8280

7678

كارشناسي ارشد

آمار اقتصادي و اجتماعي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي

1392

نه، 119ص

ص.ع:به فارسي و انگليسي

رياضي

ID7678

به فارسي و انگليسي: قابل رويت در نسخه ديجيتال

Optimal resolvable designs with minimum PV aberration Mohadese Sadat Farzam mehr ma farzam@math iut ac ir 14 September 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Saeid Pooladsaz spooladsaz@cc iut ac ir Advisor Dr Amir Hashemi amir hashemi @cc iut ac ir 2010 MSC 62Kxx 62K05 62K10 Keywords Resolvable block design A ne resolvable block design Schur optimality Mutuallyorthogonal Latin square Orthogonal array Pairwise variance aberration Abstract An incomplete block design for treatments in blocks of size k is resolvable if the blockscan be partitioned into sets containing each treatment exactly once The sets are called replicateswhich is denoted by r Thus resolvable block designs are exactly those for which the blocks may bepartitioned into replicates Using s as the number of small blocks per replicate in a resolvable design and b the total number of small blocks then sk and b rs One special class of resolvable design is said to be a ne resolvable when any two block from distinictreplicates of a resolvable design intersect in the number of treatments For an a ne resolvabledesign the number is necessarily k s and so s2 and k s where k is a multiple of s isthe limitation imposed by a neness relative to all resolvable designs The advantage gained is a hostof very nice statistical properties Amongst resolvable incomplete block designs a ne resolvable designs are optimal with respect tothe usual criteria including A D and E optimality Given these excellent statistical properties one might think that every a ne resolvable designs with the same numbers of treatments replicates and blocks size should be equally e cacious Inspection of the variances of the elementary treatmentcontrasts however shows this notion to be false as these variances are di er in how well they estimateelementary treatment contrasts

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