Runs Tests

Runs tests provide a way for people within an organization to consistently evaluate patterns on control charts.  That is, they allow two people to look at the same chart and reach the same conclusion about the need to search for special causes of variation.  Although a large number of runs tests have been developed, this page will be limited to the tests presented in this course.  These tests will be used on all of the control charts that we construct except the Moving Range Chart (Test 1 is the only runs test that we will use on that chart).  If you can answer yes to any of the following questions, you should begin to look for special causes of variation.  Note that tests 2 -6 are looking for patterns even though all of the points may plot within the control limits.

Test 1:  Does at least one point plot outside the control limits?
A point outside the control limits is an indication that some new/additional source of variation is influencing the process.  Look for what was happening different at the point in time when the data for this point was collected.

Caution:  All of the following tests look for patterns in consecutive observations.  The order that the data is plotted must have meaning for these tests to have meaning! 

Test 2:  Are there two out of three consecutive points in the same A zone?
Both Test 2 and Test 3 require the use of zones.  To determine the zones on a chart, we divide the space between the control limits and the center line into three equal width bands.  (Note:  If one of the control limits does not exist, we base the width of the bands on math from the side of the control chart where we do have values.  For example, a p or np chart will often have no lower control limit.  When this is the case, we determine the width of the bands by looking at the distance between the upper control limit an the center line.)  The bands closest to the control limits are referred to as the A zones, the next ones in are the B zones, and the zones closest to the center line are the C zones. 

This test attempts to determine if the variation has increased--i.e., there are not enough points close enough to the center line.  (Test 3 will look to see if too many points were too close to the center line.)  Cases 1 and 2 below provide examples where we would look for assignable causes for increased variation.  Case 3 does not fail this test since the two points in the A zone (Points 7 and 9) are in different A zones.

Test 3:  Are there fifteen consecutive points in the C zones?
For this test we use the same zones created for the previous test.  If too many points plot close to the center line, we say that the amount of variation displayed is less than we would expect.  This is cause for exploration.  Three primary possibilities come to mind.  First, the process could have been improved, and new limits may need to be calculated.  Second, fear may be causing people to report numbers based on what they think should be seen rather than true numbers (or the process may be being distorted to produce the desired numbers).  And third, the data may be subgrouped in such a way that excessive variation within a subgroup is inflating the control limits.  The following control chart shows a case where the observations are "hugging the center line."

Test 4:  Are there more than seven consecutive points on the same side of the center line?
If the process is stable, we expect a random scattering of points above and below the center line rather than a string of high or a string of low points.  Once more than seven consecutive points plot on the same side of the center line we look for an explanation for the shift in the process characteristic.  Generally, we ask questions about what changed at, or near, the point in time that the first point in the run occurred. 

Test 5:  Are there seven or more consecutive increases or decreases?
An upward or downward pattern signals a possible trend.  We can see such an increasing pattern on the chart below.

Test 6:  Are there fifteen or more consecutive points alternating up and down?
An alternating sequence of points can be an indication of an irrational grouping of data on a chart (e.g., sampling from two parallel processes (that are falsely believed to be identical) in an alternating fashion.  Another cause for such a pattern is tampering--making an adjustment to the process following each measurement based on that measurement.  The following control chart provides an example of an alternating, or sawtooth, pattern.  [Note:  this chart shows 15 points alternating up and down.]

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