STAT 430: Sample Midterm II - People.stat.sfu.ca

STAT 430: Sample Midterm II
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1. A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a
potentially serious problem in the final part because it can lead to nonrecoverable failure. A test
is run at the parts producer to determine the effect of four factors on cracks. The four factors are
pouring temperature (A), titanium content (B), heat treatment (C) and amount of grain refiner
used (D). A 2 4 design was run but due to time constraints, only one replicate of each run was
obtained. The length of crack induced in a sample coupon subjected to standard test is measured.
(a) Write down the design matrix for such design.
(b) What is the degree of freedom of the error term?
(c) Assume that the following following normal probability plot was obtained. Write down a
suitable model for the experiment. Remember to include the constraints and assumptions.
(d) Write down the model matrix for your proposed model.
(e) Based on your model, how many degrees of freedom are there for the error term?
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2. Consider blocking a 2 6 design into four blocks in the following 3 ways:
Option 1 B 1 : 123, B 2 : 145
Option 2 B 1 : 1234, B 2 : 3456
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Option 3 B 1 : 1234, B 2 : 1456
(a) What is the order for each option?
(b) Which is the best option?
(c) Write down a better blocking scheme than Option 1. Explain why.
3. Consider a 2 5−2 design with design generators as follow:
D = AB
E = AC
(a) Write down the defining relation for such design.
(b) What is resolution of such design? What is the general aliasing assumption for design with
such resolution?
(c) Write down the aliases for the main effect A and interaction effect BC.
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