Some results on 4~m2~n designs with clear two-factor interaction components

Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent years.Tang et al.derived upper and lower bounds on the maximum number of clear two-factor interactions(2fi's) in 2n-(n-k) fractional factorial designs of resolutions III and IV by constructing a 2n-(n-k) design for given k,which are only restricted for the symmetrical case.This paper proposes and studies the clear effects problem for the asymmetrical case.It improves the construction method of Tang et al.for 2n-(n-k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components(2fic's) in 4m2n designs with resolutions III and IV.The lower bounds are achieved by constructing specific designs.Comparisons show that the number of clear 2fic's in the resulting design attains its maximum number in many cases,which reveals that the construction methods are satisfactory when they are used to construct 4m2n designs under the clear effects criterion.

Circular neighbor-balanced designs universally optimal for total effects

In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.

Universal optimality of digital nets and lattice designs

This article considers universal optimality of digital nets and lattice designs in a regression model. Based on the equivalence theorem for matrix means and majorization theory,the necessary and sufficient conditions for lattice designs being φp-and universally optimal in trigonometric function and Chebyshev polynomial regression models are obtained. It is shown that digital nets are universally optimal for both complete and incomplete Walsh function regression models under some specified conditions,and are also universally optimal for complete Haar wavelet regression models but may not for incomplete Haar wavelet regression models.