Hello,

In Reliability FORM analysis,

Is there any function to get sensitivity of reliability index ( \beta ) and probability of failure ( P_F ) with respect to probability density function (joint PDF of all basic random variables, f_X(x) ) parameters and limit-state function g(x) parameters.

Supposedly,

f_\textbf{X} (\textbf{x}) = f_\textbf{X} ( \textbf{x} , \theta_d )

g(x) = g (\textbf{x} , \theta_l )

Where,

\theta_d are the probability distribution parameters of the basic random variables such as mean and variance.

\theta_l are the limit state function parameters such as constant parameter.

Is there any way we can get something like,

\triangledown_{\theta l} \beta or \triangledown_{\theta d} P_F

Regards,

Maitreya Manoj Kurumbhati