Even if we want to make "same" products, they are not same.
There are some causes of errors. In my experience, I did not check all causes to solve problems of errors.
There are accidental errors and systematic errors . In many cases, I think the causes are systematic errors.
I think accidental errors for the errors of repeated measurement. In this case, the approximation of normal distribution goes very well.
The cause of errors has a structure of level.
If we measure a same sample in a same way, this error is not zero in many cases.
The output of different machine is often different even if the sample is same.
If the methods of the measurement are different the error is larger.
Sampling is not easy if the phenomenon we want to measure is unstable.
In Process Analysis for Abnormal Condition , this error is often important. The small difference of process could be a large error.
The difference of the persons could be the cause.
One of the differences of the unevenness is personal abilities.
The other is the difference of the process of each person. For this problem, normalization is a popular solution.
If we understand the size of each error, decision making is easier. Standard Deviation is an index of errors.
If there are some causes of errors, calculation of the index is not easy. An application of Design of Experiments has logic to divide errors mathematically. (This site does not explain this logic because the explanation needs many pages.)
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