Some New Results On θ And θ_B Criteria

Minimum projection uniformity is introduced to compare two level designs. To explore the projection efficiency of a design under uncertainty,Tsai(2000) introduced theθcriterion to compare main-effects designs for quantitative factors that allow the cinsideration of interactions in addition to main effects. Tsai(2005) generalized the 9 criterion to the case where experimenters have some prior knowledge of the probabilities of effects being non-negligible in advance of collecting their data. Theθ_b criterion was proposed,in which each of the low-dimensional submodels is weighted to reflect experimenters' prior knoowledge about different parameters.If a model is more likely to be the best among the eligible models,then the model is given more weight. The relationship between the Minimum Projection Uniformity and theθ,θ_B criteria is explored in this paper, which will help us know more about the relationship between them.we use Double design to constract two level design,especially the resolution IV's design.the paper discuss theθ,θ_b criteria of Double design D(X),we found that theθ,θ_b criteria of Double design D(X) has close relationship with heθ,θ_b criteria of design X.