Optimal Blocked Two-level Regular Designs With Prior Estimating Two-factor Interactions

Design of experiments is a important branch of statistics, it is very important to the development of modern statistics.In different kinds of design of experiments, more factors are concerned usually. Hence, factorial experiment and its analysis are paid more attention by the researchers. Because of economy and other reasons, how to obtain suitable designs, especially the optimal designs, is significantly concerned by the researchers. Choose optimally designing factorial experiments from all fractional factorial designs is the most popular and important issue, and it has received significant attention in the recent decades. In many practical experiments, Researchers have a prior knowledge about the important factors and prefer to pay more attention to the important effects, they also hope estimate the associated interactions of the important factors effciently. In general condition, it is believed that main effects are more important than interactive effects. However, there are some designs whose two-factor interactions are the most important. For this reason,we need to develop systems theory and practical application that are suitable for this situation.My essay mainly research this important issue. In this paper, We focus on investigating the following issues:（1） For a blocked regular design 2^n-m: 2rwe introduce a new criterion for selecting optimal designs which can preferentially estimate two-factor interactions, called blocked aliased effect number pattern with the priority of two-factor interactions.（2） By using the new criterion, we give a computation method for constructing the optima 2^n-m: 2rdesigns with preferentially estimating two-factor interactions.（3） We give some theoretical results related the new criterion and some examples of this kind of optimal designs. Furthermore, we make some comparisons with the B1- GMC designs which are under the usual effect hierarchy principle. Also, we tabulate all the optimal 2^n-m: 2rdesigns when the experiment number N is 16 for application.