skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Bayesian methods for estimating the reliability in complex hierarchical networks (interim report).

Abstract

Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback.

Authors:
; ; ;  [1];  [1];
  1. (Sandia National Laboratories, Albuquerque, NM)
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
922080
Report Number(s):
SAND2007-2758
TRN: US0802168
DOE Contract Number:
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEFENSE; EVALUATION; FEEDBACK; NUCLEAR WEAPONS; POLYNOMIALS; RELIABILITY; STOCKPILES; Bayesian statistical decision theory-Mathematical models.; Nuclear weapon stockpile.-Reliability

Citation Formats

Marzouk, Youssef M., Zurn, Rena M., Boggs, Paul T., Diegert, Kathleen V., Red-Horse, John Robert, and Pebay, Philippe Pierre. Bayesian methods for estimating the reliability in complex hierarchical networks (interim report).. United States: N. p., 2007. Web. doi:10.2172/922080.
Marzouk, Youssef M., Zurn, Rena M., Boggs, Paul T., Diegert, Kathleen V., Red-Horse, John Robert, & Pebay, Philippe Pierre. Bayesian methods for estimating the reliability in complex hierarchical networks (interim report).. United States. doi:10.2172/922080.
Marzouk, Youssef M., Zurn, Rena M., Boggs, Paul T., Diegert, Kathleen V., Red-Horse, John Robert, and Pebay, Philippe Pierre. Tue . "Bayesian methods for estimating the reliability in complex hierarchical networks (interim report).". United States. doi:10.2172/922080. https://www.osti.gov/servlets/purl/922080.
@article{osti_922080,
title = {Bayesian methods for estimating the reliability in complex hierarchical networks (interim report).},
author = {Marzouk, Youssef M. and Zurn, Rena M. and Boggs, Paul T. and Diegert, Kathleen V. and Red-Horse, John Robert and Pebay, Philippe Pierre},
abstractNote = {Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback.},
doi = {10.2172/922080},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}

Technical Report:

Save / Share:
  • Bayesian reliability estimation methods are summarized in a handbook format for convenient use by reliability practitioners. The methods given consider both attribute test data based on a binomial sampling distribution and a beta prior, as well as variables test data from an exponential sampling distribution and a gamma prior. Classical, Bayes, and empirical Bayes methods are all considered. In addition, the sample test data can arise from either an item-censored life test, either with or without the replacement of failed items as they occur, or from a time-truncated life test with replacement. Real-data examples using nuclear reactor component failure datamore » are used to illustrate each of the methods presented.« less
  • Some preliminary results obtained in analyzing the reliability of wind generator-storage systems are presented. The investigation takes two separate approaches - simulation and probabilistic modeling - to reveal the trade-offs which can be made between generating capacity and storage capacity to attain a desired level of reliability. The performance criterion used throughout this work is the frequency of occurrence of empty storage. This criterion is essentially the same as the frequency of loss of load.
  • This report deals with analytical methods to calculate the unavailability, failure density, and unreliability of good, complex systems, e.g. of engineered safety systems. The methods are based on the minimal cut sets and the use of the stationary properties of systems with repair or test. An example is given, with detailed calculations, to demonstrate the ability of the methods to cope with complexity.
  • Consider a classic hierarchy tree as a basic model of a 'system-of-systems' network, where each node represents a component system (which may itself consist of a set of sub-systems). For this general composite system, we present a technique for computing the optimal testing strategy, which is based on Bayesian decision analysis. In previous work, we developed a Bayesian approach for computing the distribution of the reliability of a system-of-systems structure that uses test data and prior information. This allows for the determination of both an estimate of the reliability and a quantification of confidence in the estimate. Improving the accuracymore » of the reliability estimate and increasing the corresponding confidence require the collection of additional data. However, testing all possible sub-systems may not be cost-effective, feasible, or even necessary to achieve an improvement in the reliability estimate. To address this sampling issue, we formulate a Bayesian methodology that systematically determines the optimal sampling strategy under specified constraints and costs that will maximally improve the reliability estimate of the composite system, e.g., by reducing the variance of the reliability distribution. This methodology involves calculating the 'Bayes risk of a decision rule' for each available sampling strategy, where risk quantifies the relative effect that each sampling strategy could have on the reliability estimate. A general numerical algorithm is developed and tested using an example multicomponent system. The results show that the procedure scales linearly with the number of components available for testing.« less
  • The thermal challenge problem has been developed at Sandia National Laboratories as a testbed for demonstrating various types of validation approaches and prediction methods. This report discusses one particular methodology to assess the validity of a computational model given experimental data. This methodology is based on Bayesian Belief Networks (BBNs) and can incorporate uncertainty in experimental measurements, in physical quantities, and model uncertainties. The approach uses the prior and posterior distributions of model output to compute a validation metric based on Bayesian hypothesis testing (a Bayes' factor). This report discusses various aspects of the BBN, specifically in the context ofmore » the thermal challenge problem. A BBN is developed for a given set of experimental data in a particular experimental configuration. The development of the BBN and the method for ''solving'' the BBN to develop the posterior distribution of model output through Monte Carlo Markov Chain sampling is discussed in detail. The use of the BBN to compute a Bayes' factor is demonstrated.« less