Sigma (σ) is the standard deviation of the process. If you enter an historical value for σ, then Minitab uses the historical value. Otherwise, Minitab uses one of the following methods to estimate σ from the data.
In This Topic
Average moving range method
The average moving range, 
, of length w is given by the following formula:
where MRi is the moving range for observation i, calculated as follows:
Minitab uses 
to calculate Smr, which is an unbiased estimate of σ:
Notation
| Term | Description |
|---|---|
| n | number of observations |
| w | length of the moving range. The default is 2. |
| d2() | value of unbiasing constant d2 that corresponds to the value specified in parentheses. |
Median moving range method
The median moving range, 
, of length w is given by the following formula:
where w is the number of observations used in the moving range and MRi is the moving range for observation i, calculated as follows:
Minitab uses 
to calculate Smr, which is an unbiased estimate of σ:
Notation
| Term | Description |
|---|---|
| n | number of observations |
| w | length of the moving range. The default is 2. |
| d4() | value of unbiasing constant d4 that corresponds to the value specified in parentheses. |
Square root of MSSD method
MSSD stands for the mean of squared successive differences. The square root of the MSSD (SRMSSD) is calculated as follows:
With unbiasing constant
Without unbiasing constant
Notation
| Term | Description |
|---|---|
| di | difference between the value of observation i and the value of observation i – 1 |
| N | number of observations |
| c4'(N) | unbiasing constant from a table |
Rbar method
Minitab uses the range of each subgroup, 
, to calculate 
, which is an unbiased estimator of σ:
where
When the subgroup size is constant, the formula simplifies to the following:
where 
(Rbar) is the mean of the subgroup ranges, calculated as follows:
Notation
| Term | Description |
|---|---|
| ri | range for subgroup i |
| m | number of subgroups |
| d2(·) | value of unbiasing constant d2 that corresponds to the value specified in parentheses. |
| ni | number of observations in subgroup i |
| d3(·) | value of unbiasing constant d3 that corresponds to the value specified in parentheses. |
Sbar method
Without unbiasing constant
If you do not use an unbiasing constant, then the Sbar is the mean of the subgroup standard deviations:
With unbiasing constant
If you use the unbiasing constant, c4(ni), then Sbar is calculated as follows:
When the subgroup size is constant, Sbar is:
Notation
| Term | Description |
|---|---|
| c4 (ni) | value of the unbiasing constant c4 that corresponds to the value that is specified in parentheses. |
| Si | standard deviation of subgroup i |
| m | number of subgroups |
Pooled standard deviation method
The pooled standard deviation (Sp) is given by the following formula:
When the subgroup size is constant, Sp can also be calculated as follows:
With unbiasing constant
By default, Minitab applies the unbiasing constant, c4(), when you use the pooled standard deviation to estimate σ:
Notation
| Term | Description |
|---|---|
| xij | jth observation in the ith subgroup |
 | mean of subgroup i |
| ni | number of observations in subgroup i |
| μv | mean of the subgroup variances |
| c4(·) | value of the unbiasing constant c4 that corresponds to the value that is specified in parentheses. |
| d | degrees of freedom for Sp, given by the following formula:
 |
