Orthogonal Arrays

Abstract In this article we use a simple example to introduce the notion of orthogonality as a desirable characteristic of an experimental design. In particular, we show that a lack of orthogonality prevents us from distinguishing the effects of some of the factors. We then formally define a class of designs, known asorthogonal arrays, which possess attractive orthogonality properties. Some examples of orthogonal arrays are given. These are followed by comments about the construction of orthogonal arrays and sources where one can find tables of orthogonal arrays. Next, we discuss the use of orthogonal arrays in several applications. These include fractional factorial experiments for controlling aliasing, with special attention to designs in which no main effects are aliased; screening experiments in which orthogonal arrays have special projection properties; response surface modeling in which orthogonal arrays yield optimal designs; robust parameter designs in which orthogonal arrays are the basis for cross arrays; and in computer experiments where orthogonal arrays produce designs that space points evenly on lower‐dimensional subspaces. We conclude with an example.