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Diploma thesis

Evaluation of alternative methods for the fault tree analysis of complex systems

(Original Title:Evaluierung verschiedener Verfahren zur Fehlerbaumanalyse komplexer Systeme)



The fault tree analysis is a central component in the development and operation of security related systems, like nuclear power stations or space shuttles. It illustrates various combinations of failures and other events which lead to a critical event. The fault tree analysis helps to identify those combinations of the components that make an undesired event occur. It is the aim of the fault tree analysis to find out the minimal number of events that lead to the top event and that way identify system hazards.
The fault tree analysis was first introduced in the military. The US Air Force first used this technique in the 1960s. Since then the fault tree analysis has expanded to many fields of aviation and aerospace as well as to the nuclear power industry. Many effords are taken to create and analyse more and more extensive and complex systems as fault trees.
Fault Trees are based on boolean formulae that can be tested for prime implicants or minimal cuts with various algorithms of different efficiency. This assignment is designed to evaluate some of these algorithms and make valuing remarks on their efficiency. The method of Quine-McCluskey for minimization of boolean functions, the algorithm MOCUS, the algorithm of Rauzy on binary descision diagrams, the algorithm of Madre and Coudert with meta products as well as the CAMP DEUSTO search strategy are all parts of this document. The algorithms are based on different data structures and procedures for the determination of the prime implicants, minmal cut sets respectively. A central topic of this assignment are the two algorithms that are based on binary decision diagrams since this technique was very successful.
At the beginning of this assignment the basics of boolean algebra and of fault trees are introduced as well as the basic procedure in fault tree analysis in the lifecycle of products and software. This document is organized as follows: the first chapter points out the history of the fault tree analysis and shows the phases of product life cyle in which the fault tree analysis is applicable. Chapter 2 explains some definitions and properties of boolean algebra and basic definitions of minimal cut sets and primimplicants of boolean functions. Chapter 3 demonstrates the basic strategy of the fault tree analysis and shows how to use the fault tree analysis for software engineering. Chapter 4 introduces existing algorithms using different examples of application. In Chapter 5 the different are compared with each other. Finally chapter 6 gives an outlook on possible future developments in the field of fault tree analysis.

Author: Martin Seel

Tutor: Dr.-Ing. Norbert Oster