Quality and Process Methods • Control Chart Builder • Statistical Details for the Control Chart Builder Platform • Control Limits for XBar and S-charts

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Control Limits for XBar and S-charts
JMP generates control limits for XBar and S-charts as:
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 3 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
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 deviation of the standard deviation of n independent observations from a normal population with unit standard deviation
N is the number of subgroups for which ni ≥ 2
si is the sample standard deviation of the ith subgroup

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Help created on 3/19/2020