# Tests for randomness in a run chart

Patterns in your data indicate that the variation observed is due to causes that come from outside the system that can be corrected. Common-cause variation, however, is variation that is inherent or a natural part of the process. A process is in control when only common causes—not special causes—affect the process output.

A normal pattern for a process in control is one of randomness. If only common causes of variation exist in your process, the data will exhibit random behavior.

The run chart uses two tests to detect trends, oscillation, mixtures, and clustering in your data.
Test for number of runs about the median
This test is based on the total number of runs that occur both above and below the median. A run about the median is one or more consecutive points on the same side of the center line. A run ends when the line that connects the points crosses the center line. A new run begins with the next plotted point.
This test detects two types of non-random behavior—mixtures and clusters. Mixtures are characterized by frequent crossing of the center line. Clusters are groups of points that have similar values.
When the observed number of runs is:
• Statistically greater than the expected number of runs, then mixtures are indicated.
• Statistically less than the expected number of runs, then clusters are indicated.
Test for number of runs up and down
This test is based on the number of runs up or down. A run up is an upward run of consecutive points that exclusively increases. A run down is a downward run of consecutive points that exclusively decreases. A run ends when the direction (either up or down) changes. For example, when the preceding value is smaller, a run up begins and continues until the proceeding value is larger than the next point, then a run down begins.
This test detects two types of nonrandom behavior—oscillation and trends. Oscillation occurs when the data fluctuates up and down, indicating that the process is not steady. A trend is a sustained drift in the data, either up or down.
When the observed number of runs is:
• Statistically greater than the expected number of runs, then mixtures are indicated.
• Statistically less than the expected number of runs, then clusters are indicated.

## Test details

With both tests, the null hypotheses are that the data have a random sequence. Minitab converts the observed number of runs into a test statistic that is approximately standard normal, then uses the normal distribution to obtain p-values.

Both tests are based on individual observations when the subgroup size is equal to one. When the subgroup size is greater than one, the tests are based on either the subgroup means (the default) or the subgroup medians.

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