An algorithm of accelerated probabilistic modeling for estimation of the reliability of complex systems
Let the system consist of random vectors \[ \vec\xi(t)= (\xi_1(t),\dots, \xi_n(t)), \] where the stochastic process \(\xi_i(t)\) characterizes the state of the \(i\)th element, namely, good condition or failure. Let \(\varphi(\vec x)\) be a scalar algorithmic test function, \(\varphi(\vec x)=1\) or \(0\). Then the probability of failure of the whole system is \[ Q= E\{\varphi(\vec\xi)\}= \int_X \varphi(\vec x) P(d\vec x). \] The problem is to construct an algorithm of probabilistic simulation supplying substantial reduction of the size of the computer experiment. An accelerated Monte Carlo method is considered with the modeling results presented in the form of a sample stratified relatively into the number of failures of elements. A numerical example is presented in the case of a system with three blocks.
scientific article; zbMATH DE number 1290439