بهينگي طرح هاي عاملي 2m بلوكي شده

چكيده انگليسي :

Optimality of blocked 2m factorial designs FAHIMEH KHATAMI f khatami@math iut ac ir June 30 2019 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Saeid Pooladsaz spooladsaz@cc iut ac ir2000 MSC 62K05 62K10 62K15Keywords Factorial design Optimal Design Universal optimality Block design Hadamard matrixAbstract This M Sc thesis is based on the following papers On the use of blocked 2 level main effects plans having blocks of M J B K D different sizes Statistics and Probability Letters 107 2015 362 368 R D and E optimal blocked main effects plans with unequal block sizes when G D R S n is odd Statistics and Probability Letters 107 2015 37 43One of the important issues in the design of experiments is the study of the effect of two or more factors simultaneouslyon the response variable By a factorial design we mean that in each complete trial or replicate of the experiment allpossible combinations of the levels of the factors are investigated The main goal is to obtain a design in the class of all designs which has all needed information for the experiments Some optimization criterion are used to study the optimality of designs Since optimality criteria are different andusually have different results the best design is a design that is khown to enjoy many optimalities In this thesis westudy some of optimality criteria such as A D and E criterion that have been studied in the previous research The main purpose of using these designs is to increase efficiency by reducing the variance of blocking In this thesis some methods for finding optimal two level factor designs for main effects are introduced Thehadamard matrices are used to construct the optimal designs When n bk and k is odd two methods are proposed for constructing optimal two level factor designs Using the first method A and D optimal designs in the class n m b k are obtained when k is odd Thismethod is only used when m b The second method are related to the designs in n m b1 b2 k1 k2 so that b b1 b2 k1 and k2 are botheven and also n 0 mod 8 and n 4 mod 8 By the second method the A and D optimal designs are betterthan the designs which are obtained using the first method We suggest that when m two level factors can be studiedusing b blocks of size k it may be more efficient when k is odd to use a block design having b blocks with unequaleven block sizes Both of designs obtained using second method of construction will yield estimates for main effectsthat are orthogonal to both blocks and two factor interactions Because of these orthogonality properties certainlyprovide designs obtained using second method viable alternatives to the more traditional designs having equal sizedblocks of odd size in all such situations where both types of designs can be constructed For finding the E and D optimal designs in n m b k1 kb there are also several methods each of whichis obtained under certain conditions In these methods experimental situations are considered where a main effectsplan is to be used to study m two level factors using n runs partitioned into b blocks i th block having size ki b ki By these methods optimal factor designs are obtained only for the cases n 1 mod 4 andwhere n i 1n 3 mod 4

خاتمي، فهيمه

بهينگي طرح هاي عاملي 2m بلوكي شده

طرح عاملي , طرح بهينه , بهينگي عمومي , طرح بلوكي , ماتريس هادامارد