid line. Each weekly average bowling score (i.e., the average of the three individual games) is plotted. The top part of the figure is the X chart. The figure below is an example of the X-R chart for this bowling example. This permits you to predict what your average score will be on any night, within certain limits. You would like this variation to be small and be consistent over time. The X chart shows how much week-to-week variation there is in your weekly average bowling score. Using the three scores above, you can calculate an average score for the night by taking the average of the three individual scores. The chart for averages ( X) presents a different variation than the range chart. The range chart shows how much variation there is within each subgroup, i.e., the amount of variation in your bowling scores on one night. This is done for each subgroup (one night of bowling three games). You can plot this value on a range (R) chart. Range = Maximum - Minimum = 189 - 155 = 34 You can calculate the range of this subgroup by subtracting the minimum score from the maximum score. The three individual games you bowl on one night can be used to form a subgroup.Ĭontinuing with the bowling example, suppose that one night your three bowling scores are 169, 155, and 189. You can also rationally subgroup the data. You have data available on a fairly frequent basis (three games each week). The other source is the variation within a subgroup. One source is the variation in subgroup averages. The X-R chart is a method of looking at two different sources of variation. In situations such as this (when you want to monitor averages over time but still keep track of the variation between individual results), the X-R chart is very useful. Thus, another idea is to keep track of the range in scores for the three games each night. You are also interested in being more consistent, i.e., not having one great game followed by a poor one. You definitely would like to increase that average over time. So another idea is to plot the average of the three games each night. However, you are more interested in what your average score is on a given night. What are some different approaches you could use? One idea is that you could plot the score from each game. You are interested in determining if you are improving your bowling game. You bowl three games a night once a week in a bowling league. Suppose you are a member of a bowling team. These charts are a very powerful tool for monitoring variation in a process and detecting changes in either the average or the amount of variation in the process. The other chart is for subgroup ranges (R). Like most other variables control charts, it is actually two charts. The X-R chart is a type of control chart that can be used with variables data. Next month, we will look at a detailed example of an X-R chart. This month we introduce the chart and provide the steps in constructing an X-R chart. This month is the first in a multi-part publication on X-R charts.
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