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12 realabilty of systems 1 (2)

# 12 realabilty of systems 1 (2) - Preliminary presentation...

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MFG5350 1 October 13, 2008 (next Monday) Preliminary presentation for project

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MFG5350 2 October 20, 2008 (Monday) Mid-term exam
MFG5350 3 Due Oct 10 (this Friday) before 5:00PM Homework 3

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MFG5350 4 Reliability of Systems Serial Configuration Parallel Configuration Combined Series-Parallel
MFG5350 5 Serial Configuration Reliability Block Diagram E 1 = the event, component 1 does not fail, and E 2 = the event, component 2 does not fail, then P{E 1 } = R 1 and P{E 2 } = R 2 where R 1 = the reliability of component 1, and R 2 = the reliability of component 2. Therefore assuming independence: R s = P{E 1 E 2 } = P{E 1 } P{E 2 } = R 1 R 2

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MFG5350 6 Multiple Components in Series Generalizing to n mutually independent components in series; R s (t) = R 1 (t) x R 2 (t) x . .. x R n (t) and R s (t) min {R 1 (t), R 2 (t), . .., R n (t)}
MFG5350 7 Parallel Configuration R s = P{E1 E2} = 1 - P{(E1 E2) c } = 1 - P{E1 c E2 c } = 1 - P{E1 c } P{E2 c } = 1 - (1-R 1 ) (1-R 2 ) where E1 = event, component 1 does not fail E2 = event, component 2 does not fail, and Pr{E1} = R 1 and Pr{E2} = R 2 R 1 R 2 R n The probability at least one component does not fail!

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MFG5350 8 Parallel Configuration - Generalization s i=1 n i R (t) = - 1- R (t) 1 R s (t) >= max {R 1 (t), R 2 (t), …, R n (t)}
MFG5350 9 Parallel Configuration - CFR Model s i= n - t R (t) = - - e i 1 1 1

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12 realabilty of systems 1 (2) - Preliminary presentation...

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