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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.
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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)
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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

       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
        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)
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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
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Student Number:

                                     Average Opacities for Each Shift (n=5)

   Opacity %

                                 0     5               10                  15   20   25
                                                           Shift Num ber

                                          Standard Deviation of Opacity (n=5)

   Standard Deviation %

                                0     5               10                15      20   25
                                                        Shift Num ber
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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
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                                        Influence of Basis Weight on Burst Resistance

Burst Resistance kg per

      square cm





                                  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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