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