Retrospective factorial fitting and reverse design of experiments

Abstract

In the traditional use of design of experiments (DOE), an experiment is carried out where the input factors are varied according to a systematic plan. The data are then analysed in the usual way, but not before all of the required response values are available. A procedure called 'Reverse DOE' is presented for retrospectively selecting and fitting a fractional factorial design in situations where observed data are already available. This takes into account a set of factor effects that need to be estimated and also handles the possibility that certain treatment conditions may not be available or observed. A worked example from the steel industry is presented to illustrate the procedure. The procedure is expected to be useful in the early stages of experimentation and discovery, especially for factor screening purposes.