This paper is a state-of-the-art review of the literature related to optimal maintenance models of systems subject to failure. The emphasis is on work appearing since the 1976 survey, “A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems,” by W.P. Pierskalla and J.A. Voelker, published in this journal.

Optimal maintenance models for systems subject to failure–A Review

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

This paper is a state-of-art review of the literature related to optimal system reliability with redundancy. The literature is classified as follows. Optimal system reliability models with redundancy Series Parallel Series-parallel Parallel-series Standby Complex (nonseries, nonparallel) Optimization techniques for obtaining optimal system configuration Integer programming Dynamic programming Maximum principle Linear programming Geometric programming Sequential unconstrained minimization technique (SUMT) Modified sequential simplex pattern search Lagrange multipliers and Kuhn-Tucker conditions Generalized Lagrangian function Generalized reduced gradient (GRG) Heuristic approaches Parametric approaches Pseudo-Boolean programming Miscellaneous

Optimization Techniques for System Reliability with RedundancyߞA Review

Very few techniques exist for reliability evaluation of communication systems where links as well as nodes have certain probability of failure. This correspondence describes a technique by which the reliability expression for such a system can be conveniently derived. It is also shown that using the concept of this correspondence, it is possible to extend all the existing reliability-evaluation algorithms to communication systems with little effort.

A Simple Method for Reliability Evaluation of a Communication System

Shortest distance and reliability of probabilistic networks

The computation of reliability becomes quite tedious when one has to deal with a non series-parallel system. In this paper a proposed method is developed by taking the system as a probabilistic graph in which a component of the system is represented by a branch. The proposed method is composed of three phases: Phase 1 involves the reduction of all series, parallel, and series-parallel components to an irreducible non series-parallel system. In Phase 2 the algorithm enumerates all possible paths from the source to the sink of the graph. Phase 3 then computes the system reliability based on the path information obtained in Phase 2. An example of the use of the method to compute system reliability is given.

A Method for Computing Complex System Reliability

The two traditional methods used in improving the reliability of a multi-stage system are examined The first method is the creation of redundancy in system components, whereas the second method consists of overdesigning the system components An Integrated Reliability Optimization Model that includes both of these two methods for improving the reliability of a system is presented It is shown that under certain assumptions the integrated model reduces to a Redundancy Optimization Model and under certain other assumptions reduces to a Design Optimization Model Several methods that have been previously suggested for obtaining solutions to the Integrated Optimization Model are reviewed and a generalized solution procedure for such a model is presented This solution procedure involves the successive solution of two subproblems a number of times The first subproblem is a design optimization problem that is solved by the Davidon-Fletcher-Powell optimization algorithm The second subproblem is a reliability redundancy optimization problem that is solved with the heuristic approach of Aggarwal, et al

P. M. Ghare

Papers

A Method for Computing Complex System Reliability

Optimization of System Reliability via Redundancy and/or Design Considerations