Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 39093, 23 pages

Analysis of a k-out-of-N system with spares, repairs, and a probabilistic rule

Srinivas R. Chakravarthy

Department of Industrial and Manufacturing Engineering, Kettering University, Flint 48504, MI, USA

Received 16 April 2006; Revised 21 September 2006; Accepted 21 September 2006

Copyright © 2006 Srinivas R. Chakravarthy. 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.


We consider a k-out-of-N reliability system with identical components having exponential lifetimes. There is a single repairman who attends to failed components on a first-come first-served basis. The repair times are assumed to be of phase type. The system has K spares that can be used according to a probabilistic rule to extend the lifetime of the system. The system is analyzed using Markov chain theory and some interesting results are obtained. A few illustrative numerical examples are discussed.