MIE1727 Assignment 2
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University of Toronto Department of Mechanical and Industrial Engineering MIE1727: Quality Assurance I (Winter 2023) Assignment 2 Due: Monday, March 20, 2023, at 5pm. Submit to Crowdmark. Please post questions to Piazza Question 1 (12 points) Provide answers to the follow questions. a) In some cases, the quality characteristic that you are measuring may be eligible for variables control chart or an attributes control chart. Discuss the pros and cons of choosing one or the other. (3 points)
b) Explain the difference between control charts for nonconformity (c-chart) number of nonconforming (np-chart) and fraction of nonconforming (p-chart). (3 points)
c) What is the difference between actual process capability and process potential capability? Why should we calculate the actual process capability ratio for some cases? Explain. (3 points)
d) Estimating the process capability can be done using a histogram and probability plotting. Clearly state the advantages and disadvantages of both methods. (3 points) Question 2 (8 points) A process has an in
‐
control fraction nonconforming of p = 0.01. The sample size is n = 300. What is the probability of detecting a shift to an out
‐
of
‐
control fraction nonconforming of p = 0.05 on the first sample following the shift? Question 3 (10 points) A production line runs in batches of size 1000 where 64 units from each batch is sampled for quality assurance. The nominal fraction nonconforming is known to be ?
= 0.1. a) Set up the control chart. You do not have to provide a graphical representation. (3 points)
b) Suppose the customer risk is set to 0.5. What is the maximum fraction nonconforming that produces this risk level? You may estimate this answer using numerical tools. (3 points)
c) Determine the sample size required to force a positive lower control limit for this chart. (2 points)
d) Discuss why a positive LCL is preferable to LCL= 0. (2 points)
University of Toronto Department of Mechanical and Industrial Engineering MIE1727: Quality Assurance I (Winter 2023) Question 4 (10 points) A new scientific journal from Elsevier publisher has a new specification with managing the first decision of the new research paper submissions within 24 hours. Table 1
shows the number of decisions made each day for the last 20 days and the number of submissions that required more than 24 hours to be issued. Table 1:
research papers’ submissions data
. Day #Submissions Late decisions Day #Submissions Late decisions 1 200 3 11 219 0 2 250 4 12 238 10 3 240 2 13 250 4 4 300 5 14 302 6 5 200 2 15 219 20 6 250 4 16 246 3 7 246 3 17 251 6 8 258 5 18 273 7 9 275 2 19 245 3 10 274 1 20 260 1 a) Set up the fraction nonconforming control chart for this process, using the variable
‐
width control limit approach. Plot the preliminary data in Table 1
on the chart. Is the process in statistical control? (3 points)
b) Assume that assignable causes can be found for any out
‐
of
‐
control points on this chart. What center line should be used for process monitoring in the next period, and how should the control limits be calculated? (3 points)
c) Set up the fraction nonconforming control chart for this process, using the average sample size control limit approach. Plot the preliminary data in Table 1
on the chart. Is the process in statistical control? Compare this control chart to the one based on variable
‐
width control limits. (4 points)
University of Toronto Department of Mechanical and Industrial Engineering MIE1727: Quality Assurance I (Winter 2023) Question 5 (10 points) The IT department at the University of Toronto measures their efficacy by how many service tickets are completed within 48 hours of creation. Twenty months of data are shown in Table 2
. Table 2:
Number of service tickets resolve outside of 48 hours. Month Total tickets >48 hours Month Total tickets >48 hours 1 150 2 11 100 1 2 150 1 12 100 0 3 250 9 13 100 1 4 250 7 14 200 4 5 200 5 15 200 3 6 200 3 16 200 4 7 200 6 17 200 10 8 250 8 18 200 4 9 250 7 19 150 0 10 250 6 20 150 2 a) Construct the trial control chart for this process. You are invited (but not required) to use Minitab, but still required to show the computations for your limits. (2 points)
b) Discuss how you may use the results from part (a) to phase II control. (1 points)
c) Repeat this exercise for an average sample size. Include necessary cautions. (3 points)
d) Repeat this exercise using standard deviation units. (2 points)
e) Since there are only a few sample sizes construct a special control chart that has four different sets of control limits all on one set of axes, one for each sample size. Discuss how it would be used, and how it compares to the chart from part (a). (2 points)
Question 6 (15 points) The following fraction nonconforming control chart with ?
