Name ______Student ID ______

Prince of Songkla University

Department of Industrial Engineering, Faculty of Engineering

Final Test First Semester, Year 2002

Date: September 24, 2002 Time: 9-12 pm

Subject: 227-551 Research Methods and Research Statistics Room: R200

Instruction: 1. Open books and notes are allowed.

2. Calculators are allowed, except personal computers, notebooks.

3. There are 5 problems (total 100 pts) and do all of them.

4. Show your work clearly and legibly.

Distribution of Scores

Problem 1

/ 20 points
Problem 2 / 20 points
Problem 3 / 20 points
Problem 4 / 20 points
Problem 5 / 20 points

Test are arranged by

Nikorn Sirivongpaisal, Ph.D.

Name ______Student ID ______

1.  (20 pts) The percentage of hardwood concentration in raw pulp, the vat pressure, and the cooking time of the pulp are being investigated for their effects on the strength of paper. Three levels of hardwood concentration, three levels of pressure, and two cooking times are selected. A factorial experiment with two replicates is conducted, and the following data are obtained:

Percentage of Hardwood Concentration / Cooking Time 3.0 Hours / Cooking Time 4.0 Hours
Pressure / Pressure
400 / 500 / 650 / 400 / 500 / 650
2 / 196.6 / 197.7 / 199.8 / 198.4 / 199.6 / 200.6
196.0 / 196.0 / 199.4 / 198.6 / 200.4 / 200.9
4 / 198.5 / 196.0 / 198.4 / 197.5 / 198.7 / 199.6
197.2 / 196.9 / 197.6 / 198.1 / 198.0 / 199.0
8 / 197.5 / 195.6 / 197.4 / 197.6 / 197.0 / 198.5
196.6 / 196.2 / 198.1 / 198.4 / 197.8 / 199.8

(a)  Analyze the data and draw conclusions. Use

Name ______Student ID ______

(b)  Under what set of conditions would you operate this process? Why?

Name ______Student ID ______

2.  (20 pts) There are many different ways to bake brownies. The purpose of this experiment was to determine how the pan material, the brand of brownie mix, and the stirring method affect the scrumptiousness of brownies. The factor levels were

Factor / Low(-) / High(+)
A = pan material / Glass / Aluminum
B = stirring method / Spoon / Mixer
C = brand of mix / Expensive / Cheap

The response variable was scrumptiousness, a subjective measure derived from a questionnaire given to the subjects who sampled each batch of brownies. An eight person test panel sampled each batch and filled out the questionnaire. The design matrix and the response data shown below:

Batch / Test panel results
A / B / C / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
1 / - / - / - / 11 / 9 / 10 / 10 / 11 / 10 / 8 / 9
2 / + / - / - / 15 / 10 / 16 / 14 / 12 / 9 / 6 / 15
3 / - / + / - / 9 / 12 / 11 / 11 / 11 / 11 / 11 / 12
4 / + / + / - / 16 / 17 / 15 / 12 / 13 / 13 / 11 / 11
5 / - / - / + / 10 / 11 / 15 / 8 / 6 / 8 / 9 / 14
6 / + / - / + / 12 / 13 / 14 / 13 / 9 / 13 / 14 / 9
7 / - / + / + / 10 / 12 / 13 / 10 / 7 / 7 / 17 / 13
8 / + / + / + / 15 / 12 / 15 / 13 / 12 / 12 / 9 / 14

(a)  Analyze the data from this experiment as if there were eight replicates of a 23 design. Comment on the results. Use

Name ______Student ID ______

(b)  Is the analysis in part (a) the correct approach? There are only eight batches; do we really have eight replicates of a 23 factorial design?

Name ______Student ID ______

3.  (20 pts) An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen. Suppose this machine tool has to operate for three production shifts. And an engineer is not confident whether there are differences between each production shift or not. The results from experiments are following. If you are an engineer, what kind of experiment will you suggest? And also analyze data and draw conclusions from your suggested experiment. Use .

A / B / C / Treatment Combination / Replicate
I / II / III
- / - / - / (1) / 22 / 31 / 25
+ / - / - / a / 32 / 43 / 29
- / + / - / B / 35 / 34 / 50
+ / + / - / Ab / 55 / 47 / 46
- / - / + / C / 44 / 45 / 38
+ / - / + / Ac / 40 / 37 / 36
- / + / + / Bc / 60 / 50 / 54
+ / + / + / Abc / 39 / 41 / 47

Name ______Student ID ______

Name ______Student ID ______

4.  (20 pts) Use experimental data from problem 3, assume an engineer desires to confound ABC effect with blocks in each replicate. Analyze data and draw conclusions from this experiment.

Name ______Student ID ______

Name ______Student ID ______

5.  (20 pts) A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part. A test is run at the parts producer to determine the effect of four factors on cracks. The four factors are pouring temperature (A), titanium content (B), heat treatment method (C), and amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm*10-2) induced in a sample coupon subjected to a standard test is measured. The data are shown in the following table:

Treatment Combination / Replicate
I / II
(1) / 7.037 / 6.376
a / 14.707 / 15.219
b / 11.635 / 12.089
ab / 17.273 / 17.815
c / 10.403 / 10.151
ac / 4.368 / 4.098
bc / 9.360 / 9.253
abc / 13.440 / 12.923
d / 8.561 / 8.951
ad / 16.867 / 17.052
bd / 13.876 / 13.658
abd / 19.824 / 19.639
cd / 11.846 / 12.337
acd / 6.125 / 5.904
bcd / 11.190 / 10.935
abcd / 15.653 / 15.053

Suppose only a one-half fraction of the 24 design could be run. Construct the design and perform the analysis, using the data from replication I.

Name ______Student ID ______

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