Journal of Mathematics and Statistics

Evaluation of Reliability and Availability Characteristics of Two Different Systems by Using Linear First Order Differential Equations

Khaled M. El-Said and Mohamed S. EL-Sherbeny

DOI : 10.3844/jmssp.2005.119.123

Journal of Mathematics and Statistics

Volume 1, Issue 2

Pages 119-123


This study deals with the reliability and availability characteristics of two different series system configurations. The second system differs from the first system due to the additional feature of preventive maintenance. The failure times of a components are assumed to be exponentially distributed with parameters α,β,α' and β', respectively. The replacement time distribution of each server is also exponentially distributed with parameters γ, δ and θ. We derive the mean time-to-failure, MTTF, and the steady-state availability,AT(∞) for the two systems using linear first order differential equations and perform comparisons theoretically and graphically to observe the effect of the preventive maintenance on system performance.


© 2005 Khaled M. El-Said and Mohamed S. EL-Sherbeny. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.