Engineering Problem Solving

Engineers are problem solvers

Industrial

Nuclear

Computer Science

Mechanical

Civil

Electrical

Chemical

Engineering Problem Solving

Engineers need a strong background in many different technical fields including Physics Mathematics Chemistry Computational science

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Engineering Problem Solving

Successful resolution of engineering problems also requires Common sense Good judgment

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Engineering Problem Solving

Engineering solutions often involve balancing and making trade-offs between several competing factors

CostEfficiencyProductivity

DesignReliabilityPerformance

Engineering Problem Solving

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 Problem definition is often the

most difficult phase of engineering problem solving

Problems are often ambiguous and/or not clearly specified

Problem Definition

What is the overall purpose of the problem?

Gathering Information Gather relevant information about

the problem Examine previous solutions to similar

problems Perform experiments (e.g.,

simulation) Communicate results effectively

Collecting Data

What information is known?

What information must be determined?

Selection of Theories and Methods

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

What fundamental engineering principles apply to this problem?

Simplifying Assumptions A theory is an abstraction of how

the world works Simplify solution by making

simplifying assumptions Analyzing data helps in defining

assumptions

Iterative solutionsEngineering problems are often solved

iteratively

ProblemStatement

Is there moreproblem solving to

be done?Analyze problem

Generate Solution

Test SolutionUse Solution

End

Yes

No

Testing and Verification

Testing and verification is a critical step before any solution is implemented Misplaced decimal points Unit conversion errors (NASA satellite)

Impossible to test all feasible solutions Statistical sampling can be very

useful!!

Solution Generation

What will be the overall solution strategy?

Example You have been

hired by Flights R Us to design an electronic checklist product to be used by general aviation pilots.

Engineering Design 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 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

Computers and their applications: Personal digital assistants (PDA’s) Personal computers (PC’s) Workstations Servers Supercomputers Special purpose computers

Usage? What is the primary purpose for

each type of computer? What are the advantages? What are the limitations?

Types of Software 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

Spreadsheets Microsoft Excel

Database Microsoft Access

Web clients (browsers) Microsoft Internet Explorer Netscape Navigator

General Purpose Programs Software for developing software

C++ Java Visual Basic

Operating Systems Collection of programs that

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 Linux Windows

Computer Networks Sharing resources May be classified according to

Geographic distribution 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

Problems become Easier Less time consuming

Many summer internships require the use of a spreadsheet tool such as Excel

What is Data Analysis? Mathematical and graphical operations

that can be performed on experimental data

Used to extract the information contained in the data

Can significantly affect how information is perceived by decision maker

Data Analysis Objective

DATA INFORMATION

Mean = 93.16Std Dev = 3.18

90.74 93.9994.64 91.1193.58 99.8990.54 90.79

Data Analysis Choosing and collecting the data

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 Processing the data

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 Using the information

Involves PEOPLE!! Decision making starts when information

becomes available How people use information depends on

Intuition Experience Training Interest Ethics

Data Analysis Numerical methods

Descriptive statistics Measures of central tendency Measures of dispersion

Graphical methods Line chart Pie chart Histogram

Data Analysis ExampleStrength 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 ExampleStress Strain(Mpa) (mm/mm)

0.000 0.0005.380 0.003

10.760 0.00616.140 0.00921.520 0.01225.110 0.01430.490 0.01733.340 0.02044.790 0.03552.290 0.05257.080 0.07959.790 0.12460.100 0.16759.580 0.21257.500 0.26455.420 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

0.000

10.000

20.000

30.000

40.000

50.000

60.000

70.000

0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350

Strain(mm/mm)

Stre

ss (M

pa)

Numerical Analysis

Numerical Methods There are 2 key descriptors for a set

of data (descriptive statistics) Measures of central tendency

Mean Median Mode

Measures of dispersion Range Variance Standard deviation

Central Tendency -- Mean Also known as average Most popular measure of central

tendency

Wherexi = Observation number i

n = Total number of observations

nX

n

iix

1

Central Tendency -- Mean Features

Always exists Unique Allows further statistical manipulations,

e.g. confidence intervals Limitations

Affected by the presence of unusually small or large values (called outliers)

Central Tendency -- Median 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 thenMedian = ( xn/2 + xn/2+1) /2

Median Examples Example #1

32.3, 42.3 , 44.5, 31.3, 42.2 Median =

Example #2 31.3, 32.3, 42.2, 42.3, 44.5, 47.5 Median =

Central Tendency -- Median Features

Always exists Unique Not affected by extreme values Easier to calculate

Limitations 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

Left-skewed Mean < Median Right-skewed Mean > Median Symmetrical Mean Median

Central Tendency -- Mode Value that occurs more often than

any of the others in a data set Does not always exist

Example: Scores from a test

Is not necessarily unique, i.e. a data set can have more than one mode

= 2 modes Bimodal > 2 modes Multimodal

91 92 89 78 65 100

Central Tendency -- Mode Applicable to both quantitative and

qualitative data Particularly useful in marketing

and inventory considerations

Dispersion Consider the following problem

Canned mixed nuts suppliers Sample five cans and count # of

peanuts Supplier A: 21 20 19 20 20 Supplier B: 29 11 10 33 17

Who would you buy from? Why?

Dispersion -- Range Difference between the largest and

smallest values in a data set Supplier A: 21 20 19 20 20

Range = Supplier B: 29 11 10 33 17

Range =

Dispersion -- Variance Measures how a set of

measurements fluctuate relative to the mean of the data set

Shortcut

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Dispersion – Standard Deviation What is the problem with the

variance? It has different units of measurement

(e.g., cm2) To return data to its original units

Standard deviation =Variance