Generate Independent Identically and Lognormally Distributed Random Variables

I am trying to create a script for simple reliability analysis. It works fine with other test cases. But, whenever I tried to solve the following test case the result is incorrect. I suppose that the error is in the sampling process.

Where are the independent dentically and lognormally distributed random variables with unit means and standard deviations . The value of n is chosen to be 40.

Later, the function will be applied on points and then the Probability of failure is calculated by using:

[3]

According to the references the value of Pf should be around . Meanwhile, my Pf is 1.

References:

1. Bourinet, J.-M., Deheeger, F., & Lemaire, M. (2011). Assessing small failure probabilities by combined subset simulation and Support Vector Machines. Structural Safety, 33(6), 343–353. doi:10.1016/j.strusafe.2011.06.001 
2. Xu, J., & Zhu, S. (2019). An efficient approach for high-dimensional structural reliability analysis. Mechanical Systems and Signal Processing, 122, 152–170.
3. Echard, B., Gayton, N., & Lemaire, M. (2011). AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation. Structural Safety, 33(2), 145–154.

Here's my script:

clear;
nvar = 40;
sigma = 0.2;
nmc = 3e5;
mu = 1;
init_samp = lognrnd(mu,sigma,nmc,nvar);

% Evaluation func
gx = (nvar + 3*sigma*sqrt(nvar)) - sum(init_samp,2);

%count negative
nneg = length(find(gx < 0));
Pf = nneg/nmc;

disp(Pf)
x = -2:.1:10;
[f,xi] = ecdf(gx);
semilogy(xi,f,'LineWidth',2)
ylim([1E-4,1])
grid on;

Thank you very much!

Answer 1

[Torsten]

Note that mu and sigma you supply for "lognrnd" are not mean and standard deviation of the underlying lognormal distribution, but the distribution parameters mu and sigma.

See the first example under

https://de.mathworks.com/help/stats/lognrnd.html

[Ghifari Adam Faza]

Thank you very much, Torsten!