Families of components, and systems, exposed to a compound poisson damage process

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Authors
Esary, James Daniel
Marshall, A. W.
Subjects
Advisors
Date of Issue
1973-07
Date
1973-07
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
A fairly common failure model in a wide variety of contexts is a cumulative damage process, in which shocks occur randomly in time and associated with each shock there is a random amount of damage which adds to previously incurred damage until a breaking threshold is reached. The multivariate life distributions that are induced when several "components," each with its own breaking threshold, are exposed to the same cumulative damage process are of interest in their own right, and are important examples in the general study of multivariate life distributions. This paper is a summary of some results about the very special, but central, case in which the cumulative damage process is a compound Poisson process. It is focused on the multivariate life distributions that arise when the component breaking thresholds are random and have a Marshall-Olkin multivariate exponential distribution. There are two relevant multivariate life distributions that can be derived, an intermediate distribution for the number of shocks (cycles) to failure and the final distribution for the actual times to failure. The results have application to the life distribution of a coherent system whose components are exposed to the damage process. (Author)
Type
Technical Report
Description
Series/Report No
Department
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NPS Report Number
NPS55EY73071A
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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