Abstract
The reliability index is a useful indicator to compute the failure probability. If J is the performance of interest and if J is a Normal random variable, the failure probability is computed by \(P_f = N\left( { - \beta } \right)\) and β is the reliability index. When J is a nonlinear function of n normal random variables (X1, …, X n ), then the preceding formula can be generalized, with some approximation. One uses a nice property of the reliability index, to be the shortest distance of the origin to the failure region. This method introduced by B.M. Ayyub, provides an analytic alternative to the Monte Carlo method.
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References
Ayyub, B. M. Risk Analysis in Engineering and Economics. Boca Raton, Chapman Hall/CRC, 2003.
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© 2005 Springer
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Bensoussan, A. (2005). Reliability Index. In: Deissenberg, C., Hartl, R.F. (eds) Optimal Control and Dynamic Games. Advances in Computational Management Science, vol 7. Springer, Boston, MA. https://doi.org/10.1007/0-387-25805-1_18
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DOI: https://doi.org/10.1007/0-387-25805-1_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25804-1
Online ISBN: 978-0-387-25805-8
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