Research On The Construction And Properties Of A Type Of Special Space-filling Design

Follow-up experiments are widely applied to explore the relationship between inputs(factors)and outputs(responses)step by step in various fields such as science and engineering.When some additional resources or information become available after the initial design of experiment is carried out,some additional runs and/or factors will be added in the follow-up stage.Augmented design is a follow-up experimental method.This method can add the number of runs and/or the number of factors in the follow-up stage.For symmetrical design,the augmented design was constructed by the multiplication method,the quality of its initial design affects the quality of the augmented design,but the research on how to select a good initial design and then apply it to the augmented design is rare.For asymmetric design,at present,the research of augmented designs mainly focuses on mixed two-and three level case,but mixed two-,three-and four-level fractional factorial designs are the most popular among mixed fractional factorial in practice.Based on the above discussions,the dissertation is devoted to the following researches:Chapter 3 mainly studies the uniformity of the three-level Triple design under the average squared centered L2-discrepancy and some related problems.For three-level fractional factorial design,the uniformity of three-level Triple design is discussed under the average squared centered L2-discrepancy,and the analytic relation between the three-level Triple design and its initial design is established.Chapter 4 mainly studies the uniformity of the four-level Quadruple design under the average discrepancy and some related problems.For four-level fractional factorial design,the method of constructing the four-level Quadruple design is optimized;the relationship between the average squared centered L2-discrepancy and the average squared wrap-around L2-discrepancy of the Quadruple design and its initial design generalized word length is established;the uniformity of four-level Quadruple design is discussed under the average squared centered L2-discrepancy and average squared wrap-around L2-discrepancy,respectively.Chapter 5 mainly studies the construction theory about the asymmetrical uniform augmented design and the lower bounds of the wraparound L2-discrepancy.For the mixed two-,three-and four-level design,the construction scheme and uniformity of row augmented design and column augmented design are studied.The quantitative relationship between the row augmented designs and the initial designs or the follow-up designs based on the lower bound of wrap-around L2-discrepancy is established.The uniformity of column augmented design with additional mixed three-and four-level factors and an additional blocking factor is investigated,respectively.