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

Experimental design, as a branch of statistics, studies how to efficiently observe and analyze an examined object by designing suitable experiments, which plays an important role for the development of statistics.In many experimental, there are often many dependent variables which may af-fect the object as response variable. So a main subject in designing experiments is to consider the designs which involve many factors.With the increase of number of fac-tors, response to the exponential growth. If the number of factors in a design is large, the run number of a full design is too large so that it is often impossible to carry out in practice because of the huge cost or time consumption. So fractional factorial ex-periments are more suitable in practice. For this reason, the most of investigations in the past of decades are focused onto consider fractional factorial designs and to select optimal one among them. Zhang et al?2008? introduced a new pattern for assessing regular designs, called aliased effect-number pattern ?AENP?, and based on the AENP and effect hierarchy principle ?EHP?, proposed a general minimum lower order con-founding ?GMC? criterion for selecting design.The optimal designs selected by GMC criterion are called GMC designs. But not in all of the designs,the main effect is most important,especially in the chemical experiment, participants want to know 3th-order effect or more order effect,not only the role of each material. in this paper,we will give priority to estimating the effect of 3th-order effect fractional factorial experiments. In this paper,I mainly completed the research on some problems including the following:?1?For a priority in estimating the 3th-order effect, we introduce a new criterion for selecting optimal designs which can preferentially estimate three-factor interac-tions, called aliased effect number pattern with the priority of three-factor interactions ? U₃-AENP?.And establish corresponding optimality criteria, To get the optimal design call the U₃-GMC.?2? We give a computation method for constructing the optima designs with pref-erentially estimating three-factor interactions.?3? And then put forward in a blocked regular design 2^n-m:2^r we introduce a new criterion for selecting optimal designs which can preferentially estimate three-factor interactions and tabulate all the optimal designs when the experiment number N is 16.?4? 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 GMC designs. Also, we tabulate all the optimal designs when the experiment number N is 16,32,64 for application.