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Systems with Failure-Dependent Lifetimes of Components

Part of: Distribution theory - Probability Distribution theory

Published online by Cambridge University Press:  14 July 2016

M. Burkschat
M. Burkschat*
Affiliation:
Otto-von-Guericke University Magdeburg
*
∗Postal address: Institute of Mathematical Stochastics, Otto-von-Guericke University Magdeburg, D-39016 Magdeburg, Germany. Email address: [email protected]
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Abstract

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A model for describing the lifetimes of coherent systems, where the failures of components may have an impact on the lifetimes of the remaining components, is proposed. The model is motivated by the definition of sequential order statistics (cf. Kamps (1995)). Sequential order statistics describe the successive failure times in a sequential k-out-of-n system, where the distribution of the remaining components' lifetimes is allowed to change after every failure of a component. In the present paper, general component lifetimes which can be influenced by failures are considered. The ordered failure times of these components can be used to extend the concept of sequential order statistics. In particular, a definition of sequential order statistics based on exchangeable components is proposed. By utilizing the system signature (cf. Samaniego (2007)), the distribution of the lifetime of a coherent system with failure-dependent exchangeable component lifetimes is shown to be given by a mixture of the distributions of sequential order statistics. Furthermore, some results on the joint distribution of sequential order statistics based on exchangeable components are given.

Keywords

Coherent systemk-out-of-n systemsequential order statisticsexchangeable lifetimessignature

MSC classification

Secondary: 60E05: Distributions 62E10: Characterization and structure theory
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 4 , December 2009 , pp. 1052 - 1072
Copyright
Copyright © Applied Probability Trust 2009 

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