Construction And Related Properties Of Several Kinds Of Designs With Quantitative Factors

As an important branch of statistics,experimental design is widely used in agriculture,industry,medicine and other fields.At first,due to the limitation of industrial level and measurement accuracy,the factors of experimental design are mostly qualitative.Therefore,early experimental design pays more attention to the situation of qualitative factors.Later,with the development of productivity,industrial management became more and more sophisticated,which requires more quantitative factors to be considered when doing experiments.These practical demands also drive the development of experimental design theory,so it is of great practical significance to construct a rational design for quantitative factors.In order to measure the quality of a design,statisticians have proposed various optimality criteria.For example,criteria based on linear models include D-optimal and G-optimal while model-independent criteria include maximum-minimum distance,minimum-maximum distance,orthogonality and uniformity.Furthermore,for practical use;researchers hope to construct an optimal design based on two or more criteria.Among them,the β word-length pattern,which is based on the polynomial model,and model-independent criterion-uniformity,are two important criteria for quantitative factors.Based on the above considerations,the main work of this dissertation is to provide several construction methods for quantitative factorial design and prove the corresponding properties.Furthermore,we improve the design on the basis of satisfying the requirements of physical experiments,so as to achieve the optimal or asymptotic optimal under the corresponding criteria.First,for 3-level supersaturated uniform design,a fast calculation method of β2 has been proposed.Furthermore,level permutation and simulated annealing algorithms have been used to improve β word length pattern of the design on the basis of uniformity.In addition,taking wrap around L2-discrepancy(WD)as the criterion,this dissertation proves that in the sense of average uniformity,the design with higher level will have better uniformity,which shows that designs constructed by the good lattice point method tend to have low discrepancy.Moreover,when the number of tests N is an odd prime number,the design constructed by the good lattice point method is a uniform design under the wrap around L2-discrepancy.In addition,when N is the product of two prime numbers,this dissertation provides an improved method.It proves that by adopting two specific transformations to the design constructed by the original good lattice point method,the obtained new design will have a smaller wrap around L2-discrepancy.After that,properties of the wrap around L2-discrepancy of saturated orthogonal arrays have been studied.When the level of all factors takes the same odd prime,an improved method is proposed to construct saturated orthogonal arrays.The expression for the average wrap around L2-discrepancy of the orthogonal design is given,too.Further theoretical results show that orthogonal array constructed by the proposed method has smaller wrap around L2-discrepancy,which can asymptotically tend to the lower bound.The result is also confirmed by some numerical examples.