# rpra1 - Engineering Risk Benefit Analysis 1.155, 2.943,...

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RPRA 1. The Logic of Certainty 1 Engineering Risk Benefit Analysis 1.155, 2.943, 3.577, 6.938, 10.816, 13.621, 16.862, 22.82 ESD.72J, ESD.721 RPRA 1. The Logic of Certainty George E. Apostolakis Massachusetts Institute of Technology Spring 2007

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RPRA 1. The Logic of Certainty 2 Event: A statement that can be true or false. “It may rain tonight” is not an event. According to our current state of knowledge, we may say that an event E is TRUE, FALSE, or POSSIBLE (UNCERTAIN). Eventually, E will be either TRUE or FALSE. Event Definition
RPRA 1. The Logic of Certainty 3 Event True False Possible

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RPRA 1. The Logic of Certainty 4 Venn Diagrams Sample Space: The set of all possible outcomes of an experiment. Each elementary outcome is represented by a sample point. Examples : Die {1,2,3,4,5,6} Failure Time {0, } A collection of sample points is an event. S E Venn Diagram
RPRA 1. The Logic of Certainty 5 Important Note: X k = X, k: 1, 2, … Indicator Variables 1, If E j is T 0, j is F X j = S E Venn Diagram ___ E

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RPRA 1. The Logic of Certainty 6 ) 1 )( 1 ( 1 B A C X X X = C B A = C j C X X Union (OR operation) A B C A B
RPRA 1. The Logic of Certainty 7 C B A = B A C X X X = j C X X Intersection (AND operation) = B A Mutually Exclusive Events : C A B A B

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RPRA 1. The Logic of Certainty 8 1 N . . . . C N j N j X X X 1 1 ) 1 ( 1 = failure: Simple Systems Reliability Block Diagram for the Series System N 1 System Failure ...
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## This note was uploaded on 11/08/2011 for the course AERO 16.851 taught by Professor Ldavidmiller during the Fall '03 term at MIT.

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rpra1 - Engineering Risk Benefit Analysis 1.155, 2.943,...

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