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On the Residual and Inactivity Times of the Components of Used Coherent Systems

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  04 February 2016

S. Goliforushani ,
M. Asadi  and
N. Balakrishnan
S. Goliforushani*
Affiliation:
University of Isfahan
M. Asadi*
Affiliation:
University of Isfahan
N. Balakrishnan*
Affiliation:
McMaster University
*
∗ Postal address: Department of Statistics, University of Isfahan, Isfahan, 81744, Iran.
∗ Postal address: Department of Statistics, University of Isfahan, Isfahan, 81744, Iran.
∗∗∗ Postal address: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada. Email address: bala@univmail.cis.mcmaster.ca
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Abstract

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In the study of the reliability of technical systems in reliability engineering, coherent systems play a key role. In this paper we consider a coherent system consisting of n components with independent and identically distributed components and propose two time-dependent criteria. The first criterion is a measure of the residual lifetime of live components of a coherent system having some of the components alive when the system fails at time t. The second criterion is a time-dependent measure which enables us to investigate the inactivity times of the failed components of a coherent system still functioning though some of its components have failed. Several ageing and stochastic properties of the proposed measures are then established.

Keywords

k-out-of-n systemhazard ratereversed hazard ratestochastic orderingresidual lifetimeinactivity timeorder statisticsreliabilitysignatureconditional lifetimeincreasing failure rate

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 385 - 404
Copyright
© Applied Probability Trust 

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