Question 1: Revisit slides 17-21, Fractional Factorial Design Lecture. We went over this in class but let’s practice one more time. (a) Under Dr. Snelling’s scheme, which factor or interaction would...

Question 1:
Revisit slides 17-21, Fractional Factorial Design Lecture. We went over this in class but let’s practice one more time.

(a) Under Dr. Snelling’s scheme, which factor or interaction would be confounded with the blocks? Justify your answer using the sign method.

(b) Under Dr. Cox’s scheme, which factor or interaction would be confounded with the blocks? Justify your answer using the sign method.

(c) Under Dr. Dababneh’s scheme, which factor or interaction would be confounded with the blocks? Justify your answer using the sign method.

(d) Among the three schemes listed above, whose scheme is most optimal? Give the reason.

Question 2:
Revisit slides 31-34, Fractional Factorial Design Lecture

Using the defining contrast method, verify two treatment combinations, bce and abcde, belong to the same block.

Question 3:
Consider a 2⁵
factorial design.

(a) How many factors and levels are considered in this factorial experiment?

(b) Show all the 32 treatment combinations using a, b, c, d, and e.

(c) Suppose you are not able to complete all 32 experiments in a day but you believe 16 experiments can be done in a day. How many blocks do you need under this situation?

(d) Revisiting part (c), which interaction effect would be confounded with the blocks? Using the sign method, assign optimal treatment combinations to each block.

(e) Revisiting part (c), now assign optimal treatment combinations to each block by using the defining contrast method. Note that the optimal treatment combinations you have found in parts (d) and (e) should be the same.

Question 4:
Consider a 2^8-3
fractional factorial design with design generators F=ABC, G=ABD, and H=BCDE

a) Find the complete defining relation and generate the alias structure using the principle (positive) fraction. Second, determine the design resolution (you need to show your justification).

b) List the basic variables and the design configuration (All 32 design points with the + and – signs. You should show the setting for all 8 factors by using the design generators) (Hint: Here there are 5 basic variables which you can use to generate the entire design)