ALGEBRAIC METHODS FOR CONSTRUCTION OF MIXED ORTHOGONAL ARRAYS

Abstract

Orthogonal arrays (OAs) of strength t (also called t-balanced fractional designs) are difficult to construct, but they have useful properties that can be employed in the theory of experimental design and in practical applications to statistical quality management.

Specifically, strength 3 OAs permit estimation of all the main effects of the experimental factors, without confounding them with the two-factor interactions. Strength 4 OAs allow us to also separately estimate all twofactor interactions. These arrays are in great demand not only in wellknown areas like statistical quality control of industries and services [12], software engineering [13], but also in emerging and fast-developed areas  such as computational biology, drug designs and/or medical sciences, in particular DNA micro-array experiments [6, 21].

In this paper, we introduce some new methods for constructing mixed orthogonal arrays of strength t, with a given parameter set of run-size and factor levels. A few new arrays with run size up to 100 have been found with the proposed methods.