Unreplicated factorial designs are widely used for designed experimentation in industry. In the analysis of designed experiments, the experimental factors influencing the response must be identified and separated from those that do not. An abundance of procedures intended to perform this selection have been introduced in the literature. A recent study indicated that the procedure due to Box and Meyer outperforms the lot of the other selection procedures in terms of efficiency and robustness. The procedure of Box and Meyer rests on a quasi-Bayesian foundation and utilizes generic domain knowledge, in the form of a common-for-all-factors a priori probability, that a factor significantly influences the response, to calculate an a posteriori probability for each factor. This paper suggests a strategy for introducing more elaborate domain knowledge about the experimental factors in the procedure of Box and Meyer, aiming to further improve its performance.