The Availability of Systems with Bathtub Hazard Rate Function

Dr. Mohamad Yousef Ashkar

doi:10.24297/jam.v15i0.7953

Authors

Dr. Mohamad Yousef Ashkar University of Bahrain

DOI:

https://doi.org/10.24297/jam.v15i0.7953

Abstract

In our normal life we can see that the most realistic systems possess useful time governed by hazard rate
of bathtub shaped. The hazard rate function, however, plays a vital role in the computation of the
availability function. The repair time, however, could be modeled as any statistical distribution. In this
paper I will investigate the nature of availability function and points of availability of systems with bathtub
hazard function and exponential distribution repair time using Markovian method.

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References

Ascher, H. and Feingold, H. "The Repairable System Reliability", Marcel Dekker, New York, 1984.

Ashkar, M. Y. " Markovian Method of Finding Point of Availability of Repairable Systems", Journal of Emerging Trends in Computing and information Science, CIS Journal, pp. 243- 250, Volume 2 No.5 May 2011.

Ashkar, M. Y. "A Stochastic Approach to Problems of the Königsberg Bridges", CIS Journal of Emerging Trends in Computing and Information Sciences, Vol. 3 No.2 February 2012.

Baker, C. "Numerical Treatment of Integral Equations", Oxford University Press, London 1977.

Barlow, R. and L. Hunter, "Optimum Preventive Maintenance Policies", Operations Research, Vol. 8, pp. 90-100, 1960.

Barlow, R. and L. Hunter, "Reliability Analysis of a One-unit System", Operations Research, Vol. 9, pp. 200-2008, 1961.

Barlow, R, and Proschan, F. "Statistical theory of Reliability Theory of Reliability and Life Testing", John Wiley, New York, 1975.

Cox, D. R. "Renewal Theory", Methuen, London, 1962. 9. Cha, J. H. “An extended model for optimal burn-in procedures,” IEEE Transactions on Reliability, vol. 55, no. 2, pp. 189–198, 2006

Davis, D.J., "An Analysis of Some Failure Data", J. Am. Stat. Assoc., Vol. 47, 1952.

Elliott, D. and Warent, W.G. "An Algorithm for the Numerical Solution of Linear Integral Equation", Int. Cent. Bull., Vol. 6, pp.207-224, 1967.

Elsayed, E., "Reliability Engineering", Addison Wesley, Reading, MA, 1996.

Fox. L., and Goodwin, E. T., "The Numerical Solution of Non-Singular Integral Equation", Phil. Trans. Roy. Soc. A245, PP 501-534, 1953.

Kapur, K.C. and L.R. Lamberson, "Reliability in Engineering Design", John Wiley & Sons, Inc., New York, 1977.

Kececioglu, D., "Reliability Engineering Handbook", Volume 1, Prentice Hall, Inc., New Jersey, 1991.

Kececioglu, D., "Maintainability, Availability, & Operational Readiness Engineering", Volume 1, Prentice Hall PTR, New Jersey, 1995.

Kijima, M. and Sumita, N., "A Useful Generalization of Renewal Theory: counting process governed by nonnegative Markovian increments", Journal of Applied Probability, 23, 71-88, 1986.

Kijima, M., "Some results for repairable systems with general repair", Journal of Applied Probability, 20, pp.851-859, 1989.

Knuth, D.E., "The Art of Computer Programming", Volume 2, Semi numerical Algorithms, Third Edition, Addison-Wesley, 1998.

L'Ecuyer, P., Communications of the ACM, Vol. 31, pp.724-774, 1988.

L'Ecuyer, P., Proceedings of the 2001 Winter Simulation Conference, pp.95-105, 2001.

Leemis, L.M., "Reliability - Probabilistic Models and Statistical Methods", Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1995.

Lewis, E., "Introduction to Reliability Engineering", John Wiley, New York,1987

Mettas, A., "Reliability Allocation and Optimization for Complex Systems", Proceedings of the Annual Reliability & Maintainability Symposium, 2000.

Shooman M.L. Probabilistic Reliability; An Engineering Approaches, McGraw Hill, New York 1968

Tillman, F.A., "Numerical Evaluation of Instantaneous Availability", IEEE, Transactions on Reliability, Vol. R32, No.1, 1983.

Xie, M, Tang Y, and T. N. Goh T. N., “A modified Weibull extension with bathtub-shaped failure rate function,” Reliability Engineering and System Safety, vol. 76, no. 3, pp. 279–285, 2002.