The following equations are used for an x-bar-control chart: In the example, with n = 10 samples, the targeted mean,
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.
To be more specific: The most important goal of understanding the principle of natural process variation is to consider the natural variance in the output before we make any changes to the process.
Since SPC tends to minimize the process variations in time, as we better understand the process and have more experience with running it, we try to reduce the variation of it.
The knowledge of the principle of natural variance helps us avoid making any unnecessary changes to the process, which might add variance to the process, instead of removing it.