The technique used in statistical process control to determine if the process has become unstable is pattern tests. If the process data shows a pattern that suggests with high probability that the mean and/or variance of the process has changed (assuming independent events), then the practitioner should conclude that the process has become unstable. There are infinitely many ways a process might show instability, but the practitioner requires a small set of tests that are easy to apply and teach to operators on the floor. Dr. Shewhart gave us the original ±3s test and over the years many other pattern tests have been added. The landscape is now fairly muddled with tests, some of which are reasonable, and others that should be discarded. For example, ASQ publications and some prominent consultants continue to advocate the use of the six points increasing or decreasing test even though this test has been shown to be statistically very weak [Davis, 1988].

Table 1 below provides a list of the most well known pattern tests and my suggestion for a simple yet reasonable reduced set.

Source	Type of Instability
Shewhart (1931)
A single point beyond ± 3 sigma	Change in m or s
Western Electric (1956)
A single point beyond ± 3 sigma Two out of three consecutive points beyond ± 2 sigma on the same side of CL Four out of five consecutive points beyond ± 1 sigma on the same side of CL Eight consecutive points on the same side of the centerline	Change in m or s Change in m or s Change in m Change in m or s
Nelson (1984)
A single point outside the control limits. Applies to any distribution, continuous or discrete A run of nine points above or below the centerline. Applies to any symmetric distribution, continuous or discrete A run of six points in a row increasing or decreasing. Applies to a continuous distribution (This is a weak test [Davis 1988] Fourteen points in a row alternating up and down. Applies to a continuous distribution (Dr. Trietsch recommends thirteen points [Trietsch, 1997]). Two out of three points outside ± 2 sigma on the same side of CL. Applies to any distribution, continuous or discrete Four out of five points outside ± 1 sigma on the same side of CL. Applies to any distribution, continuous or discrete A run of fifteen points within ± 1 sigma of the centerline Applies to any distribution, continuous or discrete (Dr. Trietsch recommends thirteen points) Eight points in a row on both sides of CL but none within ± 1 sigma. Applies to any distribution, continuous or discrete (Dr. Trietsch recommends five points).	Change in m or s Change in m Change in m systematic or mixture Change in m or s Change in m or s mixture or change in s mixture or change in s
Flaig (1997)
Use Nelson’s rules 1 and 2. Any pattern that repeats itself eight times in succession non-random pattern.	Change in m or s Non random pattern

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by John J. Flaig, Ph.D.

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