Complete Enumeration of Two-Level Orthogonal Arrays of Strength d with d+2 Constraints
Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomo...
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| Veröffentlicht in: | The Annals of statistics 2007-04, Vol.35 (2), p.793-814 |
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| container_title | The Annals of statistics |
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| creator | Stufken, John Tang, Boxin |
| description | Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d+2 constraints for any d and any run size $n=\lambda 2^{d}$. Our results not only give the number of nonisomorphic orthogonal arrays for given d and n, but also provide a systematic way of explicitly constructing these arrays. Our approach to the problem is to make use of the recently developed theory of J-characteristics for fractional factorial designs. Besides the general theoretical results, the paper presents some results from applications of the theory to orthogonal arrays of strength two, three and four. |
| doi_str_mv | 10.1214/009053606000001325 |
| format | Article |
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Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d+2 constraints for any d and any run size $n=\lambda 2^{d}$. Our results not only give the number of nonisomorphic orthogonal arrays for given d and n, but also provide a systematic way of explicitly constructing these arrays. Our approach to the problem is to make use of the recently developed theory of J-characteristics for fractional factorial designs. 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Ordered structures</topic><topic>Design resolution</topic><topic>Designs and configurations</topic><topic>Exact sciences and technology</topic><topic>Experimental Design</topic><topic>Factorial design</topic><topic>Factorials</topic><topic>fractional factorial design</topic><topic>General topics</topic><topic>Hadamard matrix</topic><topic>Hadamard transform</topic><topic>indicator function</topic><topic>Indicator functions</topic><topic>Inference</topic><topic>Integers</topic><topic>isomorphism</topic><topic>J-characteristic</topic><topic>Mathematical minima</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Matrices</topic><topic>minimum aberration</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><topic>Studies</topic><topic>Variables</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Stufken, John</creatorcontrib><creatorcontrib>Tang, Boxin</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Stufken, John</au><au>Tang, Boxin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Complete Enumeration of Two-Level Orthogonal Arrays of Strength d with d+2 Constraints</atitle><jtitle>The Annals of statistics</jtitle><date>2007-04-01</date><risdate>2007</risdate><volume>35</volume><issue>2</issue><spage>793</spage><epage>814</epage><pages>793-814</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><coden>ASTSC7</coden><abstract>Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. 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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Project Euclid Complete |
| subjects | 62K15 Arrays Combinatorics Combinatorics. Ordered structures Design resolution Designs and configurations Exact sciences and technology Experimental Design Factorial design Factorials fractional factorial design General topics Hadamard matrix Hadamard transform indicator function Indicator functions Inference Integers isomorphism J-characteristic Mathematical minima Mathematical models Mathematics Matrices minimum aberration Probability and statistics Sciences and techniques of general use Statistics Studies Variables |
| title | Complete Enumeration of Two-Level Orthogonal Arrays of Strength d with d+2 Constraints |
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