11_12 Dynamic Reliability

11_12 Dynamic Reliability - CEE 597 - Lecture 11 & 12...

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EE 597 - cture 11 & 12 CEE 597 Lecture 11 & 12 Dynamic Reliability of Series & Parallel Systems 14 February 2007 Jery Stedinger Lecture 11&12 1
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PRELIM EXAM Thursday, March 8, 2007, in evening, 7:30 - 9:00 pm. Learning objectives and old exams distributed Friday, Feb. 23 . 14 February 2007 Jery Stedinger Lecture 11&12 2
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Where We Are – Reliability See top of Homework Sheets This week Wed. - Friday lectures addressing reliability of complex systems and networks. Handout Dyn. Reliability; plus in packet Yen&Tung; Hiller&Lieberman, Ch 14. Material has two lessons for us. 1. One is methodology of calculating reliability of parallel, ries and other systems and networks. series and other systems and networks. 2. Second is an appreciation of impact on system reliability of components in parallel, series and other configurations. 14 February 2007 Jery Stedinger Lecture 11&12 3
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Where We’re Going – Risk Profiles See top of Homework Sheet Next week Mon. & Wed. lectures on risk profiles lease READ Please READ *Keeney, Kulkarni & Nair, “Assessing Risk of an LNG Terminal Raj and Glickman, “ Gen. Hazardous Material Risk Profiles on RR Routes” RP Examples in CEE 597 Packet Next Week Friday lecture y is about accident response; no reading 14 February 2007 Jery Stedinger Lecture 11&12 4
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Where We’re Going– Statistics & Failures See top of Homework Sheet Starting Feb 26 review of statistical concepts followed on Feb. 28/March 2 discussion of transportation risks. ead class review material on statistics (or your own book) Read class review material on statistics (or your own book) For Feb. 28 READ Barnett et al . “Airline Safety: Some Empirical Findings” plus Barnet and Higgins This material will provide an opportunity to consider the statistical analysis of accident data. It will provide a review of statistics. A risk analysis course would not be complete without statistics. 14 February 2007 Jery Stedinger Lecture 11&12 5
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Taylor Series For continuously differentiable functions, near a point x 0 , the value of f(x) should be well approximated by the first few terms of the Taylor series: pp y y f(x) = f(x 0 ) + (x–x 0 ) f ’(x 0 ) + (1/2) (x–x 0 ) 2 f ”(x 0 ) + (1/3!) (x–x 0 ) 3 f’”(x 0 ) + … Beware that Taylor series may converge only for small neighborhood of x 0 . Taylor Series Examples [x 0 = 0] exp(x) = 1 + x + x 2 /2 + x 3 /6 + x 4 /4! + … sin(x) = x – x 3 /3! + x 5 /5! – … 14 February 2007 Jery Stedinger Lecture 11&12 6 ln(1+x) = x – x 2 /2 + x 3 /3 – x 4 /4 + …
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Integrals for Reliability Calculations Constant c is introduced in indefinite integrals because they do not specify upper and lower bounds on the interval over which the integral is to be evaluated. (See handout for more formulas.) a dx = a x + c a f(x) dx = a f(x) dx λ x x = – xp(– / c e dx exp( λ x)/ λ + c where exp(x) = e x and e = 2.718282… exp(bx) dx = (a/b) exp(bx) + c a exp(bx) dx x exp(bx) dx = x exp(bx)/b – exp(bx)/b 2 + c 14 February 2007 Jery Stedinger Lecture 11&12 7
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Poisson Process Outline Poisson Process Concept (3 assumptions) Poisson Simple Dynamic Arrival Rate λ Diff. Equations for Arrivals dp[i]/dt = - λ p[i ]+ λ p[i-1] p Multi-state Systems ds(i)/dt = . ..
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This note was uploaded on 09/28/2008 for the course CEE 5970 taught by Professor Stedinger during the Spring '07 term at Cornell.

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11_12 Dynamic Reliability - CEE 597 - Lecture 11 & 12...

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