Boolean experimental designs

Abstract

Experimental designs are generally interpreted using a polynomial mathematical model. But this mathematical model is not always appropriate and may sometimes not describe the phenomenon studied. Boolean experimental designs can conceived if the factors and the response can be treated as boolean variables. The results provided are then intrepreted using Boolean algebra. We have treated a real example, the setting of an instrument for analytical chemistry using both classical and boolean interpretations. The classical treatment give surprising results, with one strong interaction between two non-influent factors and interactions of order 3 and 4. The boolean interpretation gives comprehensive results and provides simple rules for the instrument settings. Boolean modelling for the responses of an experimental design opens a new and complementary approach to the classical method that uses generally mathematical polynoms. In some cases it can provide a better interpretation of the phenomenon than the ordinary methodology.