Engineering Probability and Statistics - SE-205 -Chap 1 By S. O. Duffuaa

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

Main Course Outcomes w 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 w “Applied Statistics and Probability for Engineers “ by D. C. Montgomery and Runger, w “Probability and Statistics for Engineers and Scientists” 5 th by Walpole and Mayers. w Statistics by Murry Speigel

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

SE- 205 Place in SE Curriculum w Central Course w 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 w Develop clear and concise problem description w Identify the important factors in the problem. w Propose a model for the problem w Conduct appropriate experimentation w Refine the model

Engineering Problem Solving w Validate the solution w 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 w Many aspects of Engineering deals with data – Product and process design w Identify sources of variability w Essential for decision making

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

Data Collection w Design of experiment Plays key role in engineering design

Statistics w Divided into : Descriptive Statistics Inferential Statistics

Forms of Data Description w Point summary w Tabular format w Graphical format w Diagrams

Point Summary w Central tendency measures Mean  x i /n Median --- Middle value Mode --- Most frequent value

Point Summary w Variability measures Range = Max x i - Min x i Variance = V =  (x i – x ) 2 / n-1 Standard deviation = S S = Square root (V) Coefficient of variation = S/ x

Dot Diagram w 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,

Dot Diagram w 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,

Time Frequency Plot

Lower control limit = x = Upper control limit = Control Charts