Process variation
Natural process variation, sometimes just called process variation, is the statistical description of natural fluctuations in process outputs.
The following equations are used for an x-bar-control chart:
In the example, with n = 10 samples, the targeted mean, , and standard error of the mean, are:
That is, independent 10-sample means should themselves have a standard deviation of 0.0316. It is natural that the means vary this much, for by the central limit theorem the means should have a normal distribution, regardless of the distribution of the samples themselves.
The importance of knowing the natural process variation becomes clear when we apply statistical process control. In a stable process, the mean is on target; in the example, the target is the filling, set to 1 litre. The variation within the upper and lower control limits (UCL and LCL) is considered the natural variation of the process.
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