How is the sigma (standard deviation) used in moving average control charts calculated?EWMA and UWMA control charts
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.
where
represents the gamma function
denotes the i subgroup mean.
Subgroup standard deviations, s i , can be included in the calculation only if n i ≥ 2.
When the observations follow a normal distribution, the expected value of s i is c 4 (n i )σ .
therefore, 
is the simple average of the N unbiased estimates of σ.
When the sample size for each subgroup is 1 ( n i =1), the process standard deviation, σ, is estimated by the following formula:
where N is the number of observations and x i ,x 2 ,...,x n are the individual measurements.
