On Experimental Planning For GMC Designs With Some Parameters

Design of experiments is an important branch of statistics and its application field is constantly expanding. Among experimental design, more factorial plan(i.e.,factorial design) is very important and basic research field. To achieve the optimization of the actual experiments, two kinds of research problems: one is how to find the optimal design; the other is how to arrange the factors to the columns of the optimal design in order to achieve the optimal accuracy of experiment and analysis. For the former there are lots of theoretical results and all kinds of optimal design structure results. While in the latter case, some of the system theory and application research results appear in recent years. For this case, to two level regular factorial design class, Zhou,Balakrishnan& Zhang[1]introduces a new pattern — factor aliased e?ect number pattern(F-AENP)as a measure, columns in the design and its associated e?ect mixed the degree of severity index.And according to e?ect hierarchy principle, provide the sorting of columns.At the same time,to two level regular factorial design class,the optimal design, GMC design class, the degree of each column aliased is provided with 5N/16 + 1 ≤ n < N/2and N/2 ≤ n ≤ N- 1 following F-AENP. These results provides a convenient for participants in arranging the important factors in turn to the corresponding columns to achieve the optimal experiments and analysis.According to Zhang & Cheng[2]has given in detail that up to isomorphism, all the GMC 2n-mdesigns with 9N/32 + 1 ≤ n < 5N/16, 17N/64 + 1 ≤ n < 9N/32 and 33N/128 + 1 ≤ n < 17N/64 uniquely are the projection of S(5N/16),S(9N/32) and S(17N/64) and consist of the last n columns of saturated design Hqwith RC Yates order,respectively. In that case,it is necessary to complete the calculation of F-AENP with n = N/2,n = 5N/16,n = 9N/32. The present dissertation is devoted to the calculation of F-AENP with n = N/2,n = 5N/16,n = 9N/32 of GMC designs, and rank the columns. It is also provided a foundation of the F- AENP of GMC in the above three areas. Each conclusion is provided in the form of propositions and attach with examples, to facilitate the reader to understand. Then calculation of F-AENP of each column with 9N/32 + 1 ≤ n < 5N/16 is provided in a theoretical formula and descends the design columns and a simple example, for later study.