Plan for the session Quiz on Constructing Orthogonal Arrays (10 minutes) Complete some advanced topics on Oas Lecture on Computer Aided robust Design Recitation on hw#5 Robust System Design mit 人 16881 Session #11
Plan for the Session • Quiz on Constructing Orthogonal Arrays (10 minutes) • Complete some advanced topics on OAs • Lecture on Computer Aided Robust Design • Recitation on HW#5 Robust System Design 16.881 Session #11 MIT
How to estimate error variance in an l 18 Consider Phadke pg 89 How would the two unassigned columns contribute to error variance? Remember li8(21X37 Hasl+1*(2-1)+7*(3-1)=16DOF But i8 rows Therefore 2 dof can be used to estimate the sum square due to error Robust System Design 16881 mit 人 Session #11
How to Estimate Error variance in an L18 • Consider Phadke pg. 89 • How would the two unassigned columns contribute to error variance? • Remember L18(21x37) – Has 1+1*(2-1)+7*(3-1) = 16 DOF – But 18 rows – Therefore 2 DOF can be used to estimate the sum square due to error Robust System Design 16.881 Session #11 MIT
Breakdown of Sum Squares GTSS sS due Total ss to mean sS due sS due etc ss due to factor A to factor B to error Robust System Design 16881 mit 人 Session #11
Breakdown of Sum Squares GTSS SS due to mean Total SS SS due to factor A SS due to factor B SS due to error etc. Robust System Design 16.881 Session #11 MIT
Column merging Can turn 2 two level factors into a 4 level factor Can turn 2 three level factors into a six level factor Need to strike out interaction column (account for the right number of DOF!) Example on an Lg Robust System Design 16881 mit 人 Session #11
Column Merging • Can turn 2 two level factors into a 4 level factor • Can turn 2 three level factors into a six level factor • Need to strike out interaction column (account for the right number of DOF!) • Example on an L8 Robust System Design 16.881 Session #11 MIT
Column Merging in an Lg Eliminate the column which is confounded with Interactions Create a new four-level column Control factors Exp nO. ABCDEFG 234 2 12 2222 2122 22121 6 222 212 22 82212112 Robust System Design mit 人 16881 Session #11
1 2 3 4 5 6 7 8 Column Merging in an L8 • Eliminate the column which is confounded with interactions • Create a new four-level column Control Factors Exp no. A B C D E F G η 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 2 1 1 2 2 1 2 2 2 1 1 1 1 1 2 2 2 2 1 1 2 2 2 2 1 2 1 2 1 2 2 1 2 1 1 2 2 1 2 1 1 Robust System Design 16.881 Session #11 MIT