Homework Assignment 8
Problem 6-1.
Solution:
a.
b.
Main effect of temperature:
ET = (15+17+16+28-12-24-24-24)/4 = -2
Main effect of pressure:
EP = (24+17+24+28-12-15-24-16)/4 = 6.5
Main effect of cycle time:
EC = (24+16+24+28-12-15-24-17)/4 = 6
c.
Temperature and pressure interaction:
ETP = ((12+17+24+28) - (15+16+24+24)) / 4 = 0.5
Temperature and cycle time interaction:
ETC = ((12+24+16+28) - (15+17+24+24)) / 4 = 0
Pressure and cycle time interaction:
EPC = ((12+24+28+15) - (24+24+16+17)) / 4 = -0.5
Three factor interaction:
ETPC = ((15+24+24+28) - (12+24+17+16))/4 = 5.5
d.
Mean = 20,
The mathematics model is:
WI = 20 - X1 +3.25X2 + 3X3 + 0.25X1X2 -0.25X2X3 + 2.75X1X2X3
Problem 6-2.
Solution:
a.
b.
Main effect of tool surface coating:
EX1 = ((32+20)-(55+44))/2= -23.5
Main effect of cutting fluids:
EX2 = ((55+20)-(44+32))/2 = -0.5
Tool surface coating and cutting fluids interaction:
EX1X2 = ((20-55) - (32-44))/2 = -11.5
c.
From the figure, we can see that the two slopes are not parallel to each
other, so interaction exists between these two variables.
Problem 6-2.
Solution:
a.
Main effect of hours of sleep:
EX1 = ((72+89+62+75)-(56+68+43+59))/4=18
Main effect of Ounces of coffee:
EX2 = ((68+89+59+75)-(56+72+43+62))/4 = 14.5
Main effect of number of donuts:
EX3 = ((43+62+59+75)-(56+72+68+89))/4 = -11.5
Interaction between the hours of sleep and ounces of coffee:
EX1X2 = ((43+56+89+75)-(68+72+62+59))/4 = 0.5
Interaction between the hours of sleep and number of donuts:
EX1X3 = ((56+68+75+62)-(43+59+72+89))/4 = -0.5
Interaction between the ounces of coffee and number of donuts:
EX2X3 = ((56+59+75+72)-(43+68+62+89))/4 = 0
Interaction between the three variables:
EX1X2X3 = ((72+68+43+75)-(56+89+59+62))/4 = 5.5
Mean value:
Mean = 20
c.
The mathematical model is:
WI = 20+9X1+7.25X2-5.75X3