Yoshifumi Hyodo

Characteristic polynomials of information matrices of some balanced fractional 2m factorial designs of resolution 2l + 1

Abstract This paper investigates fractional 2m factorial designs of resolution 2l + 1, where [ 1 2 m] and [x] denotes the greatest integer not exceeding x. By use of the algebraic structure of the triangular type multidimensional partially balanced association scheme, we obtain an explicit expression for the characteristic polynomials of the information matrices of balanced fractional 2m factorial designs of resolution 2l + 1.

Characterization of Balanced Fractional 3 m Factorial Designs of Resolution III

We consider a fractional 3 m factorial design derived from a simple array (SA), which is a balanced array of full strength, where the non negligible factorial effects are the general mean and the linear and quadratic components of the main effect, and m ≥ 2. In this article, we give a necessary and sufficient condition for an SA to be a balanced fractional 3 m factorial design of resolution III. Such a design is characterized by the suffixes of indices of an SA.

Characterization of Balanced Second-Order Designs for 3 m Factorials

We consider a fractional 3m factorial design for the second-order model derived from a simple array (SA), where m ≥ 4. In this article, we give a necessary and sufficient condition for an SA to be a balanced second-order design for 3m factorials. Such a design is characterized by the suffixes of the index of an SA.

GA-Optimal Partially Balanced Fractional 2 m 1+m 2 Factorial Designs of Resolution R({00, 10, 01, 20}|Ω) with 2 ≤ m 1, m 2 ≤ 4

We consider a partially balanced fractional 2 m 1+m 2 factorial design derived from a simple partially balanced array such that the general mean, all the m 1 + m 2 main effects, all the two-factor interactions and some linear combinations of the two-factor ones, and all of the m 1 m 2 two-factor ones are estimable, where the three-factor and higher-order interactions are assumed to be negligible and 2 ≤ m k for k = 1,2. In this article, we present optimal designs with respect to the generalized A-optimality criterion when the number of assemblies is less than the number of non negligible factorial effects, where 2 ≤ m 1, m 2 ≤ 4.

Analysis of variance of balanced fractional sm factorial designs of resolution Vp,q

Abstract By using the algebraic properties of the multidimensional relationship, this paper presents the analysis of variance and the hypothesis testing for balanced fractional s m factorial designs of resolution V p , q derived from balanced arrays of strength 4, where m ⩾4.

Existence conditions for balanced fractional 3m factorial designs of resolution R({00, 10, 01, 20, 11})

ABSTRACT We consider a fractional 3m factorial design derived from a simple array (SA) such that the non negligible factorial effects are the general mean, the linear and the quadratic components of the main effect, and the linear-by-linear and the linear-by-quadratic components of the two-factor interaction. If these effects are estimable, then a design is said to be of resolution R({00, 10, 01, 20, 11}). In this paper, we give a necessary and sufficient condition for an SA to be a balanced fractional 3m factorial design of resolution R({00, 10, 01, 20, 11}). Such a design is concretely characterized by the suffixes of the indices of an SA.

Existence Conditions for Balanced Fractional 2m Factorial Designs of Resolution 2l + 1 Derived from Simple Arrays

We consider a fractional 2m factorial design derived from a simple array (SA) such that the (ℓ + 1)-factor and higher-order interactions are negligible, where 2ℓ ⩽ m. The purpose of this article is to give a necessary and sufficient condition for an SA to be a balanced fractional 2m factorial design of resolution 2ℓ + 1. Such a design is concretely characterized by the suffixes of the indices of an SA.

GA-Optimal Partially Balanced Fractional 2 m?1+m 2 Factorial Designs of Resolutions R({10,01} ∪ Ω* | Ω) with 2 ≤ m 1,m 2 ≤ 4

We consider a partially balanced fractional 2m1+m2 factorial design derived from a simple partially balanced array such that all the m1 main effects (= θ10, say) and all the m2 ones (= θ01, say) are estimable, and in addition that the general mean (= θ00, say) is at least confounded (or aliased) with the factorial effects of the (2 m1) two-factor interactions (= θ20, say), the (2 m2) ones (= θ02, say) and/or the m1m2 ones ( = θ11, say), where the three-factor and higher-order interactions are assumed to be negligible, and 2 ≤ mk for k = 1,2. Furthermore optimal designs with respect to the generalized A-optimality criterion are presented for 2 ≤ m1,m2 ≤ 4 when the number of assemblies is less than the number of non-negligible factorial effects.

Characterization of information matrices for balanced two-level fractional factorial designs of odd resolution derived from two-symbol simple arrays

We consider a balanced fractional 2m factorial design of resolution 2l+1 which permits estimation of all factorial effects up through l-factor interactions under the situation in which all (l+1)-factor and higher order interactions are to be negligible for an integer satisfying [m/2]<lE;lm, where [x] denotes the greatest integer not exceeding x. This paper investigates algebraic structure of the information matrix of such a design derived from a simple array through that of an atomic array. We obtain an explicit expression for the irreducible matrix representation based on the above design and its algebraic properties. The results in this paper will be useful to characterize the designs under consideration.