Failure‐Conditioned Reliability Index

Abstract
A formulation of a failure‐conditioned reliability index of correlated multivariate normal distribution is developed to estimate simultaneous failure probability and, finally, system reliability. The expression is based on the evaluation of failure‐conditioned mean and standard deviation. It is simple in expression and effective for all ranges of correlation coefficients. Although the equation is just an approximate one, it appears that the errors are within the allowable limit, as shown in the examples.

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