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rpra4 - Engineering Risk Benefit Analysis 1.155 2.943 3.577...

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RPRA 4. Availability 1 Engineering Risk Benefit Analysis 1.155, 2.943, 3.577, 6.938, 10.816, 13.621, 16.862, 22.82, ESD.72, ESD.721 RPRA 4. Availability George E. Apostolakis Massachusetts Institute of Technology Spring 2007

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RPRA 4. Availability 2 Definitions Unavailability: q(t) = Pr[down at t] Availability: a(t) 1-q(t) = Pr[up at t] q(t) + a(t) = 1
RPRA 4. Availability 3 Unattended components q(t) = F(t) = Pr[T < t] Example: 2-out-of-3 system of exponential components 3 t 2 t s s ) e 1 ( 2 ) e 1 ( 3 ) t ( F ) t ( Q λ λ = =

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RPRA 4. Availability 4 Continuously monitored repairable components
RPRA 4. Availability 5 Continuously monitored repairable components (2) Average unavailability: For the exponential failure distribution: MTTR MTTF MTTR q + = 1 . 0 λτ for λτ q : Note , λτ 1 λτ λ 1 τ τ q λ 1 MTTF < + = + = =

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RPRA 4. Availability 6 Example 2 3 1 A B i MTTF (hrs) MTTR (hrs) 1 800 8 2 600 15 3 600 15
RPRA 4. Availability 7 Example (2) What is the reliability of the system for one month assuming that no repair is available?

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• Fall '03
• lDavidMiller
• Reliability theory, Availability, Unavailability, George E. Apostolakis Massachusetts Institute of Technology, RPRA

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rpra4 - Engineering Risk Benefit Analysis 1.155 2.943 3.577...

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