C onstructing Orthogonal Arrays Robust System Design mit 人 16881
Constructing Orthogonal Arrays Robust System Design 16.881 MIT
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 mit 人 16881
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? Geometr Vector algebra x 0 Robust design Form contrasts for the columns(i) V1+W;p+V;3……+V 9 =0 Inner product of contrasts must be zero W Robust System Design mit 人 16881
What is orthogonality? • Geometry v v • Vector algebra x ⋅ y = 0 • Robust design – F o rm contrasts for the columns ( i) wi1 + wi2 + wi3 L + wi9 = 0 – Inner product of contrasts must be zero w <i> ⋅w < j > = 0 Robust System Design 16.881 MIT
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 mit 人 16881
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 Each control factor(e.g, A) ( of levels ofA-1) Each two factor interaction(e.g, AxB) (OF for A)x doF for B) Example --2 X37 Robust System Design mit 人 16881
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 x a m p l e - - 2 1x37 Robust System Design 16.881 MIT