= 400 is used to control a process: UCL
=
0.0962
Center line
=
0.0500
LCL
=
0.0038
a) Find the width of the control limits in standard deviation units. (2 points)
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A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x =
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Gate AB in Figure below is 1.0 m long and 0.9 wide. Calculate force F on the gate and position X of its centre of
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161
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18
E
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Questions Gravity Review Question 31
17.
20.
21.
22
23.
24.
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27. Not Answered
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If a planet were to slowly migrate inward toward the Sun while remaining in a stable orbit, would its orbital speed increase, decrease, or stay the same? Would its angular momentum change?
O
a. As the planet migrates toward the Sun, its orbital speed would increase and its angular momentum would decrease.
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OC. As the planet migrates toward the Sun, its orbital speed would increase and its angular momentum would stay the same.
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Estimated
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Model Manufacture Transmissi
No. of
City
Cylinders Miles/Gallo Miles/Gallo
Highway
Size
Name
on
(liters)
NSX
Acura
Automatic
3.0
18
23
Manual
Automatic
Manual
Colt
Dodge
1.5
4
32
40
22
22
318i
BMW
1.8
4
30
Cаmry
Toyota
2.2
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Truncation errors are increased as the round-off errors are decreased.Group of answer choices True False
Say, you have a thermometer and you are checking the temperature of a body that has a temperature of 36o Using your thermometer five times, it gives you the following measurements: 29oC, 29.2oC, 29.3oC, 28.9oC, and 29.1oC. What can we conclude about the accuracy and the precision of the thermometer?Group of answer choices The thermometer is not accurate and not precise The thermometer is faulty. The thermometer is accurate and precise The thermometer is not accurate but precise.
Say, you have a thermometer and you are checking the temperature of a body that has a temperature of 36o Using your thermometer five times, it gives you the following measurements: 36oC, 35.6oC, 36oC, 37oC, and 36.2oC. What can we conclude about the accuracy and the precision of the thermometer?Group of answer choices The thermometer is accurate and precise. The thermometer is accurate but not precise. The…
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3.0'
B
63'
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The estimated times and immediate predecessors for the activities in a project at Howard Umrah's rotinal scanning company are given in the following tablo. Assume
that the activity times are independent.
Time (weeks)
Immediate
Time (weeks)
Immediate
Activity
b
Predecessor(s) Activity
b.
Predecessor(s)
a
a
7.
10
13
10
12
A
B
6
12
18
14
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a) Based on the activity time estimates, the expected times and variance for each of the activities are (round your response to two decimal places)
Expected
Time
Activity
Variance
A
B
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(enter as a probability and round your response to two decimal places)
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A. A customer asked you to explain your choice of a temperature sensor that you used for his PCB.
Initially, there were two sensor options. To compare between them, you decided to test their accuracy
and precision. Accuracy of a sensor is a measure of how near its reading is to the real value, the nearer
the measured value to the real value the better. While precision is a measure of how widely spread the
readings of a sensor are [relative to each other] when measuring the same variable, the narrower the
spread the better. So, you tested the two sensors by measuring the same temperature, which was 100
C of boiling water, and you recorder the following 10 measurements of each sensor. Which Sensor has
higher accuracy, and which one has higher precision.
Sensor
Sensor readings when measuring 100 C
99.65
100.05
103
102
99.3
s1
100.1
99.1
100.5
99
98.8
98.78
96.9
101.4
98.88
99
S2
99.12
98.9
99
98.69
99.2
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د ميکانيك شهري 2021.pdf
UNIVERSITY OF BASRAH - COLLEGE OF ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
Subject: Engineering Mechanics-Static
Class: 1st year, 1st term
Exam. : Semester
Date: 16/3/2021
Examiner: Dr. Mazin, Dr. Aqeel, Dr.Ahid and Dr.Jaffar
Time: 1.5Hours
Q1] (10 Marks)
A- In Fig.A , If the resultant force acting on the bracket is to be 642 N directed
along the positive x axis, determine the magnitude of F.
B- In Fig.B , Determine the magnitude of the resultant force acting on the screw
eye and its direction measured clockwise from the x axis.
C- In Fig.C , Resolve the 100N force into components along the u and v axes, and
determine the magnitude of each of these components.
D- In Fig.D, Determine the moment of the force about point O.
300 N
60N
25°
32
45°
60°
505 N
50°
40N
Fig. A
50 N
Fig. B
400 N
100N
28°
18
2.12 m
Fig. C
2.12 m
Fig.D
Q2] (10 Marks)
A- In Fig.A , Replace the loading system by an equivalent resultant force and
specify where the resultant's…
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