ON THE DETERMINATION AND CONSTRUCTION OF OPTIMAL ROW-COLUMN DESIGNS HAVING UNEQUAL ROW AND

COLUMN SIZES

MIKE JACROUX AND RITA SAHA RAY

Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 99164-2930, U.S.A.

(Received May 19, 1989; revised January 30, 1990)

Abstract. In this paper we consider experimental situations requiring usage of a row-column design where v treatments are to be applied to experimental units arranged in b_{1} rows and b_{2} columns where row i has size k_{1i}, i = 1, …, b_{1} and column j has size k_{2j}, j = 1, …, b_{2}. Conditions analogous to those given in Kunert (1983, Ann. Statist., 11, 247–257) and Cheng (1978, Ann. Statist., 6, 1262–1272) are given which can often be used to establish the optimality of a given row-column design from the optimality of an associated block design. In addition, sufficient conditions are derived which guarantee the existence of an optimal row-column design which can be constructed by appropriately arranging treatments within blocks of an optimal block design.

Key words and phrases: Row-column design, block design, incidence matrix, balanced unequal block design.