麻省理工学院：《Robust System Design》Matrix Experiments Using Orthogonal Arrays

MatriX Experiments Using Orthogonal Arrays Robust System Design mit 人 16881

Matrix Experiments Using Orthogonal Arrays Robust System Design 16.881 MIT

Comments on HW#2 and Quiz #1 Questions on the Reading Q Brief lecture Paper Helicopter Experiment Robust System Design mit 人 16881

Comments on HW#2 and Quiz #1 Questions on the Reading Quiz Brief Lecture Paper Helicopter Experiment Robust System Design 16.881 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 Robust System Design mit 人 16881

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 Robust System Design 16.881 MIT

Static Parameter Design and the P-Diagram Noise factors Induce noise Product Process Signal Factor Response Hold constant Optimize fora“ static Control Factors experiment Vary according to an experimental plan Robust System Design mit 人 16881

Static Parameter Design and the P-Diagram Noise Factors Induce noise Product / Process R esp o nse Signal Factor Hold constant Optimize for a “static” experiment Control Factors Vary according to an experimental plan Robust System Design 16.881 MIT

Parameter Design Problem Define a set of control factors(A, B, C.) Each factor has a set of discrete levels Some desired response n(a, B, c.)is to be maximized Robust System Design mit 人 16881

Parameter Design Problem • Define a set of control factors (A,B,C…) • Each factor has a set of discrete levels • Some desired response η (A,B,C…) is to be maximized Robust System Design 16.881 MIT

Full Factorial Approach Try all combinations of all levels of the factors(A B, Cl,A,B,C2, 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 Robust System Design mit 人 16881

Full Factorial Approach • Try all combinations of all levels of the factors (A 1 B 1 C 1, A 1 B 1 C 2,...) • 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 Robust System Design 16.881 MIT

additive model assume each parameter affects the response independently of the others nA, Bi, Ck, D)=u+a;+b,+Ck+d+e This is similar to a taylor series expansion f(x,y)=f(x。,y)+ x-x)+ (y-yo)+hot OX X=x y=yo Robust System Design mit 人 16881

Additive Model • Assume each parameter affects the response independently of the others η( Ai , B j , Ck , Di) = µ + ai + b j + c k + di + e • This is similar to a Taylor series expansion ∂f ∂f f ( x, y) = f ( x o , y o ) + ∂x ⋅( x − x o ) + ∂y ⋅( y − y o ) + h.o.t x = xo y = yo Robust System Design 16.881 MIT

One factor at a Time Control Factors Expt.A No 2345678 B22213 222222 222 2222 乃乃m水m Robust System Design mit 人 16881

1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 One Factor at a Time Control Factors Expt. No. A C 2 η 1 η 3 η B D 2 2 2 2 2 2 2 2 2 2 η 2 η 2 η 1 2 2 3 2 2 2 1 2 2 η 2 η 2 η 2 3 2 2 2 1 2 2 3 Robust System Design 16.881 MIT

Or rtnogona L1 Array Control factors Expt.A B CD 2 2 2 3 4 2 2 2 3 78 Robust System Design mit 人 16881

1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 Orthogonal Array Control Factors Expt. No. A C D 1 1 1 η 2 2 2 η 3 3 3 η 1 2 3 η 2 3 1 η 3 1 2 η 1 3 2 η 2 1 3 η 3 2 1 η B 1 1 1 2 2 2 3 3 3 Robust System Design 16.881 MIT

Notation for Matrix Experiments L(3 Number of experiments Number of levels Number of factors (3-1)x4 Robust System Design mit 人 16881

Notation for Matrix Experiments Number of experiments L9 (3 4) Number of levels Number of factors 9=(3-1)x4+1 Robust System Design 16.881 MIT