# All statistics and graphs for Z-MR Chart

Find definitions and interpretation guidance for every statistic and graph that is provided with the Z-MR chart.

## Plotted points

The plotted points on the Z chart are the standardized individual observations.

The plotted points on the MR chart are the moving ranges of the standardized data. The moving range is the absolute value of the difference between two or more consecutive points.

### 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.

## Center line

The center line on the Z chart is an estimate of the process average across runs. The center line is always located at 0 because the data are standardized.

The center line on the Moving Range chart is the average of all moving 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.

###### CAUTION

Do not confuse the center line with the target value for your process. The target is your desired outcome. The center line is the actual outcome.

## Control limits

Control limits are the horizontal lines that are above and below the center line. The control limits indicate whether a process is out of control, and they are based on the observed variation and the expected variation in the plotted points. By default, Minitab displays control limits at 3 standard deviations above and below the center line.
###### CAUTION

Do not confuse control limits with specification limits. Specification limits represent customer requirements and indicate the amount of variation that you want to see in the process. Control limits represent the actual amount of variation that is in the sample data. A process can be in control, yet not be capable of meeting specifications.

## Tests for special causes

The tests for special causes assess whether the plotted points are randomly distributed within the control limits.

### 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.

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.

## Standard deviation

The standard deviation measures the overall variability in the data. Minitab does not display the standard deviation on the chart, but uses it to calculate the center line and the control limits. To store the standard deviation in the worksheet, select it on the Storage tab of the Options dialog box.

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