PLACE:  319 Snedecor

SPEAKER:
Professor Ching-Shui Cheng
University of California, Berkeley

TITLE:
Projection Properties of Orthogonal Arrays

ABSTRACT:

In factor screening, often only a few factors among a large pool of potential factors are active.  Under such assumption of effect sparsity, in choosing a design for factor screening, it is important to consider projections of the design onto small subsets of factors.  Box and Tyssedal (1996) defined a factorial design to be of projectivity p if in every subset of p factors, a complete factorial (possibly with some combinations replicated) is produced.  This can be thought of as an extension of the concept of the strength of an orthogonal array.  It is well known that a regular fractional factorial design is an orthogonal array with strength R-1, where R is the resolution of the design.  While a regular fractional factorial design of resolution t+1 (or
strength t) can never have projectivity greater than t, it is possible for a non-regular orthogonal array with strength t to have projectivity greater than t.  For example, Lin and Draper (1991, 1992) and Box and Bisgaard (1993) pointed out that the 12-run Plackett-Burman design has projectivity three.  Such a design is not of projectivity four, but its projection onto any four factors has the hidden projection property that all the main effects and two-factor interactions can be estimated if the higher-order interactions are negligible (Lin and Draper, 1993; Wang and Wu, 1995).   In this talk, I will review some recent results on the projection properties of orthogonal arrays.  Connections to search designs (Srivastava, 1975) will also be discussed.
 
 
 

COFFEE: 4:00 p.m., 104 Snedecor