Masahide Kuwada

Balanced arrays of strength 2l and balanced fractional 2 m factorial designs

SummaryA connection between a balanced fractional 2m factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional 2m factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular.

Balanced arrays of strength 4 and balanced fractional 3m factorial designs

Abstract A connection between a balanced fractional 2m factorial design of resolution 2l + 1 and a balanced array of strength 2l with index set {μ0, μ1,…, μ2l} was established by Yamamoto, Shirakura and Kuwada (1975). The main purpose of this paper is to give a connection between a balanced fractional 3m factorial design of resolution V and a balanced array of strength 4, size N, m constraints, 3 levels and index set {λl0l1l2}.

Characteristic polynomials of the information matrices of balanced fractional 3m factorial designs of resolution v

Abstract An explicit expression for the characteristic polynomial of the information matrix M T of a balanced fractional 3 m factorial (3 m -BFF) design T of resolution V is obtained by utilizing the algebraic structure of the underlying multidimentional relationship. Also by using of the multidimensional relationship algebra, the trace and the determinant of the covariance matrix of the estimates of effects are derived.

Note on balanced fractional 2 m factorial designs of resolution 2l+1

AbstractIt is shown that the characteristic roots of the information matrix of a balanced fractional 2m factorial designT of resolution 2l+1 are the same as those of its complementary design

Some existence conditions for partially balanced arrays with 2 symbols

\bar T

On the characteristic polynomial of the information matrix of balanced fractional sm factorial designs of resolution Vp, q

. Necessary conditions for the existence of such a designT are also given.

On the maximum number of constraints for s-symbol balanced arrays of strength t

Abstract By use of the algebraic structure, we obtain an explicit expression for the characteristic polynomial of the information matrix of a partially balanced fractional 2m1+m2 factorial design of resolution V derived from a partially balanced array. For 4≤m1+m2≤6, A-optimal designs considered here are also presented for reasonable number of assemblies.

Analysis of variance of balanced fractional 2n factorial designs of resolution 2l+1

Abstract This paper presents some necessary and sufficient conditions for the existence of a partially balanced array of Type 1 (PBI-array) of strength ( t 1 , t 2 ), ( m 1 , m 2 ) constraints (with m 1 + m 2 ⩽ t 1 + t 2 +2) and 2 symbols. Some existence conditions for a PB2-array of strength t , ( m 1 , m 2 ) constraints (with m 1 + m 2 ⩽ t + 2) and symbols are also described.