Statistics 495, Applied Statistics for Industry I
Exam 1, Fall 2008
Name:____________________
Site:______________________
INSTRUCTIONS: You will have 90 minutes to complete the exam. There are 5 questions
worth a total of 100 points. Not all questions have the same point value so gauge your time
appropriately. Read the questions carefully and completely. Answer each question and show
work in the space provided on the exam. Turn in the entire exam when you are done or when
time is up. For essay questions, think before you write.
1. [15 pts] For each of the following situations indicate whether the data will be used for
primarily enumerative or analytic purposes. If the purpose is primarily enumerative
indicate what the universe, frame and sample are. If the purpose is primarily analytic
describe the process and what action will be taken on the process.
a) [5] A dairy fills 1,000,000 yogurt cups a day. Each day a sample of 1000 cups is
selected and the seal is checked on each of the sampled cups. If all of the sampled
cups are sealed correctly, the entire batch of 1,000,000 cups is shipped to the
distribution warehouse.
b) [5] At the end of each fiscal year a company selects a sample of 100 travel
reimbursement request forms from all the travel reimbursement request forms
submitted during that fiscal year. Each of the sampled forms is checked to see if
the amounts requested match receipts that are turned in with the forms. If many
mistakes or discrepancies are found in the 100 sampled forms all of that year’s
forms and receipts are checked. If no mistakes or discrepancies are found, no
further checking is done.
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c) [5] Over several years the company using the audit described in b) has found no
mistakes or discrepancies. On the basis of this, the company implements the
policy that receipts for items less than $50 do not have to be submitted with travel
reimbursement request forms.
2. [10 pts] For each of the following situations identify common and special cause variation
that might exist in the process.
a) [5] Every Tuesday morning I put my garbage cans out next to the road for pick
up. The garbage truck comes around 8 am, a little earlier or later depending on
how much garbage is left out at houses on the route. Occasionally, I come home
at 6 pm and the garbage has not been picked up. This happens because of short
staffing due to illness.
b) [5] The commute time from my house to work is approximately 10 minutes give
or take a few minutes for hitting, or not hitting, the lights right. On my regular
route there is a level railroad crossing. The railroad tracks are used but not on a
regular schedule. If I have to stop for the train, it adds another 5 minutes to the
commute (either waiting for the train or taking an alternate route).
2
3. [25 pts] On the next two pages of the exam there are two sheets of graphs. One sheet has
six run charts (numbered 1-6). The other sheet has four histograms (lettered A-D).
• For each run chart choose the histogram that matches. You will have to use some
histograms more than once.
• For each pair (run chart and histogram) comment briefly on what the graphs tell you
about the process. Be sure to describe each graph briefly and comment on how the
two graphs give similar or different impressions of the process.
Run Chart
Histogram
Comments
1
2
3
4
5
6
3
Run chart 2
100
100
80
80
Measurement
Measurement
Run chart 1
60
40
20
60
40
20
0
0
0
10
20
30
40
50
0
10
20
Rows
40
50
30
40
50
30
40
50
Run chart 4
100
100
80
80
Measurement
Measurement
Run chart 3
60
40
60
40
20
20
0
0
0
10
20
30
40
0
50
10
20
Rows
Rows
Run chart 5
Run chart 6
100
100
80
80
Measurement
Measurement
30
Rows
60
40
20
60
40
20
0
0
10
20
30
Rows
40
50
0
0
10
20
Rows
4
Histogram A
Histogram B
14
12
15
8
10
6
Count
Count
10
4
5
2
0
20
40
60
80
0
100
20
Histogram C
40
60
80
Histogram D
30
Count
15
Count
0
20
40
60
100
80
20
10
10
5
100
0
20
40
60
80
100
5
4. [30 pts] An injection molding process produces plastic squirrel cage fans. The quality
characteristic is the stiffness of the cage fan. A gauge is used to measure the deflection of
the fan under a 10-pound load. This deflection measure is used to quantify stiffness. The
smaller the deflection is the greater the stiffness, and vice versa. A gauge R&R study
was performed using six operators (A, B, C, D, E and F) measuring five fans. Each
operator measured the deflection of each fan three times. Below are the ranges and
means of the three repeat measurements.
Ranges of repeat measurements
Part
1
2
3
4
5
Operator A
5
2
2
3
2
Operator B
8
0
4
3
0
Operator C
4
2
4
3
2
Operator D
3
3
0
7
2
Operator E
2
3
2
0
4
Operator F
3
6
5
4
5
Operator C
87
86
87
86
86
Operator D
86
81
85
84
82
Operator E
89
83
94
87
87
Operator F
87
82
89
86
84
Means of repeat measurements
Part
1
2
3
4
5
Operator A
83
83
84
84
84
Operator B
89
87
88
84
90
a) [15] Compute estimates of the variance attributable to repeatability and reproducibility.
Also, report the percentage of total measurement variability attributable to each of these
components.
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b) [5] JMP is used to analyze the same data (remember that JMP uses a different method to
estimate the variance components than the one you used in a). From the JMP output,
reproduced below, report the variability attributable to repeatability and reproducibility as
a percentage of total measurement variability.
Component
Part-to-Part
Reproducibility
Repeatability
Total
Variance
Component
Estimate
Percent
of Total
1.9567
5.2667
3.8000
11.0234
17.75
47.78
34.47
100.00
c) [5] What is producing the most variability, the production process or the measurement
process? Support your answer with information from the JMP output above.
d) [5] Given your answer in c), what should be the focus for quality improvement? Explain
briefly.
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5. [20 pts] After a tough evening of studying statistics your mind turns to thoughts of food,
specifically pizza. This question deals with the home delivery of pizza.
a) [5] There are many factors that can affect the time it takes to deliver a pizza to
your home. List several possible causes under the general category of
Environment that might affect delivery time.
b) [5] Refer to the Pareto chart of complaints. What are the “significant few”
complaints and what percentage of total complaints do they account for,
individually and together?
100
200
90
60
50
100
40
30
50
20
Other
Upside down
Wrong size
Wrong order
Late
10
0
Cold
Count
70
Cum Percent
80
150
0
Complaint
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c) [5] Refer to the Histogram of delivery times. Describe the center, spread and
shape of the distribution.
12
10
6
Count
8
4
2
0
10
20
30
40
50
60
d) [5] Refer to the Run Chart of delivery times. Comment on trends or unusual
values.
60
Delivery Time (mins)
50
40
30
20
10
0
0
5
10
15
20
Days 1, 8, 15 and 22 are Mondays
25
30
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