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QUEEN’S UNIVERSITY
FACULTY OF APPLIED SCIENCE
Department of Chemical Engineering
CHEE 209
FINAL EXAMINATION
DECEMBER 2002
Prof. Kim McAuley
INSTRUCTIONS: This examination is THREE HOURS in length and contains 5 questions totaling
100 marks. The exam is open book. Calculators, textbooks and course notes are
permitted. Please answer all questions in the answer booklets provided. Put your
student number on the front of all answer booklets. Please remember to hand in
Page 5 along with your answer booklets.
Note: The candidate is urged to submit with the answer paper a clear statement
of any assumptions made if doubt exists as to the interpretation of any question
that requires a written answer.
Page 2 of 7
Question #1 (11 marks)
Two Chemical Engineering Professors (let’s call them Jim and Kim) travel from Toronto to Indianapolis
(on a direct flight) to present their research at the annual conference of the American Institute of
Chemical Engineers. Assume that, on each flight, one out of every 50 passengers is randomly selected
by security for a thorough search. During this search the security officer removes and inspects the articles
from the traveler’s carry-on baggage and requires the traveler to remove his or her shoes and belt. Please
state any assumptions that you make when you answer the questions below.
a) What is the probability that one of the professors (Jim) is selected for a thorough search before
the flight to Indianapolis and is selected again on the return flight to Toronto? (3 marks)
b) What is the probability that Jim is selected and searched before both flights and that Kim is not
selected on either? (3 marks)
c) What is the probability that the one or more searches of this pair of travelers is conducted during
their trip to and from Indianapolis? (3 marks)
d) What is the average number of searches that will be conducted when two professors travel to and
from Indianapolis? (2 marks)
Question #2 (20 marks)
Acme Polymers produces linear low-density polyethylene at two different production facilities and sells a
number of different grades of polyethylene to customers around the world. Some of the grades are used
to produce plastic film and garbage bags, while others are used to produce plastic toys and plastic
margarine dishes. Density, which is one of the key polyethylene quality variables, is measured every few
hours to ensure that the polymerization process is operating near the target value. The operation of the
process is adjusted whenever significant deviations from the target are identified.
Both of the Acme plants have quality control labs where the density is measured. The Acme Total Quality
Engineer is concerned that the polyethylenes that are produced at the two plants seem to be slightly
different. She wants to determine whether the density measurements performed at the two different
quality labs are comparable, so that she can assess whether biased laboratory measurements are the reason
that the products from the two plants are different. She collects representative samples from the various
polyethylene grades and sends them to the two labs for analyses. Here are the results that are obtained at
the two labs:
Polyethylene Grade Sarnia Lab Mount Belleview Lab
Density Measurement (kg/m3) Density Measurement (kg/m3)
A 918.53 918.79
B 926.14 926.45
C 935.28 935.22
D 915.32 916.02
E 923.64 924.27
F 917.82 917.96
a) Determine whether there is a significant difference between the measurements obtained at the two
labs. (18 marks)
b) State any assumptions that you made when answering part a). (2 marks)
Page 3 of 7
Question #3 (24 marks)
Acme Paper Company makes Durable Matte #3, a strong lightweight acid-free paper used in the book
publishing industry. The company has changed its production process to increase the amount of post-
consumer waste incorporated in this grade of paper from 15% to 20% by weight. The following data
table gives a comparison of the brightness of the resulting paper for paper samples produced before (16
samples) and after (11 samples) the change. The data in the table have been sorted from lowest to
highest. For all tests in the questions below, please use the 5% significance level or 95% confidence
levels.
Paper Brightness (%) Paper Brightness (%)
(15% post-consumer waste) (20% post-consumer waste)
81.3 80.1
81.4 80.3
82.7 80.6
83.5 81.1
83.8 82.5
83.8 83.2
84.1 83.7
84.3 83.7
84.6 85.1
84.8 85.7
84.9 85.8
85.2
85.4
86.5
86.7
87.2
Average = 84.39 % Average = 82.89 %
Standard Deviation = 1.69 % Standard Deviation = 2.13 %
a) Determine whether it is appropriate to use a pooled variance estimate to compare the means of the
underlying populations. (12 marks)
b) Use a hypothesis test to determine whether the increase in the amount of post-consumer waste has
significantly reduced the brightness of the resulting paper. (12 marks)
Page 4 of 7
Question #4 (27 marks)
The production technologists at Acme Paper Company have been collecting product quality data for the
past month. One of the key quality variables for their Premium Light Weight grade of paper is opacity.
