Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 4, Pages 361-380

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

Srinivas R. Chakravarthy,1 A. Krishnamoorthy,2 and P. V. Ushakumari2

1Kettering University, Department of Industrial and Manufacturing Engineering & Business, Flint 48504, MI, USA
2Cochin University of Science and Technology, Department of Mathematics, Cochin 682022, India

Received 1 June 2001; Revised 1 October 2001

Copyright © 2001 Srinivas R. Chakravarthy et al. 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.


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.