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A Study of the Role of Modules in the Failure of Systems

Published online by Cambridge University Press:  27 July 2009

Emad El Neweihi  and
Jayaram Sethuraman
Emad El Neweihi
Affiliation:
University of Illinois at Chicago, Chicago, Illinois
Jayaram Sethuraman
Affiliation:
Florida State University Tallahassee, Florida 32306
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Abstract

Since the introduction of the concept of coherent systems and the description of the reliability of such systems in terms of the reliabilities of the components, the concept of importance of a component has created a new and fruitful area of research. Two distinct concepts of importance can be found in the literature. We take the view that the importance of a component or a module that is part of a system can be derived directly from the role of the component or the module in the failure of the system. Here again, it is possible that there will be several definitions of role. In this paper we define the role of a module (or component) to be the probability that the module is among all the modules (or components) that failed at the time of system failure. The role of a module depends on the structure of the system in terms of the modules, the structure of the module in terms of its components and the distribution of lifetimes of the components. In this paper we study the role of a module under several structures and distributions for lifetimes. We establish various monotonicity properties and indicate applications of these properties to optimal allocation. Another quantity that describes the nature of the components in sustaining the system is the number of components that fail at the time of the failure of the system. We establish monotonicity properties for the expected number of failed components and also indicate applications to optimal allocation.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 2 , April 1991 , pp. 215 - 227
Copyright
Copyright © Cambridge University Press 1991

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