[1][2] Reliability is also used as a probabilistic measure of structural safety.
The reliability of a structure is defined as the probability of complement of failure
[2] In structural reliability studies, both loads and resistances are modeled as probabilistic variables.
When loads and resistances are explicit and have their own independent function, the probability of failure could be formulated as follows.
However, in most cases, the distribution of loads and resistances are not independent and the probability of failure is defined via the following more general formula.
where 𝑋 is the vector of the basic variables, and G(X) that is called is the limit state function could be a line, surface or volume that the integral is taken on its surface.