Box-Cox-Transformed I-MR Control Chart

Box-Cox transform with auto λ via Anderson-Darling, I-MR on the transformed scale, back-transformed limits.

Statusvalidated
Version1.0.0
Minitab equivalentStat > Control Charts > Variables Charts for Individuals > I-MR (Box-Cox option)

Description

Box-Cox y = (x^λ−1)/λ for λ ≠ 0, y = ln(x) for λ = 0. λ is searched on a [−3, 3] grid (step 0.05) via the Anderson-Darling statistic. I-MR is computed on y. Limits are back-transformed to the original scale for display (asymmetric — correct for right-skewed data).

Formulas

Box-Cox
x > 0 required
Inverse

References

  • Box, G. E. P. & Cox, D. R. (1964), An analysis of transformations