Sigma (σ ) is the standard deviation of the process. If you specify the standard deviation, then Minitab uses the historical value. Otherwise, Minitab uses one of the following methods to estimate σ from the data.

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:

Term | Description |
---|---|

r_{i} | range for subgroup i |

m | number of subgroups |

d_{2}(·) | value of unbiasing constant d_{2} that corresponds to the value specified in parentheses. |

n_{i} | number of observations in subgroup i |

d_{3}(·) | value of unbiasing constant d_{3} that corresponds to the value specified in parentheses. |