# Optimal Reliability Analysis by Fast Convolution

*by*Niels C. Lind, Prof. of Civ. Engrg.; Univ. of Waterloo, Waterloo, Ontario, Canada,

**Serial Information**:

*Journal of the Engineering Mechanics Division*, 1979, Vol. 105, Issue 3, Pg. 447-452

**Document Type:**Journal Paper

Discussion: Dumonteil Pierre (See full record)

Discussion: Madsen Henrik O. (See full record)

**Abstract:**When the basic random variables are approximated by normally distributed variables fitted at a point, the best point of fitting is shown to be the design point located on the failure boundary where the probability density is maximum. If the distribution function values and the values of the probability density functions are matched at this point for all variables the calculated probability of failure is minimum among the values calculated using any neighboring points of fit. This appears to be contrary to simple intuition. This result was found by variational calculus and serves to remove some arbitrariness in practical calculations of reliability and the like for example distributions of extremer of sums of random processes, as in load combination studies using the algorithm due to Rackwitz and Fiessler.

**Subject Headings:**Probability | Failure analysis | Domain boundary | Probability distribution | Arbitration | Load combinations | Load distribution

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