Mathematical Problems in Engineering
Volume 2005 (2005), Issue 1, Pages 75-85

Long-run availability of a priority system: a numerical approach

Edmond J. Vanderperre1 and Stanislav S. Makhanov2

1Department of Quantitative Management, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa
2Faculty of Information Technology, Sirindhorn International Institute of Technology, Thammasat University, P.O. Box 22, Patumthani 12121, Thailand

Received 29 June 2004

Copyright © 2005 Edmond J. Vanderperre and Stanislav S. Makhanov. 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 two-unit cold standby system attended by two repairmen and subjected to a priority rule. In order to describe the random behavior of the twin system, we employ a stochastic process endowed with state probability functions satisfying coupled Hokstad-type differential equations. An explicit evaluation of the exact solution is in general quite intricate. Therefore, we propose a numerical solution of the equations. Finally, particular but important repair time distributions are involved to analyze the long-run availability of the T-system. Numerical results are illustrated by adequate computer-plotted graphs.