An Algorithmic Approach to Constructing Supersaturated Designs

Abstract

Supersaturated designs are very cost-effective to scientists and engineers at the primary stage of scientific investigation. This article describes a method of constructing supersaturated designs from balanced incomplete block designs that is a generalization of the method of Lin for constructing these designs and a more general approach to constructing these designs.

Analysis of supersaturated designs via the Dantzig selector

“…The former suggested the use of random balanced designs and the latter proposed an algorithm to construct systematic supersaturated designs. Many methods have been proposed for constructing supersaturated designs in the last 15 years, for examples, among others, Lin (1993Lin ( , 1995, Wu (1993), Nguyen (1996), Cheng (1997), Li and Wu (1997), Tang and Wu (1997) A common application of supersaturated designs is factor screening. There are usually a large number of factors to be investigated in a screening experiment, but it is believed that only a few of them are active, or explicitly speaking, have significant impact on the response.…”

Multifaceted Evaluation of 2-Level Supersaturated Designs

“…This chapter describes how the construction methods were applied and the resultant designs that were constructed. This paper compares 2-level supersaturated designs constructed by Lin (1993), Wu (1993), Iida (1994), Nguyen (1996) and Yamada and Lin (1997) because they are constructed uniquely. Lin (1993) constructed 2-level supersaturated designs with n = N/2 and k = N − 2, from an N-order Hadamard matrix.…”

An Overview of Two-Level Supersaturated Designs with Cyclic Structure

“…If n ≡ 2 (mod 4) with k odd, then The cyclic construction method used by Plackett and Burman (1946) for orthogonal saturated designs was generalized by Liu and Dean (2004) to obtain a class of supersaturated Liu and Dean (2004) give rise to designs that are mean-orthogonal and 24 which are either Es 2 -optimal or have at least 96.4% efficiency. The following three results summarize the links between k-circulant designs, the concatenation of k individual saturated 26 cyclic (1-circulant) designs and the designs of Nguyen (1996), Eskridge, Gilmour, Mead, Butler and Travnicek (2004), and Bulutoglu and Cheng (2004) formed from the incidence 28 matrices of cyclic incomplete block designs. These links are illustrated in Example 3.1.…”

“…Lower bounds for Es 2 for supersaturated designs with n runs and m = k(n − 1) factors U n c o r r e c t e d c o p y have been derived for n = 0 mod 4 by Nguyen (1996) and Tang and Wu (1997), and bounds for other values of n and m have been given by Cheng (1997) (i) Nguyen (1996), Tang andWu (1997), Cheng (1997).…”