SurfStat.australia

Surfstat.australia: an online text in introductory Statistics

STATISTICAL INFERENCE

STATISTICAL CONTROL CHARTS

Tests for Special Causes
Having an observation beyond the control limits is the main test for an out-of-control process. Over 40 tests have been proposed for use wiht contrl charts; naturally, many of them are related to each other, so it would be silly to apply them all. Furthermore, the more tests are done the greater the chance that a false alarm will occur.
In Minitab, use the TEST subcommand to specify which of its eight tests for special causes to use. Further information on each test is contained in the HELP facility.
A point beyond control limits
This is the test which is universally associated with the idea of an in-control process. This test has a reasonable power for detecting a shift in the process mean (for the chart) of about 1.5s or more, when the subgroups contain n=4 or 5 observations. It is slow to signal a gradual drift in the mean or (say) a 0.5s shift in the mean, although it will eventually respond.
Eight points in a row on one side of the line
Suppose the distribution of the averages is roughly symmetric. Then will be close to the median, the 50^th percentile. The chance of eight in a row on one side of the median is (1/2)⁸=1/256. (This is equivalent to getting eight heads in a row when tossing a coin). We double this to take into account that the run of eight could be either above or below the centreline (in the coin analogy, this covers runs of both heads and tails), so the false alarm rate of this test is 1/128 or about .008. In the percent solids chart there is no run of eight points in a row on one side on the CL.
Violation of this criterion on the x-bar chart suggests looking first for a special cause which would produce a small change int he mean (smaller than 1s) which would have persisted through (say) eight or more sampling periods. The pattern might also be due to a slow drift of the mean.
A run of seven sample means steadily increasing or decreasing
This suggests a trend in the process mean.
Points hugging the centre line
About 2/3 of observed values should occur in the middle third of the region between the control limits. If substantially more than 2/3 of the data points lie close to - for example if 90% or more of the points in 25 subgroups lie in the middle third - one should check for

miscalculation or misplotting of control limits
stratification of observations from two or more process streams with different process means within each subgroups
editing of extreme process results (i.e. someone is tampering with the data).

Points hugging the control limits
If substantially fewer than 2/3 of the observed values lie close to - say 40% or fewer out of 25 subgroups lie in the middle third - one should check for

mixtures of process streams with different average levels such that some subgroups contain all or nearly all observations from one stream while other subgroups contatin mainly observations from the another stream.

Cycles
Sine-wave like cycles in values are another systematic pattern that indicates the presence of special causes.

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