Problem 1
A router is used to cut locating notches on a printer circuit board. The vibration level at the surface of the board as it is cut, is considered to be a major source of dimensional variation (lower the better) in the notches. Only two factors are thought to influence vibration: bit size (A) and cutting speed (B). Two bit sizes (1/16 and 1/8 inch) and two cutting speeds (40 and 90 rpm) are selected, and four boards are cut at each set of conditions shown below. The response variable is 'vibration' measured on each test circuit board, and the non-randomized data is shown in the table below. Assume that, for each factor, the lower value is -1 and the higher value is +1.
| A |
B |
Replicate I |
Replicate II |
Repilicate III |
Repilicate IV |
| -1 |
-1 |
18.2 |
18.9 |
12.9 |
14.4 |
| 1 |
-1 |
27.2 |
24 |
22.4 |
22.5 |
| -1 |
1 |
15.9 |
14.5 |
15.1 |
14.2 |
| 1 |
1 |
41 |
43.9 |
36.3 |
39.9 |
Assume that factors A and B are "numeric", and factors C is "text".
The following is the data(in MIPS) collected from the experiment(the data is fictitious):
Assume 5% level of significance.
If you decide to keep AB in the model (perhaps because it is significant), you must also keep A d B (even if either or both of those factors are not significant).
Question: At which of the 2 levels (1/16 inch? or 1/8 inch?) of bit size is the process more robust cutting speed changes? 'Robust' means that a change in cutting speed does not severely elatively speaking) impact vibration.
Problem 2
Millions of Instructions per Second (MIPS) is a way of measuring a computer's processing speed (higher the better).
Three factors were considered in an experiment to test the processing speed:
|
Factor |
Level -1 |
Level 1 |
| A |
Memory Size |
4MB |
16MB |
| B |
Cache Size |
1kB |
2kB |
| C |
Number of Processors |
1 |
2 |
Assume that factors A and B are "numeric", and factor C
Assume 5% level of significance.
If you keep a significant 2-factor interaction in the model, you must keep (in the model) both of those factors. For example, if you keep AB in the model, you must also keep A and B (even if either or both of those factors are not significant).
If you find that the 3-factor interaction is significant, remove it from the model anyway.
Questions
At which of the 2 levels (1kB? or 2kB?) of Cache Size is the processing speed robust to changes in number of processors? 'Robust' means that a change in the number of processors does not severely (relatively speaking) impact processing speed.
Write your answer here:
What should be the Memory Size? (4MB? or 16MB?)
Problem 3:
A 25-1 experiment with 1 replicate was coducted by a company to study the filling variability(standard deviation) of dry soup mix packages. The lower the variablity, the better it is,
The factors are
A: number of mixing ports though which the vegetable oil was added (1, 2)
B: temperature surrounding the mixture (cooled, ambient)
C: mixing time (60 sec, 80 sec)
D: batch weight (1500 Ibs, 2000 Ibs)
E: number of days of delay between mixing and packaging (1, 7)
A and B are "text" factors.
C, D, and E are "numeric" factors.
The data (non-randomized) is provided in Final_Exam.xls posted in Session-6 folder on Trunk. Use the default generators of Minitab and ignore the counterparts of confounded actoi s/interactions.
If you keep a significant 2-factor interaction in the model, you must keep (in the model) both of ose factors. For example, if you keep BC in the model, you must also keep B and C (even if tither or both of those factors are not significant).
Perform appropriate statistical analysis (at 5% level of significance) and answer the following questions:
a) If E = -1, what should be the levels of B, C, D?
b) If B = 1, C = 1 and D = 1, what should be E?
c) If B and C are set to -1, recommend a combination of D and E that helps keep the standard deviation to lower than 1.
d) If you set B and E to -1, and plot a Surface Plot for C and D, why doesn't the Surface Plot have any curvature?
e) Why doesn't Minitab let you choose B for X or Y-axis in the Contour Plot?
Problem 4
A new Process Improvement Manager has been hired by the soup packages company mentioned in Problem 4. She has just been given 16 additional values of the response variable (Standard Deviation) from "Replicate 2" of the experiment mentioned in Problem 4.
The data (non-randomized) is provided in Final Exam.xls posted in Session-6 folder on Trunk. Re-do the analysis with 2 replicates now.
Use the default generators of Minitab and ignore the counterparts of confounded factors/interactions.
If you keep a significant 2-factor interaction in the model, you must keep (in the model) both of those factors. For example, if you keep BC in the model, you must also keep B and C (even if either or both of those factors are not significant).
Perform appropriate statistical analysis (glitYojalth(lfg- significance) and answer the following questions:
a) If B = 1, C = 1 and D = 1, what should be E?
b) If B = -1, what should be D?
c) If B = 1, what should be D?
d) If B = 1, D = 1, what should be C?
Problem 5 (Clustering) Classify the following customers into 2 clusters. Assume that the initial clusters are Customer IV and Customer VI.
| Customer ID |
Customer Rating of Product A |
Customer Rating of Product B |
Customer Rating of Product C |
| I |
2 |
2 |
11 |
| II |
3 |
4 |
2 |
| III |
6 |
9 |
7 |
| IV |
7 |
10 |
4 |
| V |
10 |
14 |
8 |
| VI |
9 |
10 |
12 |
List the cutomers in each cluster in the space below:
Cutomers in each cluster 1:
Cutomers in each cluster 2:
Attachment:- Final_Exam.xlsx