How Sigma / Standard Deviation is Calculated in QC-CALC
Methods used by QC-CALC to calculate sigma or standard deviation
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written: 05/08/2006
last modified: 09/16/2024

QUESTION

What method of calculating Sigma does QC-CALC use?


ANSWER

All calculations and reports in QC-CALC assume that your data set is a "sample" of the total parts, and not the entire set of data. For this reason, we always calculate "Sigma by N-1". This formula corresponds to Excel’s "STDEV()" function.

There are 3 methods of calculating Standard Deviation, also known as Sigma.

  • Sigma by N-1 (Standard_Deviation)
  • Sigma by S (Sigma_by_S)
  • Sigma by R (Sigma_by_R)

Sigma by N-1:
This method assumes you have a sample and want to infer the population’s standard deviation. It uses the definition of Standard Deviation. Note that two equations are listed. They are actually one equation written in two different forms by applying the distributive property of multiplication.

Sigma by S:
This method assumes you have a sample and want to infer the population’s standard deviation. It uses an approximation based on subgroup averages and subgroup standard deviations.

Sigma by R:
This method assumes you have a sample and want to infer the population’s standard deviation. It uses an approximation based on subgroup ranges.

Sigma by N (Not used in QC-CALC):
Not on D3-D4. This method assumes you have a population (i.e. you have every single part made by this process in the database and you broke the mold after you measured the last one). You will never make more parts of this type. It uses the definition of Standard Deviation. It is the same as Sigma (either form of the Sigma equation) except you replace the n-1 with n.

Note: Although Sigma by N is not used in any calculatins or equations, it is calculated and sent to several reports. Using the report designer, you can show this value along with the others if you wish.