Systems with failure-dependent lifetimes of components

Systems with failure-dependent lifetimes of components

M. BURKSCHAT

Source: J. Appl. Probab. Volume 46, Number 4 (2009), 1052-1072.

Abstract

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.

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Primary Subjects: 60E05, 62E10

Keywords: Coherent system; k-out-of-n system; sequential order statistics; exchangeable lifetimes; signature

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Permanent link to this document: http://projecteuclid.org/euclid.jap/1261670688
Digital Object Identifier: doi:10.1239/jap/1261670688
Zentralblatt MATH identifier: 05665455
Mathematical Reviews number (MathSciNet): MR2582706

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