# Sensitivity Factors from FORM method¶

Sensitivity Factors are evaluated under the following context: denotes a random input vector, representing the sources of uncertainties, its joint density probability, the limit state function of the model. We denote by:

(1)¶

the event considered here and its boundary (also called limit state surface). The probability content of the event is :

(2)¶

In this context, the probability can often be efficiently estimated by FORM or SORM approximations. The FORM importance factors offer a way to analyze the sensitivity of the probability the realization of the event with respect to the parameters of the probability distribution of .

A sensitivity factor is defined as the derivative of the Hasofer-Lind reliability index with respect to the parameter . The parameter is a parameter in a distribution of the random vector . If represents the vector of all the parameters of the distribution of which appear in the definition of the isoprobabilistic transformation , and the design point associated to the event considered in (1) in the -space, and if the mapping of the limit state function by the is denoted by:

then the sensitivity factors vector is defined as:

The sensitivity factors indicate the importance on the Hasofer-Lind reliability index (refer to ) of the value of the parameters used to define the distribution of the random vector .

In other words, the FORM sensitivity factors rank the importance of the parameters of the input components in the realization of the event defined in (1).