Publication date: 03/23/2021

## Control Limits for XBar and S Charts

JMP generates control limits for XBar and S charts using the following formulas:

LCL for XBar chart =

UCL for XBar chart =

LCL for S chart =

UCL for S chart =

Center line for S chart: By default, the center line for the ith subgroup (where K is the sigma multiplier) indicates an estimate of the expected value of si. This value is computed as , where is an estimate of σ.

The estimate for the standard deviation for XBar and S charts is:

where:

= weighted average of subgroup means

K = the sigma multiplier and is set to 3 by default

σ = process standard deviation

ni = sample size of ith subgroup

c4(n) is the expected value of the standard deviation of n independent normally distributed variables with unit standard deviation

c5(n) is the standard error of the standard deviation of n independent normally distributed variables with unit standard deviation

N is the number of subgroups for which ni ≥ 2

si is the sample standard deviation of the ith subgroup