MIE364H1S Methods of Quality Control and Improvement

Course Instructor: Prof. V. Makis Handout #8

Quarter Fraction of a 2**5 Design Example An engineer is interested in improving the efficiency of a deburring operation. The deburring machine uses wire brushes for material removal. 5 factors are considered as affecting the rate of material removal. Factor Low Level High Level A = Penetration depth 0.12 in 0.17 in B = Brush width 1.5 in 2.0 in C = Number of filaments 20000 25000 D = Filament length 1 in 2 in E = Filament diameter 0.010 in 0.015 in The response variable is the rate of material removal in cubic inches times 10**(-7) per revolution. Fractional Factorial Design Factors: 5 Base Design: 3, 8 Resolution: III Runs: 8 Replicates: 1 Fraction: 1/4 Blocks: 1 Center pts (total): 0 * NOTE * Some main effects are confounded with two-way interactions. Design Generators: D = AB, E = AC Alias Structure (up to order 3) I + ABD + ACE A + BD + CE + ABCDE B + AD + CDE + ABCE C + AE + BDE + ABCD D + AB + BCE + ACDE E + AC + BCD + ABDE BC + DE + ABE + ACD BE + CD + ABC + ADE BCDE

Data Display Row A B C D E Y 1 -1 -1 -1 1 1 123 2 1 -1 -1 -1 -1 150 3 -1 1 -1 -1 1 115 4 1 1 -1 1 -1 105 5 -1 -1 1 1 -1 163 6 1 -1 1 -1 1 114 7 -1 1 1 -1 -1 126 8 1 1 1 1 1 76 Alias Information for Terms in the Model. Totally confounded terms were removed from the analysis. I + B*C*D*E

Fractional Factorial fit Estimated Effects and Coefficients for Y (coded units) Term Effects Coef Constant 121.5 A -20.5 -10.25 B -32 -16 C -3.5 -1.75 D -9.5 -4.75 E -29 -14.5 B*C -5.5 -2.75 B*E 9 4.5 Analysis of Variance for Y (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 5 4775.5 4775.5 955.1 * * 2-Way Interactions 2 222.5 222.5 111.3 * * Residual Error 0 0 0 0 Total 7 4998 Alias Structure I + A*B*D + A*C*E + B*C*D*E A + B*D + C*E + A*B*C*D*E B + A*D + C*D*E + A*B*C*E C + A*E + B*D*E + A*B*C*D D + A*B + B*C*E + A*C*D*E E + A*C + B*C*D + A*B*D*E B*C + D*E + A*B*E + A*C*D B*E + C*D + A*B*C + A*D*E

The design matrix:

A B C D=AB E=AC Y (i) (ii) (iii) effect SS (1) - - - + + 123 273 493 972 121.5 11809 a + - - - - 150 220 479 -82 -20.5 840.5 b - + - - + 115 277 17 -128 -32 2048 ab + + - + - 105 202 -99 -38 -9.5 180.5 c - - + + - 163 27 -53 -14 -3.5 24.5

ac + - + - + 114 -10 -75 -116 -29 1682 bc - + + - - 126 -49 -37 -22 -5.5 60.5 abc + + + + + 76 -50 -1 36 9 162

TCSS = 4998 = SS(A) + + SS(ABC) TSS = 123096

Effect

Perc

ent

403020100-10-20-30-40

99

95

90

80

7060504030

20

10

5

1

Factor NameA AB BC C

Effect TypeNot SignificantSignificant

AC

B

A

Normal Probability Plot of the Effects(response is Y, Alpha = .50)

Lenth's PSE = 14.25

From the attached plot, the following effects appear to be significant: ( )

( ) ( )

F

F

F

A A BD CE ABCDE

B B AD ABCE CDE

AC AC BCD E ABDE

= + + +

= + + +

= + + +

Conclusion: (if interactions are not significant) To maximize the rate of material removal: set A low, B low, and E low.