Some new factor screening designs using the search linear model
type: Item
instance of: scholarly article
title: Some new factor screening designs using the search linear model
zbMATH Open document ID: 0588.62128
DOI: 10.1016/0378-3758(85)90013-8
author: Subir Ghosh
author: Diana Avila
published in: Journal of Statistical Planning and Inference
publication date: 1985-01-01T00:00:00Z
review text: Factor screening designs can be effectively put into the framework of a particular type of search linear models. This can be easily seen as follows: Suppose k important factors are to be screened out of m factors each at two levels. Then under the usual assumptions of no-interactions and negligible amounts of random errors the search linear model for this is \[ E[Y]=A_ 1\xi_ 1+A_ 2\xi_ 2,\quad V[Y]=\sigma^ 2I,\quad and\quad Rank(A_ 1)=\nu_ 1, \] where \(A_ 1\) is an \(N\times 1\) column vector of all 1's, \(A_ 2\) is an \(N\times m\) (-1,1)-matrix, \(\xi_ 1\) is the general mean and \(\xi_ 2\) consists of the main effects. A factor screening design is an \(N\times m\) (0,1)-matrix T whose rows consist of m treatment combinations of a \(2^ m\) factorial. The matrix \(A_ 2\) is obtained from T by replacing 0's by -1's. It is assumed that the treatments (1,1,...,1) and (0,0,...,0) are always present in the design. This paper is concerned with the construction of factor screening designs (with a small number of treatments) which have the property \(P_{2t}\) (no 2t columns are linearly dependent) for \(t=2\) and 3. In this connection a ''packing problem'' is introduced. A list of useful designs is also presented.
Mathematics Subject Classification ID: 62K15
zbMATH DE Number: 3945154
zbMATH Keywords: P (sub t) property
zbMATH Keywords: Factor screening designs
zbMATH Keywords: search linear models
zbMATH Keywords: packing problem
zbMATH Keywords: list of useful designs
reviewed by: B. Leo Raktoe
MaRDI profile type: Publication
full work available at URL: 0378-3758(85)90013-8
OpenAlex ID: W1978882272
cites work: Q5796828
cites work: Q4176810
cites work: Q3943855
cites work: Q4072674
cites work: A Study of the Group Screening Method
description: scientific article; zbMATH DE number 3945154