Consider the problem of selecting a two-level factorial design. It is well known that two-level orthogonal arrays of strength 4 or more with "e" extra runs have various optimality properties including generalized Cheng (type 1) optimality when "e"=1, restricted Cheng (type 1) optimality when...

Schur-optimality is a very general class of optimality criteria that includes, as special cases, A- D- and E-optimality and Cheng Type 1 optimality. In this paper, Schur-optimal two-level factorial designs under a second-order model are derived for 3 and 5 factors for all numbers of runs where...

This paper provides theoretical results on the construction of two-level fractional factorial designs with minimum G2-aberration. Attention focuses on foldover designs which are shown to have minimum G2-aberration across the whole class of orthogonal designs for n=24 runs and any...

In this paper, the concepts of clear effects, alias sets and grid representations are generalized to nonregular two-level designs. Many good generalized join designs of n runs with resolution IV or more containing many clear two-factor interactions are given for n=48 up to 192 and n being a...

This paper considers the efficiency of ordinary least squares in designed experiments where the experimental runs are subject to spatial or temporal variation. The efficiency is shown to be very dependent on both the number of treatment replicates and the number of treatments as well as the...

Minimum aberration is the most established criterion for selecting a regular fractional factorial design of maximum resolution. Minimum aberration designs for n runs and n/2 = m n factors have previously been constructed using the novel idea of complementary designs. In this paper, an...

Nonregular two-level fractional factorial designs are designs which cannot be specified in terms of a set of defining contrasts. The aliasing properties of nonregular designs can be compared by using a generalisation of the minimum aberration criterion called minimum G-sub-2-aberration. Until...

Blocking of two-level factorial designs is considered for block sizes 2 and 4 using the method of fractional partial confounding. A-, D- and E-optimal designs are obtained for block size 2 within the class of orthogonal designs for which main effects and two-factor interactions are all...

Generalised minimum aberration is a recently-established design criterion for the whole class of orthogonal arrays and fractional factorial designs. The criterion is, as its name suggests, a generalisation of minimum aberration for regular designs and of minimum G-sub-2-aberration for twolevel...

This paper considers weighted design optimality criteria for polynomial responses surfaces. It is shown that there are some particularly simple parameterizations of the response surface for which weighted optimality criteria are equivalent to A-optimality or weighted A-optimality. This is useful...