5069

4766

كارشناسي ارشد

آمار رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1388

[هشت]،112ص.

ص.ع.به: فارسي و انگليسي

رياضي

ID4766

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

E optimality of Incomplete Block Designs Azam Kheyri azam kheyri@gmail com Janury 4 2010 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisors Dr Saeid Pooladsaz spooladsaz@cc iut ac ir2000 MSC Primary 62K05 Secondary 62K10 Key words Blocking Discrepancy matrix E optimality Optimal design Regular graph Abstract In this thesis we present an expanded account of Optimal Incomplete Block Designsbased on an article by J P Morgan 2007 Blocking to improve e ciency of comparative experiments deemed one of the three fun damental principles of experimentation by Fisher is a tool in every statistician s kit and aconcept known by scientists across the experimental spectrum A block design is just an assignment of Treatments to n experimental units that havebeen partitioned into b blocks of k units each Underlying problem in choice of block designin succinctly stated Given b k what is the best assignment of treatments to units LetD b k be the class of all possible assignments for given b k and d be a member ofD that is to denote available designs The problem is to choose a design d D which isoptimal In this thesis optimal incomplete block designs are pursued through the E criterion of mini mizing maximal variance methodology is developed for design choice based on graphs Alongwith the general Methodology complete solution for E optimal block designs is provided forup to 15 treatments E optimality is revealed to be a exible criterion that depending onthe application can o er many choice for good designs In last chapter we study optimal incomplete block designs when there are two blocks withequal size It turns out that a binary design of a certain pattern is A and D optimal in theclass of designs D 2 k with 2 k The same design is also E optimal design inD 2 k when 2 k 5 6 If 5 6 k a non binary design with a certain patternin E optimal If k 5 6 both the binary design and the non binary design are E optimal 1

سعيد پولادساز

غلامرضا اميدي

هوشنگ طالبي،سروش عليمرادي