Design and Analysis of Two-Level Factorial Experiments With Partial Replication
In a two-level factorial experiment, we consider construction of parallel-flats designs with two identical parallel flats that allow estimation of a set of specified possibly active effects and the pure error variance. A set of sufficient conditions is presented for the designs to be D-optimal for t...
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| Veröffentlicht in: | Technometrics 2009-02, Vol.51 (1), p.66-74 |
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| container_title | Technometrics |
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| creator | Liao, Chen-Tuo Chai, Feng-Shun |
| description | In a two-level factorial experiment, we consider construction of parallel-flats designs with two identical parallel flats that allow estimation of a set of specified possibly active effects and the pure error variance. A set of sufficient conditions is presented for the designs to be D-optimal for the specified effects, assuming that the other effects are negligible, over the class of competing parallel-flats designs. In addition, an algorithm is developed to generate the D-optimal designs with a choice of flexible degrees of freedom for the pure error variance. Because the proposed partially replicated designs are highly efficient in estimating the possibly active effects and provide a replication-based estimate of the error variance, they provide a practical compromise between the power in identifying truly active effects and the number of runs in experiments. This property is verified through a simulation study. |
| doi_str_mv | 10.1198/TECH.2009.0007 |
| format | Article |
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Utility theory</subject><subject>Design analysis</subject><subject>Exact sciences and technology</subject><subject>Experiment design</subject><subject>Experimental design</subject><subject>Experimental replication</subject><subject>Factorial design</subject><subject>Factorial experiments</subject><subject>Factorials</subject><subject>Industrial design</subject><subject>Least squares</subject><subject>Mathematics</subject><subject>Matrices</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Parallel-flats design</subject><subject>Power</subject><subject>Probability and statistics</subject><subject>Pure error</subject><subject>Random variables</subject><subject>Sciences and techniques of general use</subject><subject>Simulation</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Studies</subject><subject>Unreplicated design</subject><issn>0040-1706</issn><issn>1537-2723</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kM1LwzAYxoMoOD-u3oQieOx8k7RNcxxzU2EwkYnH8JommtE1M-nU_fe2THfz9B6eD573R8gFhSGlsrxZTMb3QwYghwAgDsiA5lykTDB-SAYAGaRUQHFMTmJcAlDOSjEg81sT3VuTYFMlowbrbXQx8TZZfPl0Zj5NnUxRtz44rJPJ99oEtzJNG5MX174njxjaXngy69ppbJ1vzsiRxTqa8997Sp6nk8X4Pp3N7x7Go1mqeVG2qbAWJNeUZkxrg6bUugJg1ORSa4a2zCrGi9yyoqqgsvYVZKmlFBlHZNRW_JRc7XrXwX9sTGzV0m9C90BUjPJC8JxCZxruTDr4GIOxat3tx7BVFFTPTPXMVM9M9cy6wPVvK0aNtQ3YaBf3KUZFzgSXne9y51vGjs1ezyAvi7zIOl3udNdYH1b45UNdqRa3tQ9_pfyfDT9yZoiN</recordid><startdate>20090201</startdate><enddate>20090201</enddate><creator>Liao, Chen-Tuo</creator><creator>Chai, Feng-Shun</creator><general>Taylor & Francis</general><general>The American Society for Quality and The American Statistical Association</general><general>American Society for Quality and the American Statistical Association</general><general>American Society for Quality</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8C1</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>FYUFA</scope><scope>F~G</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>K60</scope><scope>K6~</scope><scope>L.-</scope><scope>L6V</scope><scope>M0C</scope><scope>M2P</scope><scope>M7S</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope><scope>S0X</scope></search><sort><creationdate>20090201</creationdate><title>Design and Analysis of Two-Level Factorial Experiments With Partial Replication</title><author>Liao, Chen-Tuo ; Chai, Feng-Shun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-7ff093c1142cceae8ccd0021e59cc2af84d2365f26dd0dffb098c99743aa21fd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Active effect</topic><topic>Analytical estimating</topic><topic>Applied sciences</topic><topic>Cost control</topic><topic>Decision theory. 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| subjects | Active effect Analytical estimating Applied sciences Cost control Decision theory. Utility theory Design analysis Exact sciences and technology Experiment design Experimental design Experimental replication Factorial design Factorial experiments Factorials Industrial design Least squares Mathematics Matrices Operational research and scientific management Operational research. Management science Parallel-flats design Power Probability and statistics Pure error Random variables Sciences and techniques of general use Simulation Statistical variance Statistics Studies Unreplicated design |
| title | Design and Analysis of Two-Level Factorial Experiments With Partial Replication |
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