# Reliability Analysis for a k / n (F) System with Repairable Repair-Equipment

Zhang, Yuan Lin, Wu, Shaomin (2009) Reliability Analysis for a k / n (F) System with Repairable Repair-Equipment. Applied Mathematical Modelling, 33 (7). pp. 3052-3067. ISSN 0307-904X. (doi:10.1016/j.apm.2008.10.022) (KAR id:31013)

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## Abstract

In this paper, the reliability and replacement policy of a k / n (F) (i.e. k-out-of-n: F) system with repairable repair-equipment is analyzed. We assume that both the working and repair times of all components in the system and the repair-equipment follow exponential distributions, and the repairs on the components are perfect whereas that on the repair-equipment is imperfect. Under these assumptions, by using the geometric process, the vector Markov process and the queueing theory, we derive reliability indices for such a system and discuss its properties. We also optimize a replacement policy N under which the repair-equipment is replaced whenever its failure number reaches N. The explicit expression for the expected cost rate (i.e. the expected long-run cost per unit time) of the repair-equipment is derived, and the corresponding optimal replacement policy N* can be obtained analytically or numerically. Finally, a numerical example for policy N is given.

Item Type: Article 10.1016/j.apm.2008.10.022 Geometric process, M / M / 1 queueing system, Repairable repair-equipment, Supplementary variables, Vector Markov process, Game theory, Geometry, Markov processes, Pumps, Quality assurance, Queueing networks, Queueing theory, Reliability analysis, Reliability theory, Geometric process, M / M / 1 queueing system, Repairable repair-equipment, Supplementary variables, Vector Markov process, Repair H Social Sciences > HA Statistics > HA33 Management Science Divisions > Kent Business School - Division > Department of Analytics, Operations and Systems Shaomin Wu 17 Oct 2012 15:53 UTC 16 Nov 2021 10:08 UTC https://kar.kent.ac.uk/id/eprint/31013 (The current URI for this page, for reference purposes)

## University of Kent Author Information

### Wu, Shaomin.

Creator's ORCID: https://orcid.org/0000-0001-9786-3213