ENSE 627 Quality Management in Systems

Homework Assignment 7

Chapter 5. Design of Experiments

5.6 Assignment Problems ( Page 5-28 ~5-30 )

6. A 2⁴ factorial design was conducted producing the following test results. Calculate the estimates and derive an empirical model representing the data.

7. Use the data provided in Problem 6.
(1) Decompose the 16 runs into two data sets. The first data set resembles the results from a fractional factorial design with the generator equal to I=1234. The second data set resembles the results from a fractional factorial design with the generator equal to I=-1234. Write all the confounding patterns associated with each of the two generators.
(2) Calculate all the estimates based on the first data set and derive the empirical model.
(3) Claculate all the estimates based on the second data set and derive the empirical model.
(4) Combine the results obtained in (6) and (7) and derive the empirical model.
(5) Compare the three models derived in Problem 7 with the model derived in Probem 6. Comment on your observation.

9. A 2^4-1 fractional factorial design was conducted on a chemical process by assigning variable 4 to the 123 interaction column. The second table summarizes the 8 tests that were run, including the levels of each of the four variables and the yield (% reacted) for each test.
a. Write down all of the linear combinations of effects that can be estimated from this experiment (assume that third- and higher-order interactions are negligible).
b. Calculate numerical alues for the effect estimates and determine which effects are significant using a normal probability plot of the effect estimates.
c. Propose a tentative mathematical model for the response.