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.

On Evaluating the Performability of Degradable Computing Systems

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.

Fault Tree Analysis, Methods, and Applications ߝ A Review

: 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.

Multistate Coherent Systems.

Importance of System Components and Fault Tree Events.

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.

Network reliability and the factoring theorem

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...

J. D. Esary

Papers

Multi-Component Systems and Structures and Their Reliability