Construction And Application Of Combined Design Based On Column Foldover And Column Permutation

Foldover is a commonly used follow-up strategy in experimental designs. In order to break up the aliased effects, foldover is a commonly used follow-up method-ology by reversing the sign?s? of one or more factors in the initial design, and the resulted design is called as foldover design. The full design obtained by joining the runs in the foldover design to those of the initial design is called the combined design.Resolution is an important way to measure the merits of design. In general, the higher resolution represent more excellent for a design. The resolution of the combined design may be improved compared to the initial design under the suitable foldover plan. However, the resolution of the combined design cannot be effectively improved in general case. Therefore, a feasible and effective method to improve the resolution of the combined design is by using the combination of foldover and column permutation.There are many foldover and column permutation plans for a given initial de-sign. Moreover, the properties such as the resolution, wordlength pattern and uni-formity of the combined design are also related to the order of the combination of foldover and column permutation. Considering the above situations, it will be con-venient to the construction of the combined design if we can summarize the general theoretical results about the relationship between the resolution and the foldover and column permutation plans.Based on the above discussions, the dissertation is devoted to the following researches:?1? discussing the resolution of regular design and nonregular design in the construction of the combined design under column foldover and column permutation, and giving the relevant conclusions.?2? discussing the wordlength pattern of regular design and nonregular design in the construction of combined design under column foldover and column permutation, and discussing the relationship between the initial design and combined design in terms of uniformity measured by the centered L₂-discrepancy of is obtained.?3? discussing the condition when the combined design constructed by differ- ent order in the combination of column foldover and column permutation is same, and the condition when the combined design have same resolution, the wordlength pattern and the centered L₂-discrepancy in different column foldover and column permutation plans.In the following, let us introduce the contents of each chapter in brief.Chapter 1 summarizes some related background of experimental de-sign and the innovation and structure of this dissertation.Chapter 2 briefly introduces some basic concepts, formulas that will be used in the other chapters.Chapter 3 mainly studies resolution, the wordlength pattern and the centered L₂-discrepancy of combined design. Focus on feature of regular design and nonregular design, this chapter make use of indicator function to studies the change of resolution, the wordlength pattern and the centered L₂-discrepancy in the process of construction of combined design by column foldover and column permutation.Chapter 4 mainly studies the different way to construct combined design with same resolution, the word length pattern and the centered L₂-discrepancy by column foldover and column permutation. Given the column foldover and column permutation plan, the result will changing when the order and combination of column foldover and column permutation is exchanged. Considering the above situation, this chapter discusses the condition when the combined design constructed by different order of column foldover and column permutation is same, and the condition when the combined design have same resolution, the wordlength pattern and the centered L₂-discrepancy by different combination of column foldover and column permutation.Chapter 5 gives some examples of the application of the theoretical results in Chapters 3 and 4.Chapter 6 summarizes the dissertation and prospects in the future work.