Engineering Probability and Statistics - SE-205 -Chap 1

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Engineering Probability and Statistics - SE-205
-Chap 1

• By
• S. O. Duffuaa

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Course Objectives

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

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Main Course Outcomes

• Students should be able to perform
• Summarize and present data
• Describe probability distributions
• Compute probabilities using density/mass
  functions
• Conduct interval estimation
• Make inference about populations
• Use statistical package/Minitab

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Text Book and References

• Applied Statistics and Probability for
  Engineers by D. C. Montgomery and Runger, 1994.
• Probability and Statistics for Engineers and
  Scientists 5th by Walpole and Mayers.
• Statistics by Murry Speigel

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Course Policy

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

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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

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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

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Engineering Problem Solving

• Validate the solution
• Conclusion and recommendations

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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 ?

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Role of Statistics

• Many aspects of Engineering deals with data
  Product and process design
• Identify sources of variability
• Essential for decision making

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Data Collection

• Observational study
• Observe the system
• Historical data
• The objective is to build a system model
  usually called empirical models

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Data Collection

• Design of experiment
• Plays key role in engineering design

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Statistics

• Divided into
• Descriptive Statistics
• Inferential Statistics

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Forms of Data Description

• Point summary
• Tabular format
• Graphical format
• Diagrams

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Point Summary

• Central tendency measures
• Mean ? xi/n
• Median --- Middle value
• Mode --- Most frequent value

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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

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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
100
50
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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
100
50
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Time Frequency Plot
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Time Frequency Plot
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Control Charts
Upper control limit 100.5
x 91.50
Lower control limit 82.54