Methods and formulas for Multivariate EWMA Chart

where:

Z_i, the MEWMA vector, represents the weighting of previous subgroups.

where:

X_i, the subgroup mean vector, =

= the weighted covariance matrix

where:

S is the sample covariance matrix. For more information on calculating the S matrix, go to Tsquared plotted point.

Notation

The program used to calculate the upper control limit for the MEWMA chart is described in Bodden et al.¹

Box-Cox formula

If you use a Box-Cox transformation, Minitab transforms the original data values (Y_i) according to the following formula:

where λ is the parameter for the transformation. Minitab then creates a control chart of the transformed data values (W_i). To learn how Minitab chooses the optimal value for λ, go to Methods and formulas for Box-Cox Transformation.

Common λ values

The following table shows some commonly used λ values and their transformations.

λ	Transformation
2
0.5
0
−0.5
−1