This grade of paper is used in the text and reference book printing market. If the paper isn’t opaque
enough, then the printing on the back of a page will tend to show through on the front side. The
production technologists have collected opacity readings from 5 paper samples during each shift and they
have plotted the average opacity and the standard deviation of the opacity for each group of five samples
on the control chart shown below. The values used to plot the chart are given in the following table.
a) Determine an appropriate center line and control limits for this control chart and draw them on
the graph. State any assumptions that you make, and please make sure that you hand in the
graph with your exam booklet. (14 marks)
b) The next set of 5 opacity readings is 85.23, 84.69, 85.04, 86.29, 84.56. Determine and plot the
next point on the control charts below. (5 marks)
c) Has the process has been operating under statistical control, or does it appear that there have been
some special causes of process variability? Explain your answer. (3 marks)
d) The lower and upper specification limits for opacity are 83.5 and 86.5, respectively. Determine
the process capability, Cpk, for this process. Is the process capable of meeting the opacity
specifications 99.7% of the time? (5 marks)
Shift Number Average of Five Standard Deviation of
Measured Opacities Opacity Measurements
1 85.45968 0.653282
2 85.06558 0.548767
3 85.24658 0.403102
4 84.66379 0.432042
5 84.89961 0.806519
6 85.19508 0.303316
7 84.79467 0.460289
8 85.06747 0.525473
9 84.71668 0.459454
10 85.01464 0.299514
11 85.25717 0.634913
12 85.00817 0.522459
13 85.27386 0.50114
14 84.76183 0.271891
15 85.49107 0.601688
16 85.14095 0.615225
17 84.95285 0.766178
18 85.06419 0.404821
19 84.94553 0.487209
20 85.20354 0.587543
Average for 85.06 0.518
twenty shifts
Page 5 of 7
Student Number:
Average Opacities for Each Shift (n=5)
86.5
86
Opacity %
85.5
85
84.5
84
83.5
0 5 10 15 20 25
Shift Num ber
Standard Deviation of Opacity (n=5)
3
Standard Deviation %
2.5
2
1.5
1
0.5
0
0 5 10 15 20 25
Shift Num ber
Page 6 of 7
Question #5 (18 marks)
Acme Paper produces specialized paper used in the production of corregated cardboard boxes. This paper
must be strong and durable enough to ensure that the resulting cardboard boxes meet customer demands.
One measure of the strength and durability of paper products is the burst resistance. Burst resistance is
determined by applying hydraulic pressure to one side of a sheet of paper, and then increasing the
pressure until the paper bursts apart. As you might imagine, thicker sheets of paper tend to have a higher
burst strength than thinner sheets. Since the actual thickness of a sheet of paper can vary substantially
from location to location on a particular sheet, paper thickness is usually specified by quoting the basis
weight. Basis weight is the mass of paper per unit area. The engineers at Acme Paper have been doing
tests of the relationship between burst strength and basis weight for a particular grade of paper called
Medium Fluting WBF. They have collected the experimental data in the table below. Notice that six
replicate experiments were performed using paper with a basis weight of 127 g/m2. The sample variance
for these replicates is 0.05529 kg2/cm4 and the average burst resistance is 2.483 kg/cm2.
Basis Weight Burst Resistance
(g/m2) (kg/cm2)
100 1.749
112 2.034
120 2.095
127 2.240
127 2.170
127 2.646
127 2.700
127 2.694
127 2.448
140 2.945
150 2.807
160 3.315
170 3.336
The Acme engineers used linear least squares regression to fit the following straight line to the data:
BR = 0.0237 BW – 0.5662
where BR is the burst resistance and BW is the basis weight. They calculated the sum of the squared
residuals for the 13 data points and obtained 0.4201 kg2/cm4. A plot of the data is shown on the next
page:
Page 7 of 7
Influence of Basis Weight on Burst Resistance
4.000
Burst Resistance kg per
3.500
square cm
3.000
2.500
2.000
1.500
1.000
90 100 110 120 130 140 150 160 170 180
Basis Weight grams per square meter
a) Use the results from the replicate runs and the sum of squared residuals to test for model
adequacy. (12 marks)
b) List three other methods that you could use to help you determine whether or not the model fits
the data well. (3 marks)
c) The technicians who performed the experiments did them in the order shown in the table. Was
this a good idea? Explain why or why not. (3 marks)
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