# Methods of Structural Reliability

• Michael Havbro Faber
Part of the Topics in Safety, Risk, Reliability and Quality book series (TSRQ, volume 18)

## Abstract

Probabilistic engineering models are ultimately utilized in the context of risk-informed decision making to assess the probability of events associated with consequences. In this chapter it is shown how such models may be utilized first to represent the events associated with consequences and thereafter, how to assess their probabilities. Throughout the chapter, examples are provided illustrating the presented methods and their application in an engineering context.

In Lecture 12 first the concept of safety margins from modern structural reliability theory is introduced as an adequate means of representing events associated with consequences. Then the special case is considered where the safety margin is linear and all uncertainties may be represented by uncorrelated Normal distributed random variables. For this case it is shown that the safety margin is also Normal distributed and that the probability of interest may be determined in terms of the reliability index and the cumulative standard Normal distribution. Then, on this basis, the generalization to non-linear safety margins is made and the classical error propagation law is introduced as a means of approximating the reliability index by linearizing the safety margin in the expected values of the random variables. From this result the extension is then made to one of the strongest available techniques in structural reliability analysis, namely the First Order Reliability Method (FORM) and it is shown how this method may be implemented as a simple iteration algorithm. Finally, in this lecture the principle of the Monte Carlo simulation is introduced and the general scheme for the crude Monte Carlo method is described.

## Keywords

Failure Probability Reliability Index Design Point Failure Surface Limit State Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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