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Mathematical Problems in Engineering
Volume 2013, Article ID 192545, 10 pages
Research Article

Stochastic Analysis of a Two Non-Identical Unit Parallel System with Different Types of Failures Subject to Preventive Maintenance and Repairs

1Department of Mathematics, Faculty of Science and Arts, Rabigh-King AbdullAziz University, P.O. Box 21911, Rabigh, Saudi Arabia
2Department of Mathematics, Faculty of Science, Helwan University, P.O. Box 11795, Cairo, Egypt

Received 21 September 2012; Revised 24 December 2012; Accepted 26 December 2012

Academic Editor: Xu Zhang

Copyright © 2013 Mohamed Salah EL-Sherbeny. 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.


This paper studies the stochastic analysis of a two non-identical unit parallel system with common-cause failure, critical human error, non-critical human error, preventive maintenance, and two types of repair. The system goes for preventive maintenance at random epochs. We assume that the failure, repair, replacement, and maintenance times are independent random variables and their rates are constant for each unit. The system is analyzed by using the graphical evaluation and review technique (GERT) to obtain various related measures. We study the effect of the preventive maintenance on the system performance. Certain important results have been derived as special cases. The plots for the mean time to system failure and the steady-state availability of the system are drawn for different parametric values.