Breakdown of dof Ni n= Number of n values sS due to mean ( levels)-1 ( levels )-1 etc DOF for factor a factor B error Robust System Design mit 人 16881
Breakdown of DOF 16.881 Robust System Design MIT 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 na,Bi, Ck, Di)=u+a,+b, +Ck+d, +e How many parameters are there? How many additional equations constrain the parameters? Robust System Design mit 人 16881
DOF and Modeling Equations • Additive model 0 η( Ai , B j , Ck , Di) = µ + ai + b j + c k + di + e • How many parameters are there? • How many additional equations constrain the parameters? Robust System Design 16.881 MIT
DOF -- Analogy with Rigid Body motion How many parameters define the position and orientation of a rigid body? How do we remove these dof? (X,Y, 2 Rotation Translation Robust System Design mit 人 16881
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 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
Standard Orthogonal Arrays See table 7. 1 on Phadke page 152 Note: You can never use an array that has fewer rows than doF req'd Note: The number of factors of a given evel is a maximum You can put a factor with fewer columns into a column that has more levels But not fewer Robust System Design mit 人 16881
Standard Orthogonal Arrays • See table 7.1 on Phadke page 152 • Note: You can never use an array that has fewer rows than DOF req’d • Note: The number of factors of a given level is a maximum • You can put a factor with fewer columns into a column that has more levels – But NOT fewer! Robust System Design 16.881 MIT