| Design of experiments is one of the most important branches of statistics, it greatly promotes the development of modern statistics. With the rapid development of science and technology,both the industrial and agricultural production, or biotech-nology, medical technology, space technology and so on are all cannot do without test. But a scientific test cannot do without the test design.The frequently used experimental design involves random design, block design, factorial design, computer design, and so on.With the development of science and technology, more factors are concerned in experiments. Hence, factorial experiment is paid more attention. An experiment in-volving k(≥2) factors that respectively appear at s1,..., sk (≥2) levels is called as an s1×...× sk full factorial experiment, and the corresponding design to plan the experi-ment is full factorial design. Especially, if s1…= Sk=s, it is called a symmetrical sk factorial; otherwise it is called an asymmetrical factorial.Full factorial design are not tolerant to the experimenters and researches, because of economy and other rea-sons. Hence, fractional factorial design is introduced and applied. It is a fraction of a full factorial design, which involves all possible treatment combinations. If a frac-tional factorial design can be constructed by defining relations, it is said to be regular and means that the design has simply confounding structures; otherwise, it is said to be nonregular.[1] In recent decades, fractional factorial design in various fields have< wide range of applications.In the design, the experimental units of nonhomogeneity can not be ignored. Es-pecially when the number of the test unit is relatively large, the method of blocking Is very effective. In this method, the reasonable arrangement of the tests makes the dif-ferences in unit block smaller than the differences between the blocks of units. Then by comparing the treatment in the same block, the blocking effect is eliminated in the comparison with treatment effects, so as to make the test more effective. Therefore, blocked fractional factorial design is affected by the attention of scholars.The problem of how to find the optimal design is very important, a large num-ber of scholars research on it. Quite a few criteria for selecting optimal designs have been proposed. Among them, the maximum resolution (MR, in short), clear effects (CE, in short) maximum estimation capacity (MEC, in short), minimum aberration (MA, in short), a general minimum lower order confounding (GMC, in short) cri-terion and weak minimum aberration criteria (weak-MA, in short) become popular ones. Many literature devoted to studying and popularizing these criteria.Therefore, so far, the (MA) criterion put forward by Fries & Hunter in 1980 is often used.For any two 2k-p designs d1 and d2 r is the smallest integer making Ar(d1) not equal to Ar(d2) .If Ar(d1) is smaller than Ar(d2),we say d1 has lower order confounding than d2. If there is no design that has lower order confounding than d1,we say d1 has minimum aberration (MA). Owing to (MA) needs to compare the wordlengths of two designs, that’s too complicated. The weak minimum aberration resolves this problem.It only needs to minimize the first nonzero element.This paper is the application of weak MA criteria to find the optimal design. In this paper 《Blocked two-level regular factorial designs with weak minimum aberra-tion》 published by Zhao, Li & Karunamuni in 2013, in this case of n≤N/2, the author found the blocked two-level regular factorial designs 2n-k:2P with weak min-imum aberration. But when n> N/2, it did not give the corresponding optimal weak-MA designs. This is an interesting problem. In this paper we will focus on to solve the following problems:1. Construction of the blocked two-level regular factorial designs 2n-k:2P with weak minimum aberration and n> N/2.2. Calculation of A2,1 and A3,0 of the design 2n-k:2P with n> N/2.3. Why is the A2,1(Dt) minimized under the average distribution for constructing the optimal design?... |
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