Download Engineering Probability and Statistics

Engineering Probability and
Statistics - SE-205 -Chap 1
By
S. O. Duffuaa
Course Objectives

To introduce students to basic concepts
in probability and statistics to enable
them to apply laws of probability,
perform data analysis, estimation, make
inference about populations and relate
these
concepts to practice
Main Course Outcomes
Students should be able to perform:
 Summarize and present data using
graphs, diagrams and point summaries.
 Define, compute probability using basic
probability laws and concepts.
 Define and describe a random variable.
 Calculate probabilities from probability
mass and density functions.
Main Course Outcomes



Describe known probability distributions in
terms pmf/pdf, distribution function, mean,
variance, and suggest few applications for
each distribution.
Perform point and interval estimation.
Use a statistical package such as Minitab
and Excel to solve problems in data
analysis, probability distribution, and
estimation.
Text Book and References


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“Applied Statistics and Probability for
Engineers “ by D. C. Montgomery and
Runger, 5th Edition, 2011.
“Statistical Procedures for Engineering,
Management and Science”, by Leland
Bland, McGraw-Hill, 1980.
“Probability and Statistics for Engineers and
Scientists” 5th by Walpole and Mayers,
2008
Statistics by Murry Speigel
Course Policy





Home-works and attendance
Quizzes
Exam1
Exam II
Final Exam
10%
15%
20%
25%
30%
SE- 205 Place in SE Curriculum
Rational

Central Course
 Prerequisite for 7 SE courses
• I SE 303, SE 320, ISE 323, ISE 325,
ISE 405, ISE 447, ISE 480, I SE 463
and may be others. See SE Curriculum
Tree
Program Outcomes


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
apply knowledge of mathematics, science,
and engineering;
design and conduct experiments, as well as
analyze and interpret data;
design and improve integrated systems of
people, materials, information, facilities,
and technology;
function as a member of a multidisciplinary team;
identify, formulate, and solve industrial and
Systems engineering problems;
Program Outcomes




understand and respect professional and
ethical responsibility;
communicate effectively both orally and in
writing;
understand the impact of engineering
solutions in a global and societal context;
recognize the need for life-long learning,
and an ability to engage in it;
Program Outcomes

have a knowledge of contemporary issues;

use up to dated techniques, skills and tools
of Industrial and Systems Engineering
throughout their professional careers
Engineering Problem Solving


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Develop clear and concise problem
description
Identify the important factors in the
problem.
Propose a model for the problem
Conduct appropriate experimentation
Refine the model
Engineering Problem Solving




Manipulate the model to help in developing
a solution.
Re-visit the experimentation to confirm
results.
Validate the solution
Conclusion and recommendations
Statistics
• Science of data collection,
summarization, presentation and
analysis for decision making.
•
•
•
•
How to collect data ?
How to summarize it ?
How to present it ?
How do you analyze it and make
conclusions and correct decisions ?
Role of Statistics


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Many aspects of Engineering deals with
data – Product and process design
Identify sources of variability
Essential for decision making
Dot Diagram

A diagram that has on the x-axis the points
plotted : Given the following grades of a
class:
50, 23, 40, 90, 95, 10, 80, 50, 75, 55, 60,
40.
.
.
.
.
0
50
100
Dot Diagram

A diagram that has on the x-axis the points
plotted : Given the following grades of a
class:
50, 23, 40, 90, 95, 10, 80, 50, 75, 55, 60,
40.
.
.
.
.
0
50
100
Data Collection

Three basic methods:
Observational study
• A retrospective study using historical data..
• An observational study collect data by
observing the system.
• A designed experiment.

The objective is to build a system model
usually called empirical models
Data Collection

Design of experiment
• Plays key role in engineering design
Statistics

Divided into :
• Descriptive Statistics
• Inferential Statistics
Forms of Data Description

Point summary
 Tabular format
 Graphical format
 Diagrams
Point Summary

Central tendency measures
• Mean  xi/n
• Median --- Middle value
• Mode --- Most frequent value
Point Summary

Variability measures
• Range = Max xi - Min xi
• Variance = V =  (xi – x )2/ n-1
• Standard deviation = S
S = Square root (V)
• Coefficient of variation = S/ x
Dot Diagram

A diagram that has on the x-axis the points
plotted : Given the following grades of a
class:
50, 23, 40, 90, 95, 10, 80, 50, 75, 55, 60,
40.
.
.
.
.
0
50
100
Dot Diagram

A diagram that has on the x-axis the points
plotted : Given the following grades of a
class:
50, 23, 40, 90, 95, 10, 80, 50, 75, 55, 60,
40.
.
.
.
.
0
50
100
Time Frequency Plot
15
14
13
12
11
y 10
9
8
7
6
5
0
10
20
30
Observation number
40
50
Time Frequency Plot
15
14
13
12
11
y 10
9
8
7
6
5
0
10
20
30
Observation number
40
50
Control Charts
105
Concentration
Upper control limit = 100.5
95
x = 91.50
85
Lower control limit = 82.54
75
0
10
20
Observation number
30