How is the sigma (standard deviation) used in the Shewhart control chart calculated?Xbar-R Control Chart
Estimate of σ
N is the number of subgroups, n i ≥2, and R i is the sample range of the i -th subgroup , x i1 ,...,x in i .
Xbar-S Control Chart
Estimate of σ
N is the number of subgroups, n i ≥2, and s i is the sample standard deviation of the i -th subgroup.
and
where Γ(·) denotes the gamma function and X-bar i denotes the i -th subgroup mean.
IR Control Chart
The estimate of σ is
R-bar is the average of the moving range.
n is the number of consecutive individual measurements used to calculate the moving range.
d 2 (n) is the expected value of the range of n independent normally distributed random variables with population standard deviation 1.
supplement
d 2 (n) is a value determined by the moving average interval n , and is the following value.
d 2 (2) =1.1283791671
d 2 (3) =1.6925687506
d 2 (4) =2.058750746
d 2 (5) =2.3259289473
d 2 (6) =2.5344127212
d 2 (7) =2.7043567512
d 2 (8) =2.8472006121
d 2 (9) =2.9700263244
d 2 (10) =3.0775054617
