ISE 4404 Spring Semester

Problem 1 – (1 pts)
A chemical company is trying to determine an appropriate condition of a certain manufacturing process.
There are four factors can be controlled in this process, and each factor has two levels (please find the
following table):
Factor Number
Notation
Level
1
A
“+”, “-“
2
B
“+”, “-“
3
C
“+”, “-“
4
D
“+”, “-“
Please generate a fractional factorial design. (D=ABC, the design with have 24−1 = 8 possible
combinations/possibilities.)
Problem 2 – (1 pts)
A chemical company is trying to determine an appropriate condition of a certain manufacturing process.
There are two factors can be controlled in this process, and each factor has two levels. The table below
shows the results obtained after examining the measurements.
Factor A
Factor B
Level 1
Level 2
Level 1
10
12
Level 2
11
15
Please calculate the conditional main effect of Factor B at level 2 of A and two-factor interaction effect
between A and B.
Problem 3 – (0.5 pts)
The filling experiment are executed. There exist five factors (A,B,C,D,E) and each factor has two levels
(‘-’,’+’). Between 125 and 150 packages of soup were sampled over an eight-hour period for each run in
the design, and the standard deviation of package weight (Y) was used as the response variable. The
design and resulting data are shown in below table. What is the generator for this design? What is the
resolution of this design? Please explain the effects of different factors.
Order
A
B
C
D
E
Y
1
1.13
2
+
+
1.25
3
+
+
0.97
4
+
+
1.70
5
+
+
1.47
6
+
+
1.28
7
+
+
1.18
8
+
+
+
+
0.98
9
+
+
0.78
10
+
+
1.36
11
+
+
1.85
12
+
+
+
+
0.62
13
+
+
1.09
14
+
+
+
+
1.10
15
+
+
+
+
0.76
16
+
+
+
+
2.10
Problem 4 – (1.5 pts)
A chemical reaction experiment was carried out with the objective of comparing if a new catalyst B
would give higher yields than the old catalyst A. The experiment was run on five different batches of raw
material which were known to be quite different from one another. Each batch was divided into two
portions to which A or B was applied at random. The data collected are given in the following table:
Catalyst 1 2
3
4 5
A
10 17 40 24 9
B
12 19 40 23 11
(a). Explain the experimental design
(b). Carry out the appropriate t-test (with 𝛼 = 0.05).
Problem 5 – (2 pts)
The goal of an experiment was to test if there is any difference between two types of Factor 1 (A, B) and
among three types of Factor 2 (a, b, c). The responses are denoted by y in the table below.
number of responses (y)
Test
A
B
Treatment
a
b
c
a
b
c
1
10
7
15
15
18
15
2
11
8
16
14
16
14
3
12
9
17
13
14
13
4
13
10
18
12
12
18
5
14
11
19
11
10
17
6
15
12
20
10
8
16
7
16
13
21
9
6
14
8
17
14
22
8
4
18
Fill in the blank spaces of the following ANOVA table (Please round with two decimals).
Source
DF
SS
MS
F
Factor 1
Factor 2
Factor1*Factor2
residual
total
1204.85
9
18
15
23
7
6
15
10
19
16
24
6
8
11