Level Permutation Method For Constructing Mixed Level Uniform Designs Under The Wrap-around L₂-discrepancy

In the field of uniform experimental design, sometimes it is hard to ensure that the levels of the different factors are equal, so that it is difficult to arrange test with symmetrical uniform design directly. Recently, Tang etc. defined the concept of average centered L2-discrepancy( ACD(D)), and established a relationship between the generalized word length pattern and ACD(D). Based on this relationship, they further propose a construction method for uniform designs under the centered L2-discrepancy. Similarly, the current paper aims to propose a new method for constructing the mixed uniform designs under the wrap-around L2-discrepancy by permuting factor levels. According to the relationship between AWD(D) and generalized word length pattern, we first employ a minimum aberration design as the starting design, then conduct all the level permutations, calculate WD(D), and finally obtain the best design. The designs constructed via this approach perform well under both the generalized word length pattern and the wrap-around L2-discrepancy.