Research Article Open Access

Stochastic Behavior of Redundant Complex System with Two Types of Failure

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

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.

Journal of Mathematics and Statistics
Volume 5 No. 2, 2009, 112-117

DOI: https://doi.org/10.3844/jmssp.2009.112.117

Submitted On: 25 March 2009 Published On: 30 June 2009

How to Cite: Mokaddis, G. S., EL-Sherbeny, M. S. & Al-Esayeh, E. (2009). Stochastic Behavior of Redundant Complex System with Two Types of Failure. Journal of Mathematics and Statistics, 5(2), 112-117. https://doi.org/10.3844/jmssp.2009.112.117

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Keywords

  • Reliability to system R(t)
  • Availability to system A(t) and mean-time to failure