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Variables Charts

X-bar, R charts allow the process operator to track his/her process average (X-bar) and process variation (R, for Range) over time. See the example in the graphic on the Roles & Benefits page. Typically, the operator will take a subgroup of, say, 5 consecutive samples. You want to make sure it is likely that there will be only a minimum of variation within each subgroup, so that variation between subgroups shows up on the chart. After taking the samples for a subgroup, the operator then calculates the mean (X-bar) and the range (R) of the subgroup. The subgroup average is plotted for on the top chart, and the range is plotted on the bottom chart.

After 20 or so subgroups are plotted, a grand average (X-double bar) of all of the subgroup averages is calculated and plotted as a horizontal line on the top chart. Also, an average (R-bar) of all of the subgroup ranges is calculated and plotted on the bottom chart. The R-bar value can also be used to calculate the Upper and Lower Control Limits for both charts. These represent the normal limits (+ or - minus 3 standard deviations, or 99.7%) of the population of subgroups.

Any plot points beyond the control limits suggest a special cause of variation. In a process under statistical control, there should be about as many subgroup averages above the grand average line as there are below the line. About 2/3rds of the points should lie fairly close to the grand average line -- within the region 1/3rd of the distance to each control limit. There should not be too many points in a row above or below the grand average line, or too many in a row increasing or decreasing. (These rules are more specifically defined in most SPC courses and texts).

Attributes Charts
See a typical attributes chart (an np chart). Although it is usually preferable to use variables data and charting, attributes charts can be beneficial when you are dealing with go/no-go data, qualitative data, etc. This type of charting does not have R (subgroup range) calculations or plotting. If you are interested in plotting the number of defects per unit (which usually has many defects), then use a c (with constant sample size) or u (with varying sample sizes) chart. If it is more appropriate to chart the actual number (np) or percentage (p) of defective units in a subgroup, then use a p or np chart. The np chart requires a constant sample size, but it can vary with the p chart. The c and np charts are the easiest to use; with the varying sample sizes for the u and p charts, you have to constantly recalculate the control limits.

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