New Properties of Orthogonal Arrays and Their Statistical Applications.

Fractional factorial designs are among the most utilized statistical designs by practioners. In a series of three papers Rao 1946, 1947, 1949 identified special types of fractions with a great deal of symmetry and many desirable statistical properties. These special fractions are now known as orthogonal arrays. Numerous beautiful results have been obtained by both statisticians and mathematicians on this topic. These results are published in a wide variety of journals and presented in many different styles. In their forthcoming research monograph Hedayat and Stufken 1986 have presented the various results on this fascinating subject in a unified and comprehensive way. This paper is divided into four sections. Sections 2 reviews basic definitions and terminology of the subject. Section 3 presents an efficient way of preparing design and information matrices associated with orthogonal arrays under orthogonal polynomial models. Section 4 contains a new result and a new concept. The new result states that with orthogonal arrays of strength t we can orthogonally estimate other parametric vectors besides the one which is advocated in the literature. The author has also identified some types of orthogonal arrays which are somewhere between orthogonal arrays of strength t and t 1. These are called flexible orthogonal arrays of strength t. Practical applications of such arrays are also pointed out. These results are very useful in preparing line graphs of Taguchi for orthogonal arrays.