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Experimenters are not always aware of what the noise variables are, or can not organize an experiment with them. However, they know that the observations are heteroscedastic, i.e. their variance varies with the factor levels. In this situation once again we come across the problem of variance minimization, while keeping the mean value on a target. A model-based solution is readily obtainable on the basis of repeated observations. They make possible the estimation of mean value and variance at each design point as well as the subsequent derivation of regression equations, which can give the solution of quality improvement problem by optimization procedures similar to one of those, considered in Chapters 6 and 7. This approach is discussed further in Section 10.2. Graphical tools for studying individual location and dispersion effects of factors and their interactions are presented in subsection 10.2.4. They use repeated observations, but with some modifications are applicable for non-replicated experiments (Section 10.3) as well. In Section 10.4 we discuss how the information about the individual effects can simplify the optimization procedures using PERformance Measures Independent of Adjustment (PERMIA). Multiple response optimization via constrained confidence regions is briefly discussed in this section as well. |
