How is the standard deviation calculated for different Shewhart control charts?
XR Charts The estimate for σ is where N is the number of subgroups for which ni>2, and Ri is the sample range of the observations xi1,…,xin in the ith subgroup XS Charts The estimate for σ is where N is the number of subgroups for which ni>2, and si is the sample standard deviation of the ith subgroup and Here Γ(·) denotes the gamma function and X-bari denotes the ith subgroup mean.