Optimality Of Several Kind Of Important Designs Under Q And Q_B Criteria

First order maximal model is usually used for screening a few important main effects from a large number of potential factors. Q and Q_B criteria can find theoptimal design under many eligible model uncertainty. This paper aims to explore the optimal relationship of original design and the several kind of important designs under first order maximal model based on Q and Q_B criteria. This paper also gives analyticrelationship of Q and Q_B value between original design and these kind of importantdesign separately. Therefore we obtain these kind of important design are the optimal when the original design is the optimal. In addition, some lower bounds of the original design and its double design are derived under Q and Q_B criteria according to the majorization theory of Marshall and Olkin.