An alternative strategy to the use of center points in the analysis of fractionated experiments

In preliminary experimentation, fractionated factorial designs are sometimes augmented with a few runs at the center point, which allow to estimate the error variance and thus perform conventional tests of significance for assessing factor influence. Unfortunately these analyses may not lead to firm conclusions. In this paper, we argue that a better strategy is to only conduct the factorial portion of the design, and analyze the data through an available Bayesian method that helps uncover the active factors in unreplicated fractional designs. If the results of this analysis are conclusive, we save additional runs. Alternatively, a few follow-up experiments may be added with a method, still in a Bayesian framework, especially useful for sorting out the active factors. In this case, a Bayesian analysis can be carried out using all the available data. This further analysis generally allows to clearly identify the factors with major influence. Our reasoning is explained with an illustrative chemical example.