Shinji Kuriki

On a composition of cyclic 2-designs

A CB(v,k,@l) means a cyclic 2-design of block size k coincidence number @l, and with v points. In this paper, a recursive construction of a CB(v,k,@l) from two or three cyclic 2-designs is given.

Some existence conditions for partially balanced arrays with 2 symbols

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.

Cyclic orthogonal and balanced arrays

Abstract Kuriki and Fuji-Hara (1994) introduced an ( r , λ )-design with mutually balanced nested subdesigns (( r , λ )-design with MBN), which is equivalent to a balanced array of strength 2 with s symbols, and gave some constructions of such ( r , λ )-designs. In this paper, we consider cyclic orthogonal and balanced arrays, and we give a cyclic version of the results obtained by them. Furthermore, we give a construction of a cyclic ( r , λ )-design with MBN by a product method. By the construction, new cyclic balanced arrays with s ⩾ 3 are presented.

Incomplete Split-Plot Designs Supplemented by a Single Control

The article deals with the constructing methods for experiments carried out in an incomplete split-plot design supplemented by an additional treatment, called a single control. The control treatment has been treated usually as one specific factor level while not necessarily. The control cannot be connected with treatment combinations in an experiment. This distinguishes this article from others in the area considered. The proposed supplementation of whole incomplete split-plot designs leads to the designs with generally accepted methodological requirements, especially randomization. Moreover, we propose a few methods for constructing considered types of the designs with desirable statistical properties such as general balance and efficiency balance of the design with respect to treatment contrasts.

Square Lattice Designs in Incomplete Split-Plot Designs

We construct an incomplete split-plot design by the semi-Kronecker product of two resolvable designs. We use any resolvable design for the treatments of whole-plots and a square lattice design for the treatments of subplots. We give the stratum efficiency factors for such incomplete split-plot designs, which have the general balance property.

Balanced nested designs and balanced n-ary designs

We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (J. Numer. Theory 4 (1972) 17). By use of these constructions, we show some constructions for regular balanced n-ary designs.

On existence and construction of balanced arrays

Abstract This paper surveys existence conditions and construction procedures for balanced arrays. A necessary and sufficient condition for the existence of an s -symbol balanced array of strength t with m constraints is discussed. The construction of an s -symbol balanced array of strength 2, based on an ( r , λ)-design with mutually balanced nested subdesigns, is presented. Related open problems are exhibited.

Youden Square with Split Units

In this chapter we present the most important problems connected with the design of experiments using Youden squares with split units. In fact we consider two types of designs. The first is connected with different arrangements of subplot treatments on the units of Youden squares. The second is connected with the design of experiments when one or more treatments arranged in Youden squares are control or standard treatments. We characterize some of these designs with respect to general balance property and with respect to design efficiency factors.

System of equations related to the existence conditions for arrays

Abstract A system of equations was introduced by Yamamoto, Kuriki and Yuan (1983) and Kuriki (1984) in order to obtain the existence conditions for a balanced array. A generalized form of the system is discussed here. The results will be useful to give the existence conditions for several classes of arrays which contain balanced arrays.

On balanced complementation for regular t-wise balanced designs

Abstract Vanstone has shown a procedure, called r -complementation, to construct a regular pairwise balanced design from an existing regular pairwise balanced design. In this paper, we give a generalization of r -complementation, called balanced complementation. Necessary and sufficient conditions for balanced complementation which gives a regular t -wise balanced design from an existing regular t -wise balanced design are shown. We characterize those aspects of designs which permit balanced complementation. Results obtained here will be applied to construct regular t -wise balanced designs which are useful in Statistics.