International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2001 / Article

Open Access

Volume 14 |Article ID 930934 | https://doi.org/10.1155/S1048953301000326

Srinivas R. Chakravarthy, A. Krishnamoorthy, P. V. Ushakumari, "A k-out-of-n reliability system with an unreliable server and phase type repairs and services: the (N,T) policy", International Journal of Stochastic Analysis, vol. 14, Article ID 930934, 20 pages, 2001. https://doi.org/10.1155/S1048953301000326

A k-out-of-n reliability system with an unreliable server and phase type repairs and services: the (N,T) policy

Received01 Jun 2001
Revised01 Oct 2001

Abstract

In this paper we study a k-out-of-n reliability system in which a single unreliable server maintains n identical components. The reliability system is studied under the (N,T) policy. An idle server takes a vacation for a random amount of time T and then attends to any failed component waiting in line upon completion of the vacation. The vacationing server is recalled instantaneously upon the failure of the Nth component. The failure times of the components are assumed to follow an exponential distribution. The server is subject to failure with failure times exponentially distributed. Repair times of the component, fixing times of the server, and vacationing times of the server are assumed to be of phase type. Using matrix-analytic methods we perform steady state analysis of this model. Time spent by a failed component in service, total time in the repair facility, vacation time of the server, non-vacation time of the server, and time until failure of the system are all shown to be of phase type. Several performance measures are evaluated. Illustrative numerical examples are presented.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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