Multi-Component Systems and Structures and Their Reliability
TL;DR: The present study deals with general classes of systems which contain two-terminal networks and most other kinds of systems considered previously as special cases, and investigates their combinatorial properties and their reliability.
Abstract: A number of recent publications have dealt with problems of analyzing the performance of multi-component systems and evaluating their reliability. For example, a comprehensive theory of two-terminal networks was presented in [I] by Moore and Shannon who, among other results, have developed methods for obtaining highly reliable systems using components of low reliability; some of their procedures are credited to earlier work by von Neumann [2]. Several of the concepts and results of the present paper are generalizations of the corresponding concepts and results of the Moore-Shannon paper. A discussion of complex systems interpreted as Boolean functions may be found in the paper [3] by Mine. The present study deals with general classes of systems which contain two-terminal networks and most other kinds of systems considered previously as special cases, and investigates their combinatorial properties and their reliability. These classes consist, with several variants, of systems such that the more components...
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TL;DR: A hierarchical modeling scheme is used to formulate the capability function and capability is used, in turn, to evaluate performability, and techniques are illustrated for a specific application: the performability evaluation of an aircraft computer in the environment of an air transport mission.
Abstract: If the performance of a computing system is "degradable," performance and reliability issues must be dealt with simultaneously in the process of evaluating system effectiveness. For this purpose, a unified measure, called "performability," is introduced and the foundations of performability modeling and evaluation are established. A critical step in the modeling process is the introduction of a "capability function" which relates low-level system behavior to user-oriented performance levels. A hierarchical modeling scheme is used to formulate the capability function and capability is used, in turn, to evaluate performability. These techniques are then illustrated for a specific application: the performability evaluation of an aircraft computer in the environment of an air transport mission.
760 citations
TL;DR: This paper reviews and classifies fault-tree analysis methods developed since 1960 for system safety and reliability and classified the literature according to system definition, fault- Tree construction, qualitative evaluation, quantitative evaluation, and available computer codes for fault-Tree analysis.
Abstract: This paper reviews and classifies fault-tree analysis methods developed since 1960 for system safety and reliability. Fault-tree analysis is a useful analytic tool for the reliability and safety of complex systems. The literature on fault-tree analysis is, for the most part, scattered through conference proceedings and company reports. We have classified the literature according to system definition, fault-tree construction, qualitative evaluation, quantitative evaluation, and available computer codes for fault-tree analysis.
582 citations
TL;DR: Basic theory is developed for the study of systems of components in which any of a finite number of states may occur, representing at one extreme perfect functioning and at the other extreme complete failure.
Abstract: : The vast majority of reliability analyses assume that components and system are in either of two states: functioning or failed. The present paper develops basic theory for the study of systems of components in which any of a finite number of states may occur, representing at one extreme perfect functioning and at the other extreme complete failure. Axioms are laid down extending the standard notion of a coherent system to the new notion of a multistate coherent system. For such systems deterministic and probabilistic properties are obtained for system performance which are analogous to well-known results for coherent system reliability.
331 citations
TL;DR: The importance measure is a useful guide during the system development phase as to which components should receive more urgent attention in achieving system reliability growth.
281 citations
TL;DR: In this article, a combinatorial invariant of a graph, called the domination, is established and several important properties of the domination with regard to the topology of the graph are investigated.
Abstract: In network reliability analysis, an important problem is to determine the probability that a specified subset of vertices in an undirected graph is connected. It is well known that, by using Moskowitz's factoring theorem, the reliability of a graph can be expressed in terms of the reliabilities of a graph with one fewer vertex and another with one fewer edge. The theorem can be applied recursively on the reduced graphs. The computations involved in this recursion can be represented by a binary structure such that its leaves correspond to reduced graphs whose reliabilities can be readily evaluated. In general, as the recursion progresses, series and parallel edges are created which can be reduced by using series and parallel rules of reliability assuming edges fail independently of each other. The computational complexity is a function of the number of leaves in the binary structure, and for a given graph, an optimal binary structure is the one with minimal number of leaves. In this article, a combinatorial invariant of a graph, called the domination, is established. Several important properties of the domination with regard to the topology of the graph are investigated. It is shown that for a given graph, the number of leaves in the optimal binary structure is equal to the domination of the graph and recursive application of the factoring theorem yields an optimal structure if and only if at each step the reduced graphs generated have nonzero dominations. Finally, an algorithm is presented that guarantees optimal binary structure generation and therefore an efficient implementation of the factoring theorem to compute the network reliability.
262 citations
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01 Jan 1956
2,140 citations
TL;DR: It is shown that by using a sufficiently large number of relays in the proper manner, circuits can be built which are arbitrarily reliable, regardless of how unreliable the original relays are.
Abstract: An investigation is made of relays whose reliability can be described in simple terms by means of probabilities. It is shown that by using a sufficiently large number of these relays in the proper manner, circuits can be built which are arbitrarily reliable, regardless of how unreliable the original relays are. Various properties of these circuits are elucidated.
665 citations
"Multi-Component Systems and Structu..." refers background or methods in this paper
...It contains among others the two-terminal networks whose reliability has been studied by Moore and Shannon in their fundamental paper [1] and all k out of n structures....
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...A function f e , therefore is either identically 0, or identically 1, or it maps the closed interval [0, 1] onto the closed interval [0, 1]....
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...For example, a comprehensive theory of two-terminal networks was presented in [1] by Moore and Shannon who, among other results, have developed methods for obtaining highly reliable systems using components of low reliability; some of their procedures are credited to earlier work by von Neumann [2]....
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71 citations
TL;DR: This paper presents the general concept of the reliability of the complex physical system which consists of a number of unreliable elements, analyzed systematically by means of algebraic and topological theory.
Abstract: This paper presents the general concept of the reliability of the complex physical system which consists of a number of unreliable elements. Such a system is analyzed systematically by means of algebraic and topological theory. Various properties concerning the system reliability are established. The methods of linear graph theory are used to find the theoretical relationship between element reliability and system complexity. The optimizing the reliability of a basic system under certain constraints can be accomplished by the application of the theory described. A numerical procedure for finding the optimum solution is developed to facilitate computation.
59 citations