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

Several upper bounds on the maximum number of constraints for s-symbol balanced arrays of strength t are given. Some bounds derived here include the results obtained by Rafter and Seiden (1974), Chopra (1982, 1983) and Saha, Mukerjee and Kageyama (1983).     

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

A connection between a balanced fractional 2^m factorial design of resolution 2l + 1 and a balanced array of strength 2l with index set {μ₀, μ₁,…, μ_2l} was established by Yamamoto, Shirakura and Kuwada (1975). The main purpose of this paper is to give a connection between a balanced fractional 3^m factorial design of resolution V and a balanced array of strength 4, size N, m constraints, 3 levels and index set {λ_l0l1l2}.     

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

We consider a fractional 3^m 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 3^m 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.     

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

By use of the algebraic structure of the triangular multidimensional partially balanced association scheme, we present the analysis of variance and the hypotheses testing of a balanced fractional 2ⁿfactorial design of resolution 2l+1, which is derived from a balanced array of strength 2l.     

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

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

On some optimal fractional 2m factorial designs of resolution V

This paper presents the trace of the covariance matrix of the estimates of effects based on a fractional 2^m factorial (2^m-FF) design T of resolution V for the following two cases: One is the case where T is constructed by adding some restricted assemblies to an orthogonal array. The other is one where T is constructed by removing some restricted assemblies from an orthogonal array of index unity. In the class of 2^m-FF designs of resolution V considered here, optimal designs with respect to the trace criterion, i.e. A-optimal, are presented for m = 4, 5, and 6 and for a range of practical values of N (the total number of assemblies). Some of them are better than the corresponding A-optimal designs in the class of balanced fractional 2^m factorial designs of resolution V obtained by Srivastava and Chopra (1971b) in such a sense that the trace of the covariance matrix of the estimates is small.     

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

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.