E(s2)- and UE(s2)-optimal supersaturated designs

Ching Shui Cheng, Ashish Das, Rakhi Singh, Pi Wen Tsai

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Supersaturated designs are useful for factor screening experiments under the factor sparsity assumption that only a small number of factors are active. The popular E(s2)-criterion for choosing two-level supersaturated designs minimizes the sum of squares of theentries of the information matrix over the designs in which the two levels of each factor appear equal number of times. Jones and Majumdar (2014) proposed the UE(s2)-criterion which is essentially the same as the E(s2)-criterion except that the requirement of factor-level-balance is dropped. Removing this constraint makes UE(s2)-optimal designs easy to construct, but it also produces many UE(s2)-optimal designs with diverse performances. It is necessary to choose better designs from them, especially those with good lower-dimensional projection properties. While E(s2)-optimal designs tend to have better lower-dimensional projections than arbitrary UE(s2)-optimal designs, they are usually very difficult to construct. We propose a secondary criterion and provide simple and systematic constructions of superior UE(s2)-optimal designs having good projection properties. We also derive conditions under which E(s2)-optimal designs are UE(s2)-optimal as well and identify several families of designs that are optimal under both criteria.

Original languageEnglish
Pages (from-to)105-114
Number of pages10
JournalJournal of Statistical Planning and Inference
Volume196
DOIs
Publication statusPublished - 2018 Aug

Fingerprint

Supersaturated Design
Projection Property
Screening Experiment
Information Matrix
Sum of squares
Sparsity
Optimal design
Screening
Choose
Factors
Projection
Tend
Minimise
Necessary
Requirements
Arbitrary
Design

Keywords

  • Active factor
  • Factor sparsity
  • Hadamard matrix
  • Projection property
  • Screening design

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

E(s2)- and UE(s2)-optimal supersaturated designs. / Cheng, Ching Shui; Das, Ashish; Singh, Rakhi; Tsai, Pi Wen.

In: Journal of Statistical Planning and Inference, Vol. 196, 08.2018, p. 105-114.

Research output: Contribution to journalArticle

Cheng, Ching Shui ; Das, Ashish ; Singh, Rakhi ; Tsai, Pi Wen. / E(s2)- and UE(s2)-optimal supersaturated designs. In: Journal of Statistical Planning and Inference. 2018 ; Vol. 196. pp. 105-114.
@article{0c775b71e68d435e97a798bdcc8e3591,
title = "E(s2)- and UE(s2)-optimal supersaturated designs",
abstract = "Supersaturated designs are useful for factor screening experiments under the factor sparsity assumption that only a small number of factors are active. The popular E(s2)-criterion for choosing two-level supersaturated designs minimizes the sum of squares of theentries of the information matrix over the designs in which the two levels of each factor appear equal number of times. Jones and Majumdar (2014) proposed the UE(s2)-criterion which is essentially the same as the E(s2)-criterion except that the requirement of factor-level-balance is dropped. Removing this constraint makes UE(s2)-optimal designs easy to construct, but it also produces many UE(s2)-optimal designs with diverse performances. It is necessary to choose better designs from them, especially those with good lower-dimensional projection properties. While E(s2)-optimal designs tend to have better lower-dimensional projections than arbitrary UE(s2)-optimal designs, they are usually very difficult to construct. We propose a secondary criterion and provide simple and systematic constructions of superior UE(s2)-optimal designs having good projection properties. We also derive conditions under which E(s2)-optimal designs are UE(s2)-optimal as well and identify several families of designs that are optimal under both criteria.",
keywords = "Active factor, Factor sparsity, Hadamard matrix, Projection property, Screening design",
author = "Cheng, {Ching Shui} and Ashish Das and Rakhi Singh and Tsai, {Pi Wen}",
year = "2018",
month = "8",
doi = "10.1016/j.jspi.2017.10.012",
language = "English",
volume = "196",
pages = "105--114",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",

}

TY - JOUR

T1 - E(s2)- and UE(s2)-optimal supersaturated designs

AU - Cheng, Ching Shui

AU - Das, Ashish

AU - Singh, Rakhi

AU - Tsai, Pi Wen

PY - 2018/8

Y1 - 2018/8

N2 - Supersaturated designs are useful for factor screening experiments under the factor sparsity assumption that only a small number of factors are active. The popular E(s2)-criterion for choosing two-level supersaturated designs minimizes the sum of squares of theentries of the information matrix over the designs in which the two levels of each factor appear equal number of times. Jones and Majumdar (2014) proposed the UE(s2)-criterion which is essentially the same as the E(s2)-criterion except that the requirement of factor-level-balance is dropped. Removing this constraint makes UE(s2)-optimal designs easy to construct, but it also produces many UE(s2)-optimal designs with diverse performances. It is necessary to choose better designs from them, especially those with good lower-dimensional projection properties. While E(s2)-optimal designs tend to have better lower-dimensional projections than arbitrary UE(s2)-optimal designs, they are usually very difficult to construct. We propose a secondary criterion and provide simple and systematic constructions of superior UE(s2)-optimal designs having good projection properties. We also derive conditions under which E(s2)-optimal designs are UE(s2)-optimal as well and identify several families of designs that are optimal under both criteria.

AB - Supersaturated designs are useful for factor screening experiments under the factor sparsity assumption that only a small number of factors are active. The popular E(s2)-criterion for choosing two-level supersaturated designs minimizes the sum of squares of theentries of the information matrix over the designs in which the two levels of each factor appear equal number of times. Jones and Majumdar (2014) proposed the UE(s2)-criterion which is essentially the same as the E(s2)-criterion except that the requirement of factor-level-balance is dropped. Removing this constraint makes UE(s2)-optimal designs easy to construct, but it also produces many UE(s2)-optimal designs with diverse performances. It is necessary to choose better designs from them, especially those with good lower-dimensional projection properties. While E(s2)-optimal designs tend to have better lower-dimensional projections than arbitrary UE(s2)-optimal designs, they are usually very difficult to construct. We propose a secondary criterion and provide simple and systematic constructions of superior UE(s2)-optimal designs having good projection properties. We also derive conditions under which E(s2)-optimal designs are UE(s2)-optimal as well and identify several families of designs that are optimal under both criteria.

KW - Active factor

KW - Factor sparsity

KW - Hadamard matrix

KW - Projection property

KW - Screening design

UR - http://www.scopus.com/inward/record.url?scp=85043227184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043227184&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2017.10.012

DO - 10.1016/j.jspi.2017.10.012

M3 - Article

AN - SCOPUS:85043227184

VL - 196

SP - 105

EP - 114

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

ER -