Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

A bit-parallel tabu search algorithm for finding E(s2s^2)-optimal and minimax-optimal supersaturated designs

We prove the equivalence of two-symbol supersaturated designs (SSDs) with $N$ (even) rows, $m$ columns, $s_{\rm max} = 4t +i$, where $i\in\{0,2\}$, $t \in \mathbb{Z}^{\geq 0}$ and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most $(N+4t+i)/4$ points. Using this equivalence, we formulate the search for two-symbol E($s^2$)-optimal and minimax-optimal SSDs with $s_{\max} \in \{2,4,6\}$ as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found E($s^2$)-optimal and minimax-optimal SSDs achieving the sharpest known E($s^2$) lower bound with $s_{\max} \in \{2,4,6\}$ of sizes $(N,m)=(16,25), (16,26), (16,27), (18,23),(18,24),(18,25),(18,26),(18,27),(18, 28),$ $(18,29),(20,21),(22,22),(22,23),(24,24)$, and $(24,25)$. In each of these cases no such SSD could previously be found

A Bit-Parallel Tabu Search Algorithm for Finding Es2-Optimal and Minimax-Optimal Supersaturated Designs

We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, and smax=4t+i, where i∈0,2 and t∈ℤ≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most N+4t+i/4 points. Using this equivalence, we formulate the search for two-symbol Es2-optimal and minimax-optimal SSDs with smax∈2,4,6 as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found Es2-optimal and minimax-optimal SSDs achieving the sharpest known Es2 lower bound with smax∈2,4,6 of sizes N,m=16,25, (16, 26), (16, 27), (18, 23), (18, 24), (18, 25), (18, 26), (18, 27), (18, 28), (18, 29), (20, 21), (22, 22), (22, 23), (24, 24), and (24, 25). In each of these cases, no such SSD could previously be found

The maximum number of columns in supersaturated designs with sMax = 2

Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle