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The ANOM Procedure

Constructing ANOM Charts for Two-Way Layouts

This section provides the computational details for constructing an ANOM chart for the th factor in an experiment involving two factors ( = 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:

th response at the th level of factor 1 and the th level of factor 2, where

number of groups (levels) for the th factor,

number of replicates in cell

total sample size

variance of a response

average response in cell

average response for th level of factor 1

average response for th level of factor 2

sample variance of the responses for the th level of factor 1 and the th 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 th 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 th 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

In addition you can:

  • 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.

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