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Quality and Process Methods > Control Chart Builder > Statistical Details for Control Chart Builder > Control Limits for XBar and R Charts
Publication date: 09/28/2021

Control Limits for XBar and R Charts

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

LCL for XBar chart = Equation shown here

UCL for XBar chart = Equation shown here

LCL for R chart = Equation shown here

UCL for R chart = Equation shown here

Center line for R chart: By default, the center line for the ith subgroup (where K is the sigma multiplier) indicates an estimate of the expected value of Ri. This value is computed as follows: Equation shown here, where Equation shown here is an estimate of σ.

The standard deviation for XBar and R charts is estimated using the following formula:

Equation shown here

where:

Equation shown here = 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

d2(n) is the expected value of the range of n independent normally distributed variables with unit standard deviation

d3(n) is the standard deviation of the range of n independent normally distributed variables with unit standard deviation

Ri is the range of ith subgroup

N is the number of subgroups for which ni ≥ 2.

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