The allocation of resources in a 2𝑘-factorial experiment is crucial when the experimental resources are limited.In practice,when resources are limited,it is common for investigators to use all the information ...The allocation of resources in a 2𝑘-factorial experiment is crucial when the experimental resources are limited.In practice,when resources are limited,it is common for investigators to use all the information at their disposal to reduce the amount of resources needed for an experiment without trading the accuracy of the experiment.Suppose we have k+1 factors and the investigator knows one of the factors(we call this factor an extra factor throughout the paper)does not interact with any of the remaining k factors.Furthermore,the investigator believes among the remaining k factors,one factor potentially interacts with the rest of the k−1 factors.In this paper,we show how a D-optimal saturated design can be constructed for this problem with the minimum number of runs.In the process,we show the investigator can even forgo the presence of the extra factor in certain runs without compromising the D-optimality of the saturated design.展开更多
In a 2^(k)-factorial experiment with limited resources,when practitioners can identify the nonnegligible effects and interactions beforehand,it is common to run an experiment with a saturated design that ensures the u...In a 2^(k)-factorial experiment with limited resources,when practitioners can identify the nonnegligible effects and interactions beforehand,it is common to run an experiment with a saturated design that ensures the unbiased estimation of the non-negligible parameters of interest.We propose a method for the construction of D-optimal saturated designs for the mean,the main effects,and the second-order interactions of one factor with the remaining factors.In the process,we show the problem is just as hard as the Hadamard determinant problem.展开更多
基金supported by the US National Science Foundation[grant number 1809681].
文摘The allocation of resources in a 2𝑘-factorial experiment is crucial when the experimental resources are limited.In practice,when resources are limited,it is common for investigators to use all the information at their disposal to reduce the amount of resources needed for an experiment without trading the accuracy of the experiment.Suppose we have k+1 factors and the investigator knows one of the factors(we call this factor an extra factor throughout the paper)does not interact with any of the remaining k factors.Furthermore,the investigator believes among the remaining k factors,one factor potentially interacts with the rest of the k−1 factors.In this paper,we show how a D-optimal saturated design can be constructed for this problem with the minimum number of runs.In the process,we show the investigator can even forgo the presence of the extra factor in certain runs without compromising the D-optimality of the saturated design.
基金partially supported by the US National Science Foundation(NSF)[grant number 1809681].
文摘In a 2^(k)-factorial experiment with limited resources,when practitioners can identify the nonnegligible effects and interactions beforehand,it is common to run an experiment with a saturated design that ensures the unbiased estimation of the non-negligible parameters of interest.We propose a method for the construction of D-optimal saturated designs for the mean,the main effects,and the second-order interactions of one factor with the remaining factors.In the process,we show the problem is just as hard as the Hadamard determinant problem.
