Engineering Probability and Statistics - SE-205 -Chap 1

By

S. O. Duffuaa

Course Objectives

Introduce the students to basic probability and statistics and demonstrate its wide application in the area of Systems Engineering.

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.

• Describe known probability distributions in terms pmf/pdf, distribution function, mean, variance, and suggest few applications for each distribution.

Main Course Outcomes

• Calculate probabilities from probability

mass and density functions..• Perform point and interval estimation.• Use a statistical package such as

Minitab/Statistica to solve problems in data analysis, probability distribution, and estimation.

• Work in teams and communicate effectively through class presentations and group meetings.

Text Book and References

“Applied Statistics and Probability for Engineers “ by D. C. Montgomery and Runger, 2007.

“Probability and Statistics for Engineers and Scientists” 5th by Walpole and Mayers.

Statistics by Murry Speigel

Course Policy

Home-works and attendance 15% Quizzes 15% Exam1 20% Exam II 20% Final Exam 30%

SE- 205 Place in SE Curriculum

Central Course Prerequisite for 7 SE courses

• SE 303, SE 320, SE 323, SE 325,

SE 447, SE 480, SE 463 and may be others. See SE Curriculum Tree

Engineering Problem Solving

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

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

Many aspects of Engineering deals with data – Product and process design

Identify sources of variability Essential for decision making

Data Collection

Observational study• Observe the system• Historical data

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 10050

..

.

.

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 10050

..

.

.

5

6

7

8

9

10

11

12

13

14

15

0 10 20 30 40 50

Observation number

y

Time Frequency Plot

5

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15

0 10 20 30 40 50

Observation number

y

Time Frequency Plot

Lower control limit = 82.54

x = 91.50

Upper control limit = 100.5

75

85

95

105

0 10 20 30

Observation number

Co

nce

ntra

tion

Control Charts