Transcript week2_slides_W04

Engineering Problem Solving
Engineers are problem solvers
Civil
Nuclear
Electrical
Industrial
Computer Science
Chemical
Mechanical
Engineering Problem Solving
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Engineers need a strong background in
many different technical fields including
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Physics
Mathematics
Chemistry
Computational science
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Engineering Problem Solving
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Successful resolution of engineering
problems also requires
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Common sense
Good judgment
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Engineering Problem Solving
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Engineering solutions often involve
balancing and making trade-offs
between several competing factors
Cost
Efficiency
Productivity
Design
Reliability
Performance
Engineering Problem Solving
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Define the problem
Determine what information is known.
Determine what information is needed.
Decide which engineering principles apply to
the problem.
Select an appropriate methodology or
solution strategy to apply to the problem.
Make simplifying assumptions.
Iterate.
Test and verify solution.
Example
Plastic milk-crates, like many other
products in use, are designed by "feel".
The uncertainty of the effects of unknown
factors is resolved by over-dimensioning
the crates and, as a consequence, making
them heavier. Your company has been
hired by the crate manufacturer to
improve the design of the crate in an
effort to reduce manufacturing costs.
Defining the problem
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Problem definition is often the most
difficult phase of engineering problem
solving
Problems are often ambiguous and/or
not clearly specified
Problem Definition
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What is the overall
purpose of the
problem?
Gathering Information
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Gather relevant information about the
problem
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Examine previous solutions to similar
problems
Perform experiments (e.g., simulation)
Communicate results effectively
Collecting Data
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What information
is known?
What information
must be
determined?
Selection of Theories and
Methods
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Depends heavily on engineer’s educational
background and training
Computers are often used to analyze existing
data
Computers are often used to test different
models and theories
Many methods need the computing power of
today’s PC’s due to the volume of data, the
need for graphical or statistical analyses, or
the application of mathematical solutions
Theories and Methods
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What
fundamental
engineering
principles apply
to this problem?
Simplifying Assumptions
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A theory is an abstraction of how the
world works
Simplify solution by making simplifying
assumptions
Analyzing data helps in defining
assumptions
Iterative solutions
Engineering problems are often solved iteratively
Problem
Statement
Is there more
problem solving to
be done?
Yes
Analyze problem
Generate Solution
No
Use Solution
End
Test Solution
Testing and Verification
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Testing and verification is a critical step
before any solution is implemented
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Misplaced decimal points
Unit conversion errors (NASA satellite)
Impossible to test all feasible solutions
Statistical sampling can be very useful!!
Solution Generation
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What will be the
overall solution
strategy?
Example
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You have been hired
by Flights R Us to
design an electronic
checklist product to
be used by general
aviation pilots.
Engineering Design
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Define the design objectives
Determine what information is known.
Determine what information is needed.
Decide which engineering principles apply to
the design.
Select an appropriate methodology or
solution strategy to apply to the design.
Make simplifying assumptions.
Iterate.
Test and verify solution.
Engineering Design and
Computers
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Outline the basic steps to approach the
engineering design problem given.
Where would computers and software
be used?
What type of computer and software
would be most relevant to the problem
at each step of the problem solving
process?
Computers and Computing
Computers and Computing
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Computers and their applications:
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Personal digital assistants (PDA’s)
Personal computers (PC’s)
Workstations
Servers
Supercomputers
Special purpose computers
Usage?
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What is the primary purpose for each
type of computer?
What are the advantages?
What are the limitations?
Types of Software
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Files: Named collection of information stored on
a computer
 Word processing document or spreadsheet
 Database
 Drawing
 Program instructions
Programs: Ordered set of instructions that tell a
computer what to do
 Application programs
 Operating systems
General Purpose Applications
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Spreadsheets
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Database
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Microsoft Excel
Microsoft Access
Web clients (browsers)
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Microsoft Internet Explorer
Netscape Navigator
General Purpose Programs
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Software for developing software
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C++
Java
Visual Basic
Operating Systems
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Collection of programs that
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Interface with the user
Store, organize, and provide access to files
Provide access to disks and other devices
Start and stop application programs
Provide services to application programs
Examples
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Linux
Windows
Computer Networks
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Sharing resources
May be classified according to
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Geographic distribution
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Local area network (LAN)
Wide area network (WAN)
Interconnection structure (topology)
Communication mode employed
Speed or data rate of the links
ENGR 112
Data Analysis in Excel
Engineers and Excel
Excel is used extensively by many engineers
and in all types of engineering functions –
manufacturing, product development, research,
marketing and sales
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Problems become
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Easier
Less time consuming
Many summer internships require the use of a
spreadsheet tool such as Excel
What is Data Analysis?
