Methods and formulas for Multivariate EWMA Chart

Select the method or formula of your choice.

Methods and formulas for MEWMA statistic for Multivariate EWMA chart


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


Xi, the subgroup mean vector, =

= the weighted covariance matrix


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


nsubgroup size
Ssample covariance matrix. For more information on calculating the S matrix, see T-squared statistic

Methods and formulas for control limits for Multivariate EWMA chart

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

Methods and formulas for Box-Cox

Box-Cox formula

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

where λ is the parameter for the transformation. Minitab then creates a control chart of the transformed data values (Wi). 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
1 K M. Bodden and S E. Rigdon (1999). A Program for Approximating the In-Control ARL for the MEWMA Chart. Journal of Quality Technology, 31,January, 120−123.