ISE+4404+HW7
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University of Colorado, Boulder *
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Course
4404
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
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2
Uploaded by nurav01
ISE4404 Homework 7
Please submit this homework through Canvas. The format of the file must be pdf. The file should be named HW7_{Student_NAME}.
DEADLINE: NOV 27
th
11:00 AM
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 and list all the alias effect with the main effect and two-way interactions. (I=ABCD, the design will have 2
4
−
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 that can be controlled in this process, and two levels are chosen for each factor. The
table below shows the results obtained after examining the measurements.
Factor A
Level 1
Level 2
Factor B
Level 1
12, 8
12, 12
Level 2
9, 13
14, 16
Please calculate the (a) conditional main effects of Factor B at two levels of Factor A, and (b) two-factor interaction effect between A and B.
Problem 3
- (1 pts)
A factory is evaluating quality control methods. Two Inspection Techniques: (1) Manual and (2) Automated, and two Inspection Frequencies: (1) Every 2 hours and (2) Every 4 hours are being tested. Here's a summary of the average percentage of defects detected for each combination based on in control process: Every 2 hours:
Manual: 94%; Automated: 90%
Every 4 hours:
Manual: 88%; Automated: 92%
a)
Is there a main effect for the type of inspection technique? If so, describe the effect.
b)
Is there a main effect for the frequency of inspection? If so, describe the effect.
c)
Is there an interaction effect between the inspection technique and frequency of inspection? Plot the interaction effect plot and describe the effect.
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
6
A
29
21
40
25
19
55
B
32
23
40
26
20
54
d
3
2
0
1
1
-1
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 recorded in the table below.
Replications
Test
Treatment
1
2
3
4
5
6
7
8
9
10
A
a
40
23
20
28
27
27
24
23
37
22
b
38
33
21
20
22
26
27
36
39
20
c
37
26
40
37
33
27
34
38
28
20
B
a
25
33
30
28
24
26
30
23
22
32
b
23
31
31
39
28
21
34
37
23
32
c
22
37
29
40
39
31
38
26
22
21
Fill in the blank spaces of the following ANOVA table (Please round with two decimals).
Source
DF
SS
MS
F Statistics
Factor 1
0.27
Factor 2
164.43
Interaction
12.82
Error
/
total
2466.33
/
/
Is Factor 2 a significant factor based on the F-test?
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