Engineering Probability and Statistics - SE-205 -Chap 4 By S. O. Duffuaa.
Engineering Probability and Statistics - SE-205 -Chap 1 By S. O. Duffuaa.
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Transcript of Engineering Probability and Statistics - SE-205 -Chap 1 By S. O. Duffuaa.
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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 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.
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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.
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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
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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 10050
..
.
.
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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 10050
..
.
.
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Observation number
y
Time Frequency Plot
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Observation number
y
Time Frequency Plot
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Lower control limit = 82.54
x = 91.50
Upper control limit = 100.5
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Observation number
Co
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Control Charts