### Orthogonal Arrays with Variable Numbers of Symbols

Ching-Shui Cheng
Source: Ann. Statist. Volume 8, Number 2 (1980), 447-453.

#### Abstract

Orthogonal arrays with variable numbers of symbols are shown to be universally optimal as fractional factorial designs. The orthogonality of completely regular Youden hyperrectangles ($F$-hyperrectangles) is defined as a generalization of the orthogonality of Latin squares, Latin hypercubes, and $F$-squares. A set of mutually orthogonal $F$-hyperrectangles is seen to be a special kind of orthogonal array with variable numbers of symbols. Theorems on the existence of complete sets of mutually orthogonal $F$-hyperrectangles are established which unify and generalize earlier results on Latin squares, Latin hypercubes, and $F$-squares.

First Page:
Primary Subjects: 62K05
Secondary Subjects: 62K15, 05B15
Full-text: Open access