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== Description == Reliability theory deals with estimating the probability of failure of engineering systems. Reliability methods are conventionally divided into three levels (JCSS: Joint Committee on Structural Safety, 1981): * Level 1 methods use specified quantiles of distributions and applying ‘partial safety factors’ to ensure that the probability of failure is sufficiently low. Level 1 methods are based on probabilistic principles but do not in practice require probabilistic calculations. * Level 2 methods estimate the probability of failure analytically, based on first (FORM) or second order (SORM) approximations to the limit state function (the function separating ‘failed’ from ‘non-failed’ system states) and transformation of the basic variables of the limit state function to standard Normal space. * Level 3 methods use Monte Carlo sampling methods to estimate the probability of failure. Because the probability of failure is small and its location in basic variable space can usually be approximated, importance sampling methods can greatly improve the sampling efficiency (Melchers, 1999). == Software == none == Advantages == * Application of reliability methods is essential in any flooding situation where the probability of flooding is modified by an engineering system which may fail under some circumstances. * Reliability methods are well established and widely used in other engineering disciplines. * Reliability methods explicitly deal with systems of engineering components and how they interact with each other. == Disadvantages == * Reliability methods calculate the probability of system failure. For flood risk analysis the probability of system failure may not be the main quantity of interest and it will often be necessary to estimate the probability of different combinations of failure modes (Dawson et al., in press). Reliability methods can be adapted for this purpose. * Because systems are usually designed to have low probabilities of failure and because failures are usually destructive unrepeatable events, there is no direct mechanism for validation of failure probability estimates. == References and Further reading == Melchers, R. E., Structural reliability analysis and prediction. 2nd Edition, John Wiley & Sons, New York, 1999 Benjamin, J. R. and C. A. Cornell, Probability, Statistics and Decision for Civil Engineers, McGraw-Hill, 1970 Ang, A. H-S. and Tang, W.H., Probability Concepts in Engineering Planning and Design, Vol. 2 -Decision, Risk and Reliability, John Wiley & Sons, New York, 1984 Ang, A.H.-S. and Tang, W.H., 1984. Probability Concepts in Engineering Planning and Design, Vol. 2 -Decision, Risk and Reliability. John Wiley & Sons, New York. Benjamin, J.R. and Cornell, C.A., 1970. Probability, Statistics and Decision for Civil Engineers, McGraw-Hill. Dawson, R.J., Hall, J.W., Sayers, P.B., Bates, P.D. and Rosu, C., in press. Sampling-based flood risk analysis for fluvial dike systems. Stochastic Environmental Research and Risk Analysis. JCSS: Joint Committee on Structural Safety, 1981. 1 General principles on reliability for structural design. Int. Assoc. for Bridge and Structural Engineering. Melchers, R.E., 1999. Structural reliability analysis and prediction. 2nd Edition, Wiley.
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