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چكيده انگليسي :

Abstract One of the main basis in experiment of design is reducing experiment error block designs often serve this purpose If there are two flexible sources of confusion then the omission of these two sources is possible only through blocking in two directions In other word two blocking factors are used with one factor representing the rows of the design and the other factor representing columns This kind of design is called row column design For instance in a agricultural experiment the rows and columns of a design might be used to control field gradient and soli type respectively Row column designs with p rows and q columns include pq plots More generally an experiment may involve groups of row column designs each with pq plots These groups may represent a further blocking factor or provide repeats of the basic experimental design For example the agricultural experiment mentioned above may be carried out at a number of different location Such designs have $ treatments in b blocks of size pq in a way that treatments within each block set out in a row column design consist of p rows and q columns Since the rows and the columns are nested within blocks these designs are called nested row column designs NRC Multiple blocking structures play an important part in the control of experimental trend and are used extensively in the design and analysis of experiments in agricultural horticulture and forestry Nested row column designs provide a powerful structural base for the two dimensional control of experimental trend Analysis of nested row column designs is usually carried out using a mixed model specification For example in a variety trial laid out in a resolvable row column design we specify the rows and columns within replicates as random effects and thereby recover variety or treatment information that is partially confounded with row and column differences If the estimated values of the stratum variances in the rows and columns strata are very much bigger than that of the variance in the bottom stratum that is the rows by columns stratum then the estimators of treatment differences are almost the same as those from the model in which rows and columns are specified as fixed effects In chapter two intra block and inter block analysis are examined and moreover It also introduces criteria of universal optimality and several criteria of special optimality In order to construct row column designs treatments can be devoted to $ treatment combinations using pseudo factors Then by double confounding method a row column design is constructed In chapter three factorial designs are described briefly and a method for confounding in row column designs has been expressed Resolvable row column designs are an important type of nested row column designs in which each treatment occurs exactly one time in each group or block An important class of resolvable row column designs is the lattice square designs in which treatments are placed in r blocks in such a way that each block is a array The design in blocks is a complete block design while the design in rows and the design in columns are both square lattice designs In chapter four A optimal lattice square designs A optimal restricted lattice square designs and A optimal generally balanced lattice square designs are examined In chapter five universally optimal nested row column designs and A optimal resolvable nested row column designs are considered

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بهينگي طرح هاي سطري-ستوني آشيانه اي

بهينه عمومي , كلي-متعادل , عامل كارايي , ﴿M وS﴾بهينگي