Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 39093, 23 pages
doi:10.1155/JAMSA/2006/39093

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

Abstract

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.