For replicated two level factorial experiments, DOE++ provides the option of conducting variability
analysis (using the Variability Analysis icon in the Control Panel). The
analysis is used to identify the treatment that results in the least amount
of variation in the product or process being investigated. Variability
analysis is conducted by treating the standard deviation of the response
for each treatment of the experiment as an additional response. The standard
deviation for a treatment is obtained by using the replicated response
values at that treatment run. As an example, consider the 2 design shown in Figure 7.30
where each run is replicated four times. A variability analysis
can be conducted for this design. DOE++ calculates eight standard deviation
values corresponding to each treatment of the design (see Figure 7.31). Then, the design is analyzed as an unreplicated
2 design with the standard deviations
(displayed as Y Std. in Figure 7.31) as the response.
The normal probability plot of effects identifies as the effect that influences variability
(see Figure 7.32). Based on the effect coefficients
obtained in Figure 7.33, the model for Y Std. is:Based on the model, the experimenter
has two choices to minimize variability (by minimizing Y Std.). The first
choice is that should be (i.e. should be set at the high level) and
should be (i.e. should be set at the low level). The
second choice is that should be (i.e. should be set at the low level) and
should be (i.e. should be set at the high level).
The experimenter can select the most feasible choice.
Figure 7.30: A 2³ design with four replicated response
values that can be used to conduct a variability analysis.
Figure 7.31: Variability analysis in DOE++.
Figure 7.32: Normal probability plot of effects for the
variability analysis example.
Figure 7.33: Effect coefficients for the variability analysis
example.
design shown in Figure 7.30
where each run is replicated four times. A variability analysis
can be conducted for this design. DOE++ calculates eight standard deviation
values corresponding to each treatment of the design (see Figure 7.31). Then, the design is analyzed as an unreplicated
2
design with the standard deviations
(displayed as Y Std. in Figure 7.31) as the response.
The normal probability plot of effects identifies 
as the effect that influences variability
(see Figure 7.32). Based on the effect coefficients
obtained in Figure 7.33, the model for Y Std. is:
Based on the model, the experimenter
has two choices to minimize variability (by minimizing Y Std.). The first
choice is that 
should be 
(i.e. 
should be set at the high level) and
should be 
(i.e. 
should be set at the low level). The
second choice is that 
should be 
(i.e. 
should be set at the low level) and
should be 
(i.e. 
should be set at the high level).
The experimenter can select the most feasible choice.
