The Properties And Applications Of Fractional Factorial Designs Under Quaternary Code

Scientific experiments are essent,ial to the exploration of nature,which are widely used in agriculture,industry,natural sciences and high-tech fields.Experiments aim to compare the importance of various factors in a phenomenon and the effects of their different states;it also can find the numerical regularity between variables in a specific process.In experimental design,the theoretical system of low-level designs is more perfect and it is easier to study and deal with,compared with which of high-level designs.This paper is intended to establish the relationships between low-level designs and high-level designs via quaternary codes,so as to use low-level designs to study the construction and related properties of high-level designs.Based on the above discussions,the dissertation is devoted to the following researches:(1)Construction and properties of large four-level designs under quaternary code.A general method which recursively constructs large four-level designs and quaternary code is proposed for an initial two-level design,and the relationships between large four-level designs and the initial two-level design under generalized minimum aberration criterion and minimum moment aberration criterion are discussed;secondly,the relationships between the average Lee discrepancy of large four-level designs and the generalized minimum aberration criterion and the minimum moment aberration criterion of the initial two-level design are discussed by using the level permutation method respectively;finally,two lower bounds of the mean Lee discrepancy are given for large four-level designs.(2)Theories of J-characteristics for four-level designs under quaternary code.Firstly,the relationship between the minimum G2-aberration criterion of two-level designs and the generalized minimum aberration criterion of their projection sub-designs is discussed;secondly,the definition of J-characteristics for fourlevel designs is given,and the J-characteristics between four-level designs and their corresponding effective two-level sub-designs are connected;finally,relevant upper bounds of J-characteristics for four-level designs are obtained.The confounding frequency vector of the four-level design is given based on the upper bounds,and minimum G-aberration criterion of four-level design is proposed.(3)The uniformity of mixed two-and four-level designs under quaternary code.Firstly,mixed two-and four-level designs are transformed to twolevel designs based on two types of replacement rule,respectively;then,three lower bounds of wrap-around L2-discrepancy are obtained respectively under each type of replacement rule;finally,the uniformity of two-level designs is used to evaluate the uniformity of mixed two-and four-level designs.Four-level designs and mixed two-and four-level designs have extensive and important application in reality,so it is essential to study the properties of fourlevel designs and mixed two-and four-level designs.This paper mainly studies the construction and properties of four-level designs,the J-characteristics of four-level designs and the uniformity of mixed two-and four-level designs from the perspective of quaternary code.And the constructed four-level designs can meet practical application needs to a certain extent.Some theoretical results obtained are in favour of the further study of the J-characteristics of four-level designs,and the obtained bounds of warp-around L2-discrepancy of mixed two-and four-level designs can be served as a benchmark in search of uniform mixed two-and four-level designs.