1. Solve problem 8.51 (the 16-run Chrysler number of defects experiment with 9 factors)
from 8th edition of the book.
2. Solve problem 11.34 from 8th edition of the book (the first of the two paper helicopter
problems).
3. In a factorial design with four factors, the following runs were performed: ad = 10,
b = 12, c = 15, abcd = 20.
a) What is the full defining relation for this design and what is its resolution?
b) Find the estimates for the main factor effects.
c) Suppose additional four runs have been performed: d = 5, ab = 8, ac = 12, bcd = 10.
Is is a fold-over? What kind of a fold-over is it?
d) Combine the two sets of runs to find the estimates of the main effects.
e) What is the full defining relation for the second fraction and the combined design?
d) What is the resolution of the original and of the combined design?
4. Using a response surface design, the fitted second order model of the form
ˆy = 20 10x1 + 10x2 + 10x3 2x21 7x22 5x23 + 4x1x2 6x1x3 2x2x3
for the response y was obtained.
a) Write down the matrix B for this model.
b) Find the stationary point.
c) Find the value ˆys of the predicted response at the stationary point.
d) Find the eigenvalues of B.
e) Write the model in the canonical form. What is the type of the stationary point? Can
it be considered a ridge system?
f) Find the coordinate transformation from the original to the canonical coordinates.
5. A factorial experiment with four factors is conducted. Factor A is fixed, and factors
B, C and D are random. D is nested under C and C is nested under B. The number of levels
1
is 3, 2, 4 and 3 for A, B, C and D, respectively. There are 3 replicates. Assume the restricted
model.
a) Write downs the full ANOVA model including all possible interactions.
b) Write down the expressions for all expected mean squares.
c) Propose F-tests for the significance of all effects. In case an exact F-test is not possible,
propose an approximate F-test.