2kmpFactorialDesign - CPE 619 2k-p Factorial Design...

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CPE 619 2 k-p Factorial Design Aleksandar Milenković The LaCASA Laboratory Electrical and Computer Engineering Department The University of Alabama in Huntsville http://www.ece.uah.edu/~milenka http://www.ece.uah.edu/~lacasa
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2 PART IV: Experimental Design and Analysis How to : Design a proper set of experiments for measurement or simulation Develop a model that best describes the data obtained Estimate the contribution of each alternative to the performance Isolate the measurement errors Estimate confidence intervals for model parameters Check if the alternatives are significantly different Check if the model is adequate
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3 Introduction 2 k-p Fractional Factorial Designs Sign Table for a 2k-p Design Confounding Other Fractional Factorial Designs Algebra of Confounding Design Resolution
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4 2 k-p Fractional Factorial Designs Large number of factors ) large number of experiments ) full factorial design too expensive ) Use a fractional factorial design 2 k-p design allows analyzing k factors with only 2 k-p experiments 2 k-1 design requires only half as many experiments 2 k-2 design requires only one quarter of the experiments
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5 Example: 2 7-4 Design Study 7 factors with only 8 experiments!
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6 Fractional Design Features Full factorial design is easy to analyze due to orthogonality of sign vectors Fractional factorial designs also use orthogonal vectors That is The sum of each column is zero i x ij =0 8 j j th variable, i th experiment The sum of the products of any two columns is zero i x ij x il =0 8 j l The sum of the squares of each column is 2 7-4 , that is, 8 i x ij 2 = 8 8 j
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7 Analysis of Fractional Factorial Designs Model : Effects can be computed using inner products
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Example 19.1 Factors A through G explain 37.26%, 4.74%, 43.40%,
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This note was uploaded on 12/13/2011 for the course CPE 619 taught by Professor Milenkovic during the Fall '09 term at University of Alabama - Huntsville.

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2kmpFactorialDesign - CPE 619 2k-p Factorial Design...

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