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BOOLEAN DIFFERENCE TECHNIQUES IN FAULT TREE ANALYSIS

IP.com Disclosure Number: IPCOM000128690D
Original Publication Date: 1975-Dec-31
Included in the Prior Art Database: 2005-Sep-16
Document File: 8 page(s) / 25K

Publishing Venue

Software Patent Institute

Related People

M. G. Thomason: AUTHOR [+4]

Abstract

For an electrical, mechanical, or hybrid system descrihed diagramatically as a network of interconnected components, fault tree modeling of system reliability as a function of individual component failure probabilities gives rise to logic expressions obtained from the network connections. Application of the method of Boolean differences in the analysis of such .Boolean expressions is discussed, and it is shown that the influence of the status of specific components on the reliability of the total system, may be investigated by straightforward algebraic operations on the network failure function. 3/7/75

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

BOOLEAN DIFFERENCE TECHNIQUES IN FAULT TREE ANALYSIS

M. G. Thomason . E. W. Page*

March 1975

*Department of Electrical Engineering Rice University Houston, Texas M. G. Thomason Department of Computer Science The University of Tennessee 104 Alumni Hall Knoxville, Tennessee 37916

E. W. Page Department of Electrical Engineering Rice University Houston, Texas 77001,

Abstract

For an electrical, mechanical, or hybrid system descrihed diagramatically as a network of interconnected components, fault tree modeling of system reliability as a function of individual component failure probabilities gives rise to logic expressions obtained from the network connections. Application of the method of Boolean differences in the analysis of such .Boolean expressions is discussed, and it is shown that the influence of the status of specific components on the reliability of the total system, may be investigated by straightforward algebraic operations on the network failure function.

3/7/75

I Introduction

Reliability analysis of a large, complex system of interconnected components is often a difficult task, even when substantial information about its consistent parts is available. One approach is to organize the data for computer processing by developing a fault tree model which reflects the network connections directly [4, 5, 111. There can then be obtained from the tree a "failure function" (or alternatively a complementary "success function") for the system.

Since this yields a conventional Boolean expression defining a binary-valued function of binary variables, the theory of Boolean algebra applies. In particular, stochastic considerations [3, 7, 8] can be combined with the Boolean difference method of analysis of switching functions [1, 6, 9,
10] in order to study the dependence of an entire system on individual components or collections of components forming subsystems.

We first indicate by a simple illustration how fault trees and the cor-responding failure expressions arise. The Boolean difference is then defined in Section III, and its use in failure expression analysis is examined in SectionsIV and V.

II. Fault Trees and Failure Functions

University of Tennessee Page 1 Dec 31, 1975

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BOOLEAN DIFFERENCE TECHNIQUES IN FAULT TREE ANALYSIS

Fault trees have become an important tool for evaluating the relia-bility of complex systems. Consider a network (electrical, mechanical, hybrid) of interconnected units as in Fig. l(a), a simple network with re-dundancy where X represents the system input; A,B,C, the system components; and Y,the system output. Let A,B,C also denote independent.,binary-valued, random variables where by convention the~ event A = I denotes failure of component A and P(A) = a is the probability-that component A fails.

A model of system reliability can be developed by constructing a fault tree which defines conditions for network failure. Specifically, a fau...