Quality and Process Methods • Control Chart Builder • Statistical Details for the Control Chart Builder Platform • Control Limits for 3-way charts

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Control Limits for 3-way charts
Within Sigma
The within sigma estimate for 3-way charts is estimated using the average of ranges, so it is only appropriate for the Individual on Means, Moving Range on Means and R chart.
The formula uses the following notation:
Ri = range of ith subgroup
ni = sample size of ith subgroup
d2(ni) = expected value of the range of ni independent normally distributed variables with unit standard deviation
N = number of subgroups for which ni ≥ 2
Between Sigma
The between sigma estimate for 3-way charts is estimated using the moving range of subgroup means.
The formula uses the following notation:
= the mean of the nonmissing moving ranges computed as (MR2+MR3+...+MRN)/(N-1) where MRi = |yi - yi-1|.
d2(2) = expected value of the range of two independent normally distributed variables with unit standard deviation.
, the harmonic mean of subgroup sample sizes.
Note: If between Sigma is estimated as a negative value, it is set to 0.
Between-and-Within Sigma
The between-and-within sigma estimate for 3-way charts is estimated using a combination of the within sigma and between sigma estimates.

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Help created on 3/19/2020