Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 407457, 12 pages
Research Article

The Optimal Warranty and Preventive Maintenance Policy for the Four-State System

1Department of Mathematical Statistics, Institute of Statistical Studies & Research, Cairo University, Giza 12613, Egypt
2Department of Statistics, Faculty of Commerce, Al-Azhar University (Assiut), Assiut, Egypt
3Mathematical Institute, University of Cologne, 50923 Cologne, Germany

Received 28 March 2011; Accepted 28 April 2011

Academic Editor: A. Bellouquid

Copyright © 2011 Ahmed F. Attia 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.


A complete view for the multistate system considering the four-state system is here introduced. The exponential distribution for failure times and repair times is considered. The steady state availability is established via the Markov process. Different warranty and preventive maintenance policies are introduced, and also the cost of these policies for the manufacturer and the buyer is evaluated.