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