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Reliability of a Cascade System with Stress & Strength Follow Pareto Distribution
Abstract
Failure of a system may occur due to certain type of stresses or loading acting on the system. If these stresses does not
exceed a certain threshold value (minimum strength k ) the system may work for a long period. On the other hand, if the stresses exceed the threshold they may fail within no time . For this reason pareto distribution can be used to find the reliability for stress-strength model and cascade redundancy system. Comparison with five different distributions (Geometric, Weibull, Rayleigh, Pareto, and Lognormal) pareto distribution is the best fit in the context of system
reliability. Pareto distribution is used for decreasing hazard model. In this paper the reliability has been derived for cascade redundancy stress-strength system when stress and strength follow pareto distribution of the first kind. It is observed by the computations that if * = 1 i k then the reliability for n − cascade system when stress and strength follow pareto distribution of the first kind is same as the
reliability for exponential distribution even though the means are not same for these distributions.
Keywords
References
Kapur, K.C and L.R.Lamberson, “ Reliability in Engineering Design” ,Jhon Wiley and Sons, Inc., New York, 1977.
S.N.Narahari Pandit and G.L.Sriwastav , “ Studies in Cascade Reliability–I”, IEEE Transactions on Reliability , Vol.R-24, No.1, 1975, pp.53-57.
Beg, M.Afzal and Singh, N, “Estimation of Pr(Y
A.C.N.Raghava char, B.Kesava Rao and S.N.Narahari Pandit, “The Reliability of a Cascade system with Normal Stress and Strength distribution”. ASR, Vol. No.2, Sept.1987, pp. 49-54.
T.S.Uma Maheswari, “Reliability of single strength under stresses”, Micro Electron Reliability, Pergamon Press, OXFORD, Vol.32, No.10, 1992, pp: 1475-1478.
T.S.Uma Maheswari , “ Reliability comparison of an – cascade system with the addition of an - strength systems”, Micro Electron Reliability, Pergamon Press, OXFORD, Vol.33, No.4, 1993, pp: 477- 479.
T.S.Uma Maheswari, “Reliability of cascade system with normal stress and exponential strength”, Micro Electron Reliability, Pergamon Press, OXFORD, Vol.33, 1993, pp: 927-936.
T.S.Uma Maheswari, “Reliability of single stress under – strengths of life distribution”, Micro Electron Reliability, Pergamon Press, OXFORD, Vol.34, No.3, 1994, pp: 569-572.
Hanagal, D.D. , “A multivariate Pareto distribution”, it communications in Statistics, Theory and Methods, 25(7), 1996, 1471-88.
David D Hanagal, “Note on estimation of reliability under bivariate pareto stress-strength model”, Statist. Papers, 38, 1997, 453-459.
Rekha, A. and Shyam Sunder, T., “Reliability of a cascade system with exponential strength and gamma stress”, Microelectronics and Reliability, 37, 1997, 683-685.
Rekha, A. and Chenchu Raju, V.C. “Cascade system reliability with Rayleigh distribution”, Botswana Journal of Technology, 8, 1999, 14-19.
Saralees Nadarajah – Samuel Kotz, “Reliability for Pareto Models”, International Journal of Statistics, Vol.LXI, n.2, 2003, pp: 191-204.
Mette Rytgaard, “Estimation of the pareto distribution”, ASTIN Bulletin, Vol. 20, No. 2.
Naser Odat, “Estimation of reliability based on Pareto distribution”, Applied Mathematical Sciences, Vol. 4, no. 55, 2010, 2743-2748.
Catherine Forbes, Merran Evans, Nicholas Hastrings and Brian Peacock, “Statistical Distributions”, Fourth edition, John Wiley & Sons, New Jersey, 2011.
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