# 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:

- 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}

}