Quality and Reliability Methods - SAS

160 Variability Charts Chapter 10
Variance Components
Set Alpha Level
is used for setting the alpha level for the test.
Show Summary Report
given in the plot.
shows or hides a summary report for the test. The report gives the same values
Display Options
is used to show or hide the decision limits, shading, center line, and needles.
Note: The values given in the plots and the Summary Reports are not the group standard deviations, but
the values used in performing the test.
Variance Components
You can model the variation from measurement to measurement with a model. The response is assumed to
be a constant mean plus random effects associated with various levels of the classification. The exact model
depends on how many new random values exist. For example, in a model where B is nested within A,
multiple measurements are nested within both B and A, and there are na•nb•nw measurements. na random
effects are due to A; na•nb random effects due to each nb B levels within A; and na•nb•nw random effects
due to each nw levels within B within A:
y ijk
= u + Za i
+ Zb ij
+ Zw ijk
.
The Zs are the random effects for each level of the classification. Each Z is assumed to have mean zero and
to be independent from all other random terms. The variance of the response y is the sum of the variances
due to each z component:
Var( y ijk
) = Var( Za i
) + Var( Zb ij
) + Var( Zw ijk
).
To request variance components, select Variance Components from the platform popup menu. If you ask
for Variance Components estimates and did not select the type of model in the launch dialog, the window
shown in Figure 10.8 appears.
Figure 10.8 Variance Component Dialog
Table 10.1 shows the models supported and what the effects in the model would be.