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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 “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 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 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 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