A Model Robustness Under The Effect Sparsity Principle

In optimal criteria on fractional factorial designs, the minimum aberration (MA) and maximum estimation capacity (MEC) criteria have a kind of model robustness. This model robustness means that it can take care of as many as prssible the models which contain all the main effect and a part of two-factor interactions (2fi's). According to this robustness, any model which contains a large number of effects is treated as the same as the model which contains a few effects. The two criteria and the robustness are based on having no any prior of factors in experiments, i.e. a experimenter does not have any prior about the importance ordering of the factors in his/her experiments. However, in practice usually any experimenter has some information on this. Also, according to the principle of the effect sparsity, which is a common one recognized by people, a model that contains less effects is much more important an more likely appearing than the one which contains a large number of effects. Therefore, the model robustness the MA, MEC criteria have is not suitable for the most of practical situations.Recently, Zhang, Li, Zhao and Ai (2008) proposed a new criterion for choosing oplimal designs, called general minimum lower order confounding criterion. Later on, all the GMC 2n-m designs with N/4+1≤n<≤N-1 have been obtained, where N is the run number of a two-level design. In the paper, we propose a new model robustness which is based on the principle of effect sparsity. We give a basic statement of this new model robustness and make a comparison of GMC designs and MA design. On this new model robustness, including some theoretic results and some examples. We conclude that under this robustness the GMC designs are better than the MA designs.