Construction Of Factorial Designs Research Articles

A new foldover strategy and optimal foldover plans for three-level design

The foldover is a useful technique in construction of factorial designs. It is also a standard follow-up strategy discussed in many textbooks by adding a second fraction called a foldover design. In this paper uniformity criterion measured by the wrap-around $$L_2$$ -discrepancy is used to further distinguish the optimal foldover plan for three-level designs. For three-level fractional factorials as the original designs, a new foldover strategy is provided based on level permutation of each factor, which vastly enlarge the full foldover space. Some theoretical properties of the defined foldover plans are obtained, a tighter lower bound of the wrap-around $$L_2$$ -discrepancy of combined designs is also provided, which can be used as a benchmark for searching optimal foldover plans. For illustration of our theoretical results and comparison with the existing results, a catalog of optimal foldover plans of the new strategy for uniform initial designs with s three-level factors is tabulated, where $$2\le s \le 11$$ .

Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy

Literatures reveal that foldover is a useful technique in construction of factorial designs. The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around \(L_2\)-discrepancy to assess the optimal foldover plans for asymmetric fractional factorials. A general foldover strategy and combined design under a foldover plan are developed for asymmetric fractional factorials, some theoretical properties on the equivalence between the defined foldover plan and its complementary foldover plan are discussed. A new lower bound for the wrap-around \(L_2\)-discrepancy of combined designs is obtained, which can be used as a benchmark for searching optimal foldover plans. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.

Kronecker factorial designs for multiway elimination of heterogeneity

This paper considers the application of Kronecker product for the construction of factorial designs, with orthogonal factorial structure, in a set-up for multiway elimination of heterogeneity. A technique involving the use of projection operators has been employed to show how a control can be achieved over the interaction efficiencies. A modification of the ordinary Kronecker product yielding smaller designs has also been considered. The results appear to have a fairly wide coverage.