An algorithm of accelerated probabilistic modeling for estimation of the reliability of complex systems
type: Item
instance of: scholarly article
title: An algorithm of accelerated probabilistic modeling for estimation of the reliability of complex systems
zbMATH Open document ID: 0928.93058
author: K. Appert
published in: Automation and Remote Control
publication date: 1999-09-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 90B25
Mathematics Subject Classification ID: 93E99
Mathematics Subject Classification ID: 94C12
Mathematics Subject Classification ID: 93E25
zbMATH DE Number: 1290439
zbMATH Keywords: probability of failure
zbMATH Keywords: probabilistic simulation
zbMATH Keywords: Monte Carlo method
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1290439