In the previous section, we highlighted the lack of invariance problem that occurs when the limit state function is non-linear. We start this section by outlining a strategy for dealing with non-linear limit state functions.

With the bones of our plan established, next, we move on to determine an iterative algorithm that allows us to progressively iterate towards the design point of our limit state function.

By expanding our linear Taylor Series Expansion about a point close to the design point, we effectively eliminate the inaccuracy in our approximation that would otherwise arise due to the nonlinearity of the limit state function. Having covered all of the theory, we then put it into practice with some more worked examples.

In the second half of this section, we turn our attention to addressing one of the remaining limitations of our analysis method which is the fact that, up to this point, all variables are assumed to be normally distributed.

In reality, we regularly come across non-normally distributed variables, and we need to be able to accommodate these in our reliability analysis. To achieve this and widen the applicability of our analysis methods, we introduce the Normal Tail Approximation. This allows us to transform any non-normal distribution into an equivalent normal distribution, allowing us to apply the First Order Reliability Method.

By the time you’ve completed this section, you’ll have built a library of utility functions that will allow you to easily and efficiently reuse the algorithms we’ve developed during this course.

Finally, we’ll briefly reflect on the challenges associated with sourcing suitable data for reliability analysis in the field before recapping our progress so far and highlighting what we’ll cover in part 2.