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Mathematical and graphical operations that
can be performed on experimental data
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Used to extract the information contained in
the data
Can significantly affect how information is
perceived by decision maker
Data Analysis Objective
DATA
90.74
94.64
93.58
90.54
INFORMATION
93.99
91.11
99.89
90.79
Mean = 93.16
Std Dev = 3.18
Data Analysis
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Choosing and collecting the data
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Decide what data is needed such as time,
temperature, date, equipment number, etc
Collect data manually or through
automated means such as a scanner,
sensors, file transfer, etc.
Data Analysis
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Processing the data
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Generate useful information
The same data set may be used to produce
information for different purposes
Consider the who needs the data, for what
purpose, and how the data will be used.
Data Analysis
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Using the information
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Involves PEOPLE!!
Decision making starts when information becomes
available
How people use information depends on
 Intuition
 Experience
 Training
 Interest
 Ethics
Data Analysis
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Numerical methods
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Descriptive statistics
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Measures of central tendency
Measures of dispersion
Graphical methods
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Line chart
Pie chart
Histogram
Data Analysis Example
Strength testing of materials often
involves a tensile test in which a
sample of the material is held
between two mandrels and
increasing force (stress) is applied.
A stress-strain curve is generated
to provide information about a
particular material. Strain is the
amount of elongation of the
sample divided by the original
sample length.
Data Analysis Example
Stress Strain
(Mpa) (mm/mm)
0.000
0.000
5.380
0.003
10.760
0.006
16.140
0.009
21.520
0.012
25.110
0.014
30.490
0.017
33.340
0.020
44.790
0.035
52.290
0.052
57.080
0.079
59.790
0.124
60.100
0.167
59.580
0.212
57.500
0.264
55.420
0.300
The stress-strain data taken from
a soft, ductile material tested in
this way is tabulated to the left.
Data Analysis Example
Stress vs. Strain
70.000
Stre ss (M pa)
60.000
50.000
40.000
30.000
20.000
10.000
0.000
0.000
0.050
0.100
0.150
0.200
Strain(mm/mm)
0.250
0.300
0.350
Numerical Analysis
Numerical Methods
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There are 2 key descriptors for a set of
data (descriptive statistics)
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Measures of central tendency
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Mean
Median
Mode
Measures of dispersion
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Range
Variance
Standard deviation
Central Tendency -- Mean
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Also known as average
Most popular measure of central
tendency
n
 xi
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Where
X  i 1
n
xi = Observation number i
n = Total number of observations
Central Tendency -- Mean
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Features
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Always exists
Unique
Allows further statistical manipulations,
e.g. confidence intervals
Limitations
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Affected by the presence of unusually small
or large values (called outliers)
Central Tendency -- Median
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Middle observation within a data set
when the observations are arranged in
increasing order
If number of values (n) in data set is
odd, then the median is the middle
observation
If number of values (n) in data set is
even then Median = ( xn/2 + xn/2+1) /2
Median Examples
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Example #1
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32.3, 42.3 , 44.5, 31.3, 42.2
Median =
Example #2
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31.3, 32.3, 42.2, 42.3, 44.5, 47.5
Median =
Central Tendency -- Median
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Features
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Always exists
Unique
Not affected by extreme values
Easier to calculate
Limitations
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Not always representative of entire data set
Size of data set does not impact weighting of
values
Central Tendency
Mean vs. Median
 If distribution of values is
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Left-skewed  Mean < Median
Right-skewed  Mean > Median
Symmetrical  Mean @ Median
Central Tendency -- Mode
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Value that occurs more often than any
of the others in a data set
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Does not always exist
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Example: Scores from a test
91 92 89 78 65 100
Is not necessarily unique, i.e. a data set
can have more than one mode
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= 2 modes  Bimodal
> 2 modes  Multimodal
Central Tendency -- Mode
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Applicable to both quantitative and
qualitative data
Particularly useful in marketing and
inventory considerations
Dispersion
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Consider the following problem
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Canned mixed nuts suppliers
Sample five cans and count # of peanuts
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Supplier A: 21 20 19 20 20
Supplier B: 29 11 10 33 17
Who would you buy from? Why?
Dispersion -- Range
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Difference between the largest and
smallest values in a data set
Supplier A: 21 20 19 20 20
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Range =
Supplier B: 29 11 10 33 17
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Range =
Dispersion -- Variance
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Measures how a set of measurements
fluctuate relative to the mean of the
data set
2
 (x  x)
s 
n 1
2
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Shortcut
2
n
x
  x 

s2 
n (n  1)
2
Dispersion – Standard
Deviation
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What is the problem with the variance?
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It has different units of measurement (e.g.,
cm2)
To return data to its original units
Standard deviation = Variance