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Journal ArticleDOI

Multi-Component Systems and Structures and Their Reliability

Z. W. Birnbaum, +2 more
- 01 Feb 1961 - 
- Vol. 3, Iss: 1, pp 55-77
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TLDR
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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Citations
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Mean life of series and parallel systems

TL;DR: In this paper, the authors obtained bounds for the mean life of series and parallel systems in the case of component life distributions that have properties such as a monotone failure rate, monotonous failure rate average, or decreasing density.
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Improved Method of Inclusion-Exclusion Applied to k-out-of-n Systems

TL;DR: In this article, the reliability analysis of k-out-of-n systems was improved to use only noncancelling terms in evaluating bounds on the reliability of K-out of n systems, which converge to the exact system reliability in at most n? k + 1 steps.
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Analytical method for reliability and MTTF assessment of coherent systems with dependent components

TL;DR: Using the Markov process approach, a coherent system of components with multivariate phase type life distribution is introduced to model the components working in a common random environment, which is flexible enough to comprise many realistic situations, and also manages to yield the explicit matrix representations of the system reliability measures.
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Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons

TL;DR: A discrete k-out-of-n: G system with multi-state components is modelled by means of block-structured Markov chains and several performance measures of interest, such as the conditional probability of failure for the units and for the system, are built into the transient and stationary regimes.
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Survey of maintenance policies for the Last 50 Years

TL;DR: In this article, a survey summarizes, classifies, and compares various existing maintenance policies around 170 Authors and their research works are presented in the Reference section, which will help to look into the different policies which are appropriate to the organization and for further study the reference section will be helpful for the researchers for further knowledge.
References
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Journal ArticleDOI

Reliable circuits using less reliable relays

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.
Journal ArticleDOI

Reliability of physical system

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.