l8_orth_arrays

# L8_orth_arrays - Constructing Orthogonal Arrays 16.881 Robust System Design MIT Learning Objectives Introduce explore orthogonality Study the

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Constructing Orthogonal Arrays Robust System Design 16.881 MIT

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Learning Objectives • Introduce & explore orthogonality • Study the standard OAs • Practice computing DOF of an experiment • Learn how to select a standard OA • Introduce means to modify OAs • Consider studying interactions in OAs Robust System Design 16.881 MIT
What is orthogonality? • Geometry v v • Vector algebra x y = 0 • Robust design –Form contrasts for the columns ( i ) w i 1 + w i 2 + w i 3 L + w i 9 = 0 – Inner product of contrasts must be zero w < i > w < j > = 0 Robust System Design 16.881 MIT

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Before Constructing an Array We must define: • Number of factors to be studied • Number of levels for each factor • 2 factor interactions to be studied • Special difficulties in running experiments Robust System Design 16.881 MIT
Counting Degrees of Freedom Grand mean –1 • Each control factor (e.g., A) – (# of levels of A -1) • Each two factor interaction (e.g., AxB) – (DOF for A)x(DOF for B) •E xample -- 2 1 x3 7 Robust System Design 16.881 MIT

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Breakdown of DOF Robust System Design MIT 16.881 n 1 SS due to mean n -1 (# levels) -1 factor A n = Number of η values (# levels) -1 factor B DOF for error etc.
DOF and Modeling Equations • Additive model 0 η ( A i , B j , C k , D i ) = µ + a i + b j + c k + d i e + • How many parameters are there? How many additional equations constrain the parameters? Robust System Design 16.881 MIT

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DOF -- Analogy with Rigid Body Motion • How many parameters define the position and orientation of a rigid body? • How do we remove these DOF? γ y z ( X,Y,Z ) y z α β x x Rotation Translation Robust System Design 16.881 MIT
Notation for Matrix Experiments Number of experiments L 9 (3 4 ) Number of levels Number of factors 9=(3-1)x4+1 Robust System Design 16.881 MIT

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Standard Orthogonal Arrays • See table 7.1 on Phadke page 152
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## This note was uploaded on 11/08/2011 for the course AERO 16.851 taught by Professor Ldavidmiller during the Fall '03 term at MIT.

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L8_orth_arrays - Constructing Orthogonal Arrays 16.881 Robust System Design MIT Learning Objectives Introduce explore orthogonality Study the

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