Journal of Mathematics and Statistics

Stochastic Behavior of Redundant Complex System with Two Types of Failure

G. S. Mokaddis, M. Salah EL-Sherbeny and Entesar Al-Esayeh

DOI : 10.3844/jmssp.2009.112.117

Journal of Mathematics and Statistics

Volume 5, Issue 2

Pages 112-117

Abstract

Problem statement: This study presented the reliability and Mean Time To System Failure (MTTF) analysis of a two-state complex with repairable system, consisting of two sub-systems A and B arranged in series, incorporating the concept of hardware and human failures. The failure times of operating units and repair time of failed units were exponential distributed. Approach: Markov-renewal processes and properties of Laplace transforms had been used to measure the system effectiveness Results: Laplace transforms of the various state probabilities had been derived and then reliability of the complex system, at any time t, had been computed by inversion process. MTTF had also been evaluated; availability and steady-state availability for system was derived. Certain important result had been evaluated as special cases. Also, few graphical illustrations were also given at the end to high-light the important results. Conclusion: The additional repair led to improve the values of the MTTF and the reliability at any time t.

Copyright

© 2009 G. S. Mokaddis, M. Salah EL-Sherbeny and Entesar Al-Esayeh. 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.