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Robust System Design MIT MatrixExperiments Using Orthogonal Arrays

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Robust System Design MIT Comments on HW#2 and Quiz#1 Questions on the Reading Quiz Brief Lecture Paper Helicopter Experiment

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Robust System Design MIT Learning Objectives Introduce the concept of matrix experiments Define the balancing property and orthogonality Explain how to analyze data from matrix experiments Get some practice conducting a matrix experiment

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Robust System Design MIT Static Parameter Design and the P-Diagram Noise Factors Induce noise Product / Process Signal Factor Response Hold constant for a static experiment Control Factors Vary according to MIT an experimental plan Optimize

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Robust System Design MIT ParameterDesignProblem Define a set of control factors (A,B,C…) Each factor has a set of discrete levels Some desired response h (A,B,C…) is to be maximized

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Robust System Design MIT FullFactorial Approach Try all combinations of all levels of the factors (A1B1C1, A1B1C2,...) If no experimental error, it is guaranteed to find maximum If there is experimental error, replications will allow increased certainty BUT...#experiments =#levels#control factors

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Robust System Design MIT Additive Model Assume each parameter affects the response independently of the others h( Ai, B j, Ck, Di ) = m + ai + b j + ck + di + e This is similar to a Taylor series expansion

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Robust System Design MIT One Factor ata Time

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Robust System Design MIT Orthogonal Array

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Robust System Design MIT Notation forMatrix Experiments Number of experiments Number of levels 9=(3-1)x4+1 Number of factors

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Robust System Design MIT Why isthis efficient? One factor at a time – Estimated response at Orthogonal array – Estimated response at A 3 is – Variance sums for independent errors – Error variance ~ 1/replication number

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Robust System Design MIT FactorEffectPlots Which CF levels will you choose? What is your scaling factor? Factor Effects on the Mean Factor Effects on the Variance

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Robust System Design MIT PredictionEquation Factor Effects on the Variance

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Robust System Design MIT Inducing Noise Control Factors Noise factor Expt. No.

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Robust System Design MIT Analysis of Variance (ANOVA) ANOVA helps to resolve the relative magnitude of the factor effects compared to the error variance Are the factor effects real or just noise? I will cover it in Lecture 7 You may want to try the Mathcad resource center under the help menu

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Introduction to estimation theory Seoul Nat’l Univ.

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