استواري طرح هاي بلوكي دودويي تحت معيار همبندي و كارايي

چكيده انگليسي :

Robustness of Binary Block Design According to Connectedness and Eficiency CriterionAbstract The optimal design theory has been developed under various assumption like independence and normality errors The optimal design theory assumes absence from disturbances like missing observations outlying observations orinadequacy of assumed model etc These assumptions may however be violated in real life thus rendering even anoptimal design poor In order to overcome such a situation we have to think of designs which are insensitive orrobust against such disturbances A design is said to be robust against one or more of above disturbances if itremains insensitive to presence of one or more of the above disturbances in terms of design properties In the field ofexperimentation once the experiment has been laid in the field the observation can be destroyed or lost during thecourse of experimentation Missing data can cause serious problem and may render even a well planned experimentuseless This is one of the main reason for the popularity of this area of research over last two decades However there are several experiments where the loss of a whole block is more likely than the loss of an individualobservation The consequences of disconnected block design may be so sever that the original aims of experiment will bespoiled pair wise treatment contrast will not be estimable and it will not be possible to test the usual null hypothesisthat all treatments have the same effect Although the design may be robust in the sense of connectedness against thetype of disturbances described above the residual design obtained may not be efficient as compared to the originaldesign The efficiency criterion is therefore based on the efficiency of the residual design According to thiscriterion a design is robust against loss of observations if the efficiency of residual design is close to the efficiencyof original design Researchers have investigates methods for guarding against a disconnected design because of observation lossduring the experiment and there are various criteria for studding robustness of designs One of these criterion ofrobustness is connectedness and other is efficiency criterion which are introduced in chapter two In chapter three some conditions for an arbitrary binary block design to be maximally robust against the unavailability of data areexpressed in terms of design parameters These conditions do not take full account of the information given by basicdesign parameters thus further stronger conditions are also introduced in this chapter In chapter four and five theoptimality and relative efficiency of eventual designs which are obtained after the loss of fixed number of blockswhen the planned design is a BIBD and binary variance balanced block design are considered

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استواري طرح هاي بلوكي دودويي تحت معيار همبندي و كارايي

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