Reading and Comprehension Questions for Chapter 14
1. Designed experiments can be used for
a. Process characterization
b. Process optimization
c. Product design
d. All of the above.
Answer – d.
2. In a factorial experiment, all of the factors are varied one-at-a-time.
True False
False – in a factorial experiment, all of the factors are varied together.
3. The main effect of a factor is the change in the average level of the response when the factor is changed from the low level to the high level.
True False
True
4. An interaction is the failure of one main effect to remain the same at different levels of another factor.
True False
True
5. One-factor-at-a-time experiments can discover interaction effects.
True False
False – factorial experiments are the only way to discover interactions.
6. The basic ANOVA identity for a two-factor factorial experiment is
True False
True
7. If all of the factors in a two-factor factorial experiment are fixed factors, the ANOVA F-test statistics are
True False
True
8. In a 23 design, +, +, + denotes the run where all three factors are at the high level.
True False
True – this is the notation for two-level designs.
9. In a 22 design, the symbols (1), a, b, and ab are used to represent the totals of the replicates at the four design points.
True False
True
10. After conducting an experiment using a 22 design, the experimenter found that the repose could be predicted by the following equation:
The predicted response at the design point where both factors are at the low level is:
a. 6
b. 4
c. 8
d. 5
Answer – b. The predicted response is
11. The relationship between a contrast and an effect in a 2k design is
True False
False – the correct relationship is .
12. In a 2k design the sum of squares for any factor can be calculated from the contrast for that factor.
True False
True
13. An unreplicated 2k design is a design where there are no runs at some of the treatment combinations.
True False
False – an unreplicated 2k design is a design where there is one run at the each of the treatment combinations.
14. An important part of the analysis of an unreplicated 2k design is to construct a normal probability plot of the effect estimates.
True False
True
15. Adding center points to a 2k design allows the experimenter to obtain an estimate of pure error and to perform a statistical test for the presence of pure quadratic effects.
True False
True
16. When 6 center points are added to unreplicated 2k design, the number of degrees of freedom for pure error is:
a. 6
b. 4
c. 5
d. None of the above.
Answer – b.
17. An unreplicated 2k design can be run in two blocks by confounding one effect with blocks.
True False
True
18. The 2k-1 design is a one-half fraction of the full 2k design.
True False
True
19. In a 24-1 design with D = ABC as the generator, the alias of A would be:
a. BCD
b. ACD
c. ABD
d. ABC
Answer – a. With D = ABC as the generator the defining relation is I = ABCD, so the alias of A is AI = AABCD = A2BCD, or A = BCD.
20. The resolution of the 25-1 design is:
a. III
b. IV
c. V
d. None of the above.
Answer – c.
21. In a 2k-2 fractional factorial design, each effect has three aliases.
True False
True
22. The method of steepest ascent is use to find optimum operating conditions in a process.
True False
False – the method of steepest ascent is used to move from the current operating conditions to a region that likely contains the optimum.
23. A second-order response surface model is often used when the experimenter is close to the optimum.
True False
True
24. The central composite design is often used to fit a second-order response surface model.
True False
True
25. The central composite design requires fewer runs that a 2k design.
True False
False – the central composite design consists of a 2k design plus axial and center runs, so it always has more runs that the 2k design.