STAT 402 Take Home Exam Questions
Final exam on Wednesday, May 3, 9:45am to 11:45am
1. A fractional factorial experiment is performed to assess the effect of six factors on the
cutting force produced during the machining of an aluminum alloy. The factors, and
their levels, are given below.
Factor Low Level (–) High Level (+)
A: Cutting speed (sf/min) 2000 2500
B: Tool Geometry Negative Positive
C: Machine American Monarch
D: Cutting Fluid Absent Present
E: Feedrate (in/rev) 0.005 0.010
F: Depth of cut (in) 0.050 0.100
The experiment uses the two design generators: E=ABC and F=BCD to get the
plus/minus levels for the last two factors. The data are given below.
A B C D E=BCD F=ABD Force
–––– – – 21
+– – – – + 45
– + – – + + 119
++ – – + – 61
––+– + – 59
+–+– + + 110
–++– – + 65
+++ – – – 35
– – – + + + 122
+– –+ + – 52
–+–+ – – 31
++ – + – + 57
––++ – + 57
+–++ – – 29
–+++ + – 70
++++ + + 121
You should analyze this experiment and be prepared to answer questions on the design
and analysis during the final exam. Some things you should think about are: What is
the defining relation for this experiment? What is the resolution of this experiment?
What are values for the estimated effects? According to a normal plot, what effects
appear to be large? Can you project this experiment into a smaller experiment and
pick up pseudo-replication? What effects are statistically significant? What recom-
mendations can you make to produce the lowest cutting force? What is the predicted
cutting force for a specific combination of factor levels?
