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In Quality Control charting, we are interested in monitoring a process to assure the process stays within given specifications.  It is also assumed that samples are independent of one another. This independence manifests in a random sequence of samples means. Of course, samples that fall outside of the control limits indicate that the process target has shifted, but another indicator is patterns across samples.  When a process is in control, sequential samples should exhibit no pattern. Runs tests can detect patterns in a sequence of samples and at times give an earlier warning of a shift in a process.

For this exercise, the example data set, Cover.sta, will be used to show how runs tests can test for patterns in a sequence of samples. The variable of interest, Width, gives measurements taken from single observation samples. When samples are taken of size 1, the Individuals & Moving range chart is appropriate.

An individuals and moving range chart plots the sample measurements in sequence.  Samples beyond 3 standard deviations from the mean are considered out of control and marked in red on the plot.  In this control chart, sample 6 is more than 3 standard deviations below the process mean.

This control chart allows a visual inspection of the sequence of samples. Given that each sample is selected independently, and if the process is in control, samples should display no pattern. At the end of this run, we see several samples fall below the mean. Can this pattern be attributed to random chance or is a true pattern emerging?  Runs tests can help to decide.

To view what runs tests are and what they test, select the X (MA..) specs tab of the control chart’s results dialog box. This tab contains the Runs tests button. Click it to display the Runs Tests for Control Chart dialog box. Below are the default settings for runs tests in STATISTICA. These are the specific patterns for which the tool will test.  

The following plot illustrates the zones of the runs tests.

Click the OK (compute tests) button in the Runs Tests for Control Chart dialog box to output the results.

The runs test output shows which runs tests were violated. In this example, samples 54 to 58 violate the runs test that 4 of 5 samples are in Zone B or beyond. Looking back at the control chart, the pattern circled in red is found to be significant. The likelihood of this pattern occurring by chance is small. This indicates that the sequence of samples was not drawn randomly from a population with the given mean and standard deviation, as we expect in a process that is in control. The runs test has detected a pattern, indicating a quality control issue before an out of control sample is found.

Note that step by step examples for using Quality Control Charting are available in STATISTICA’s online documentation.