AVAILABILITY AND RELIABILITY ANALYSIS OF THREE ELEMENTS PARALLEL SYSTEM WITH FUZZY FAILURE AND REPAIR RATES
Keywords:
Fuzzy Rates, Availability, Reliability, Markov Model, Vague Sets, Statistical Data.Abstract
The present study proposes an algorithm to evaluate the fuzzy availability, reliability, steady state availability, and mean time to failure of a repairable parallel system which consists of three identical and independent components by using Markov model. This system fails when the three components fail or it goes to the critical case. The failure rate and the repair rate of each component is represented by triangular shaped vague set determined by using statistical data. Two numerical examples are given to illustrate the introduced algoithm and discribe the performance of the model when the life times and the repair times of the system follow exponential or Rayleigh distribution with fuzzy parameters.
Downloads
References
Høyland, Arnljot, and Marvin Rausand (2009). System Reliability Theory:
Models and Statistical Methods, Vol. 420. Wiley. com.
Stapelberg, Rudolph Frederick (2009). Handbook of Reliability, Availability,
Maintainability and Safety in Engineering Design, Springer, ISBN:
Carrasco, Juan A (2003). Markovian Dependability/Performability Modeling
of Fault-Tolerant Systems- Handbook of Reliability Engineering, Springer
London, p. 613-642.
Singh, C. J. and Jain, M. (2000). Reliability of repairable multicomponent
redundant system, International Journal of Engineering, Vol. 13(4), p. 17-22.
Sharifi, M., M. Ganjian, and P. Shafiee (2006). Reliability of a System with n
Parallel and Not Identical Elements with Constant Failure Rates,
Computational Intelligence for Modelling, Control and Automation, 2006 and
International Conference on Intelligent Agents, Web Technologies and
Internet Commerce, International Conference on IEEE.
Zhang, Tieling, and Horigome, Michio (2001). Availability and reliability of
system with dependent components and time-varying failure and repair
rates, IEEE Transactions on Reliability, 50(2), p. 151-158.
Hassett, Thomas F., Duane L. Dietrich and Ferenc, Szidarovszky (1995).
Time-varying failure rates in the availability and reliability analysis of
repairable systems, IEEE Transactions on Reliability, 44(1), p. 155-160.
Tang, Shengdao and Fengquan, Wang (2005). Reliability analysis for a
repairable parallel system with time-varying failure rates, Applied
Mathematics-A Journal of Chinese Universities, 20(1), p. 85-90.
Jain, M. and Singh, C.J. (2000). Reliability of repairable multi-component
redundant system, Int. J. Eng., Vol. 3, p. 107-114.
Srinivasan, S. K., and Subramanian, R. (2006). Reliability analysis of a three
unit warm standby redundant system with repair, Annals of Operations
Research, 143(1), p. 227-235.
Zadeh, L. A. (1965). Fuzzy sets, Information and control, 8(3), p. 338-353.
Buckley, James J., and Eslami, Esfandiar (2008). Fuzzy Markov chains:
uncertain probabilities, Mathware & soft computing, 9(1), p. 33-41.
Sharifi, M., Ganjian, M. and Ghajar, H.R. (2005). Expansion of Reliability
Models based on Markov Chain with Consideration of Fuzzy Failure Rates:
System with two Parallel and Identical Elements with Constant Failure Rates,
Computational Intelligence for Modelling, Control and Automation, 2005 and
International Conference on Intelligent Agents, Web Technologies and
Internet Commerce, International Conference on. Vol. 2. IEEE
