| Design of experiment plays a vital role in statistics,which has been widely used in food science,biomedicine,aerospace and so on.It is inseparable from the design of experiment to carry out the experiment scientifically.In order to facilitate practical application,it is of great significance to construct excellent designs with different run sizes.With the development of science and technology,there are more and more factors involved in the experiment,and the levels of each factor are much more than before.At this time,the number of run sizes in full factorial designs greatly exceed the tolerance of researchers.For reasons of run size economic,fractional factorial design is widely used,which is a subset of the full factorial design.One of the most important tasks of the experiment is to select the "good" design from many factorial designs,which get the most useful information with the least run sizes.As for the“good”designs,various optimality criteria have been proposed from certain balance properties.Such as:resolution,generalized minimum aberration,minimum moment aberration and discrepancy.With the increase of the number of factors and run sizes in design,it will be difficult to construct directly,while the small designs with excellent properties are easy to obtain.There are many symmetrical amplified designs are constructed by using the small designs with excellent properties through amplifying in the literature.Through the study,it is easy to find that the design constructed by amplifying also has excellent properties.However,compared with symmetrical design,the constructions and properties of asymmetrical ones are more complex.Based on the above discussions,this paper mainly focuses on the following researches:(1)Discussing the method of constructing mixed two-and three-level uniform designs with large run sizes by level permutation and foldover,and the connections between the constructed designs and the initial designs under the uniformity criterion,E(fNOD)criterion and generalized minimum aberration criterion is studied.(2)Discussing the method of constructing mixed two-and four-level uniform designs with large run sizes by level permutation and foldover,and the connections between the constructed designs and the initial designs under the uniformity criterion,generalized minimum aberration criterion,E(fNOD)criterion and minimum moment aberration criterion is studied.(3)Discussing the method of constructing mixed two-and q-level uniform designs with large run sizes by level permutation and foldover,and the connections between the constructed designs and the initial designs under the uniformity criterion,E(fNOD)criterion and minimum moment aberration criterion is studied.In this paper,a series of large run sizes and optimal space-filling designs are obtained.These designs will have a wide application prospect in the fields of industry and agriculture,chemical industry,biomedicine,computer experiments and natural sciences.At the same time,it provides convenience and guidance for the arrangement and implementation of the experiment.The theoretical and numerical results of the study will further enrich and improve the theory of factorial designs and space-filling designs. |
