# XCHART Statement: ANOM Procedure

#### Constructing ANOM Charts for Two-Way Layouts

This section provides the computational details for constructing an ANOM chart for the lth factor in an experiment involving two factors (l = 1 or 2). It is assumed that there is no interaction effect. See Example 4.5 for an illustration.

The following notation is used in this section:

 kth response at the ith level of factor 1 and the jth level of factor 2, where number of groups (levels) for the lth factor, number of replicates in cell N total sample size variance of a response average response in cell average response for ith level of factor 1 average response for jth level of factor 2 sample variance of the responses for the ith level of factor 1 and the jth level of factor 2 mean square error (MSE) in the two-way analysis of variance degrees of freedom associated with the mean square error in the two-way analysis of variance significance level critical value for analysis of means in a one-way layout for groups (treatment levels) when the sample sizes for each level are constant and is the degrees of freedom associated with the mean square error; see the section Constructing ANOM Charts for Means.

##### Plotted Points

The points on the ANOM chart for factor 1 represent , and the points on the ANOM chart for factor 2 represent , .

##### Central Line

The central line on the ANOM chart for the lth factor is the overall weighted average . Some authors use the notation for this average.

##### Decision Limits

It is assumed that

where the quantities are independent and at least approximately normally distributed with

The correct decision limits for a given factor in a two-way layout are not computed by default when the lth factor is specified as the group-variable in the XCHART statement, since the mean square error and degrees of freedom are not adjusted for the two-way structure of the data. Consequently, and must be precomputed and provided to the ANOM procedure, as illustrated in Example 4.5.

In the case of a two-way layout with equal group sizes (), the appropriate decision limits are:

where the mean square error (MSE) is computed as in the ANOVA or GLM procedure:

and the degrees of freedom for error is . For details concerning the function , see Nelson (1982a, 1993).

You can provide the appropriate values of MSE and by

• specifying with the MSE= option or with the variable _MSE_ in a LIMITS= data set

• specifying with the DFE= option or with the variable _DFE_ in a LIMITS= data set

• Specify with the ALPHA= option or with the variable _ALPHA_ in a LIMITS= data set. By default, .
• Specify a constant nominal sample size for the decision limits in the balanced case with the LIMITN= option or with the variable _LIMITN_ in a LIMITS= data set.
• Specify with the LIMITK= option or with the variable _LIMITK_ in a LIMITS= data set.
• Specify with the MEAN= option or with the variable _MEAN_ in a LIMITS= data set.