# New Mathematical Derivations Applicable to Safety and Reliability Analysis

### Description

Boolean logic expressions are often derived in safety and reliability analysis. Since the values of the operands are rarely exact, accounting for uncertainty with the tightest justifiable bounds is important. Accurate determination of result bounds is difficult when the inputs have constraints. One example of a constraint is that an uncertain variable that appears multiple times in a Boolean expression must always have the same value, although the value cannot be exactly specified. A solution for this repeated variable problem is demonstrated for two Boolean classes. The classes, termed functions with unate variables (including, but not limited to unate functions), ... continued below

6 p.

### Creation Information

Cooper, J.A. & Ferson, S. April 19, 1999.

## Who

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### Publisher

• Sandia National Laboratories
Publisher Info: Sandia National Labs., Albuquerque, NM, and Livermore, CA (United States)
Place of Publication: Albuquerque, New Mexico

### Provided By

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## What

### Description

Boolean logic expressions are often derived in safety and reliability analysis. Since the values of the operands are rarely exact, accounting for uncertainty with the tightest justifiable bounds is important. Accurate determination of result bounds is difficult when the inputs have constraints. One example of a constraint is that an uncertain variable that appears multiple times in a Boolean expression must always have the same value, although the value cannot be exactly specified. A solution for this repeated variable problem is demonstrated for two Boolean classes. The classes, termed functions with unate variables (including, but not limited to unate functions), and exclusive-or functions, frequently appear in Boolean equations for uncertain outcomes portrayed by logic trees (event trees and fault trees).

6 p.

### Notes

OSTI as DE00005835

Medium: P; Size: 6 pages

### Source

• ESREL (European Safety and Reliability Conference), Munich (DE), 09/13/1999--09/17/1999

### Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

• Report No.: SAND99-0970C
• Grant Number: AC04-94AL85000
• Office of Scientific & Technical Information Report Number: 5835

### Collections

#### Office of Scientific & Technical Information Technical Reports

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Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

## When

### Creation Date

• April 19, 1999

### Added to The UNT Digital Library

• Aug. 14, 2015, 8:43 a.m.

### Description Last Updated

• April 11, 2017, 1:07 p.m.

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