The Heuristic Approach to the Selection of Experimental Design, Model and Valid Pre-Processing Transformation of DoE Outcome

Abstract

The typical problem in design of experiments methodology is to avoid risk of obtaining predictions outside of ranges with technological or physical sense. Such situation occurs very often if a simple linear regression or other unbounded is involved as a predictive model. The possible solution is to provide mappings of the outcome from the range of interest into the full range from negative to plus infinity before the linear regression is applied. The intermediate values obtained from unbounded predictive model is re-transformed into the physical domain by the inverse transformation. The key issue is to decide if the mapping is required and subsequently what mapping is necessary. Author proposed a simple heuristic supporting this decision and tested such solution in some examples described in this paper.