Transcript Probability and Statistics in Engineering

Chap 11
Engineering Statistics
PREP004 – Introduction to Applied Engineering
College of Engineering - University of Hail
Fall 2009
Statistics
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Statistics is the area of science that deals with
collection, organization, analysis, and
interpretation of data.
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It also deals with methods and techniques that
can be used to draw conclusions about the
characteristics of a large number of data points-commonly called a population–
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By using a smaller subset of the entire data.
For Example…
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You work in a cell phone factory and are asked
to remove cell phones at random off of the
assembly line and turn it on and off.
Each time you remove a cell phone and turn it
on and off, you are conducting a random
experiment.
Each time you pick up a phone is a trial and the
result is called an outcome.
If you check 200 phones, and you find 5 bad
phones, then
relative frequency of failure = 5/200 =
0.025=2.5%
Statistics in Engineering
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Engineers apply physical
and chemical laws and
mathematics to design,
develop, test, and
supervise various
products and services.
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Engineers perform tests
to learn how things
behave under stress, and
at what point they might
fail.
Statistics in Engineering
 As
engineers perform experiments, they
collect data that can be used to explain
relationships better and to reveal
information about the quality of products
and services they provide.
Statistics : Major Engineering Areas
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Quality control and process control use statistics as a tool to
manage conformance to specifications of manufacturing
processes and their products.
Design of Experiments (DOE) uses statistical techniques to test
and construct models of engineering components and systems.
Time and methods engineering use statistics to study repetitive
operations in manufacturing in order to set standards and find
optimum procedures.
Reliability engineering which measures the ability of a system
to perform for its intended function (and time) and has tools for
improving performance.
Probabilistic design involving the use of probability in product
and system design
Frequency Distribution:
Scores for an engineering class are as follows: 58, 95, 80,
75, 68, 97, 60, 85, 75, 88, 90, 78, 62, 83, 73, 70, 70, 85,
65, 75, 53, 62, 56, 72, 79
To better assess the success of the class, we make a
frequency chart or a Histogram:
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With Statistics the information can be better
analyzed.
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The data are presented in a frequency
distribution or histogram.
Divide each no. by 26
Analysis of Histograms
Graph A is class distribution of numbers 1-10
Graph B is class distribution of semester credits
Data for A = 5.64 +/- 2.6 (much greater spread than B)
Data for B = 15.7 +/- 1.96 (smaller spread)
Skew of A = -0.16 and Skew B = 0.146
CV of A = 0.461 and CV of B = 0.125 (CV = SD/Mean)
Frequency B
Frequency A
9
8
7
6
5
4
3
2
1
0
7
6
5
4
3
2
1
0
2
3
4
5
6
7
8
9
10
12
13
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15
16
17
18
19
20
Measures of Central Tendency &
Variation
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Central Tendency Measures:
Mean (Average) , and Median, Mode
1 n
x   xi
n i1
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
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Variation and Dispersion Measures:
Range R, Standard Deviation and Variance
n
R = Xmax - Xmin
s

i1
(x i  x ) 2
n 1
Normal Distribution
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Any probability distribution with a bell-shaped
curve is called a normal distribution.
 The detailed shape of a normal distribution
curve is determined by its mean and standard
deviation values.
THE NORMAL CURVE
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zi = (xi - x) / s
approx. 68% of the data will fall in the interval of
-s to s, one std deviation
 ~ 95% of the data falls between -2s to 2s, and
approx all of the data points lie between -3s to 3s
 Normal Curve has many applications in
Engineering : Product design, Quality, Reliability,
Engineering Statistical
Software : Microsoft Excel
Statistics in Excel
1
Select
Tools/Data Analysis
Business Statistics: A DecisionMaking Approach, 6e © 2005
Prentice-Hall, Inc.
Chap 2-14
Histograms in Excel
(continued)
2
Choose Histogram
3
Input data and bin ranges
Select Chart Output
Business Statistics: A DecisionMaking Approach, 6e © 2005
Prentice-Hall, Inc.
Chap 2-15
Engineering Statistical
Software : Minitab
Home Work 7
Use Excel to determine the average, the
range and the standard deviation of the
following set of numbers:
(a)
24, 35, 17, 21, 24, 37, 26
(b)
59.4, 51.3, 84.15 , 96.3 ,71.1 , 95.4
78.75 , 66.15 ,77.85
Chapter Summary
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Data in raw form are usually not easy to use for
decision making -- Some type of organization is
needed:
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Table
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Graph
Techniques reviewed in this chapter:
 Frequency Distributions, Histograms
Many Other Tools are available (Scatter Diagrams
and Control Charts, Pareto diagram etc…)
Engineer use computer software to perform
statistical calculations and data analysis.