Improved safety analysis through enhanced mathematical structures

In probabilistic safety analyses, the input data and logical combinations of the data can involve considerable subjectivity. It is important that mathematical processing be done in as meaningful a manner as possible, especially for assessing the safety of high consequence operations. We have begun an investigation of some innovative mathematical structures that are potentially useful in such safety analyses, and have developed some practical illustrations of the utility of the approaches. We have addressed active and passive safety systems, independent and dependent inputs, fault trees and event trees, and crisp and distributed logic. Our long-range intent is to provide analysts with a comprehensive selection of mathematically based tools, so that the best match possible is available for a particular system or portions of systems. Some of the mathematical structures investigated are based on various logical norms: ordered weighted averaging, implication operations, gamma operators, sigmoid operators, inference networks, failure "race" comparators, min/max ordinate logic, threshold logic, conditional possibility, and Frechet-based dependence operators.