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On optimal operational sequence of components in a warm standby system

Part of: Distribution theory - Probability Special processes Operations research and management science

Published online by Cambridge University Press:  16 January 2019

Maxim Finkelstein ,
Nil Kamal Hazra  and
Ji Hwan Cha
Maxim Finkelstein*
Affiliation:
University of the Free State and ITMO University
Nil Kamal Hazra*
Affiliation:
IIITDM Kancheepuram
Ji Hwan Cha*
Affiliation:
Ewha Womans University
*
* Postal address: Department of Mathematical Statistics and Actuarial Science, University of the Free State, 339 Bloemfontein 9300, South Africa, and ITMO University, Saint Petersburg, Russia.
** Postal address: Department of Mathematics, Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram, Chennai 600127, Tamil Nadu, India.
*** Postal address: Department of Statistics, Ewha Womans University, Seoul 120-750, Republic of Korea. Email address: [email protected]
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Abstract

We consider an open problem of obtaining the optimal operational sequence for the 1-out-of-n system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order and its generalization. Only specific cases of this optimal problem were considered in the literature previously.

Keywords

Cumulative exposure modelstochastic precedence ordervirtual agewarm standby system

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1014 - 1024
Copyright
Copyright © Applied Probability Trust 2018 

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