All statistics and graphs for Xbar-R Chart

Interpretation

If the process is in control, the points vary randomly around the center line, and the process exhibits only common-cause variation. Investigate points that fall outside the control limits or that exhibit nonrandom patterns for possible special-cause variation.

The center line for the Xbar chart represents the average of the plotted points (also called the process mean).

The center line for the R chart represents the process variation. If the subgroup size is constant, then the center line on the R chart is the average of the subgroup ranges. If the subgroup sizes differ, then the value of the center line depends on the subgroup size, because larger subgroups tend to have larger ranges.

Interpretation

Use the center line to observe how the process performs compared to the average. If the process is in control, then the points vary randomly around the center line.

Interpretation

Use the tests for special causes to determine which observations you may need to investigate and to identify specific patterns and trends in your data. Each of the tests for special causes detects a specific pattern or trend in your data, which reveals a different aspect of process instability. For example, Test 1 detects a single out-of-control point. Test 2 detects a possible shift in the process.

Eight tests are available with this control chart. Only Tests 1−4 apply to the R chart portion of this control chart.

Test 1: One point more than 3σ from center line

Test 1 identifies subgroups that are unusual compared to other subgroups. Test 1 is universally recognized as necessary for detecting out-of-control situations. If small shifts in the process are of interest, you can use Test 2 to supplement Test 1 in order to create a control chart that has greater sensitivity.

Test 2: Nine points in a row on the same side of the center line

Test 2 identifies shifts in the process centering or variation. If small shifts in the process are of interest, you can use Test 2 to supplement Test 1 in order to create a control chart that has greater sensitivity.

Test 3: Six points in a row, all increasing or all decreasing

Test 3 detects trends. This test looks for a long series of consecutive points that consistently increase in value or decrease in value.

Test 4: Fourteen points in a row, alternating up and down

Test 4 detects systematic variation. You want the pattern of variation in a process to be random, but a point that fails Test 4 might indicate that the pattern of variation is predictable.

Test 5: Two out of three points more than 2σ from the center line (same side)

Test 5 detects small shifts in the process.

Test 6: Four out of five points more than 1σ from center line (same side)

Test 6 detects small shifts in the process.

Test 7: Fifteen points in a row within 1σ of center line (either side)

Test 7 detects a pattern of variation that is sometimes mistaken as evidence of good control. This test detects control limits that are too wide. Control limits that are too wide are often caused by stratified data, which occur when a systematic source of variation is present within each subgroup.

Test 8: Eight points in a row more than 1σ from center line (either side)

Test 8 detects a mixture pattern. In a mixture pattern, the points tend to fall away from the center line and instead fall near the control limits.

Interpretation

This historical control chart shows three stages of a process, which represent before, during, and after the implementation of a new procedure.