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 timevariance, 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 stockpilerelated, it is applicable to any reasonablystructured hierarchical system, including systems with feedback.
 Authors:
 (Sandia National Laboratories, Albuquerque, NM)
 Publication Date:
 Research Org.:
 Sandia National Laboratories
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 922080
 Report Number(s):
 SAND20072758
TRN: US0802168
 DOE Contract Number:
 AC0494AL85000
 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 theoryMathematical models.; Nuclear weapon stockpile.Reliability
Citation Formats
Marzouk, Youssef M., Zurn, Rena M., Boggs, Paul T., Diegert, Kathleen V., RedHorse, 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., RedHorse, 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., RedHorse, 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 RedHorse, 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 timevariance, 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 stockpilerelated, it is applicable to any reasonablystructured 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}
}

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 itemcensored life test, either with or without the replacement of failed items as they occur, or from a timetruncated life test with replacement. Realdata examples using nuclear reactor component failure datamore »

Methods of estimating the reliability of wind energy systems with storage
Some preliminary results obtained in analyzing the reliability of wind generatorstorage systems are presented. The investigation takes two separate approaches  simulation and probabilistic modeling  to reveal the tradeoffs 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. 
The availability and reliability of complex systems: some analytical methods
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. 
Determining the Bayesian optimal sampling strategy in a hierarchical system.
Consider a classic hierarchy tree as a basic model of a 'systemofsystems' network, where each node represents a component system (which may itself consist of a set of subsystems). 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 systemofsystems 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 » 
Validation of the thermal challenge problem using Bayesian Belief Networks.
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 »