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On new aging classes based on the reversed mean residual life order

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce new concepts of aging for lifetime distributions. The main idea is the comparison between reversed mean residual life of the random variables X and (X − t | X > t), for all t > 0. Firstly, with some examples, we highlight the role of the proposed aging classes in reliability and life testing. Then, we try to find the connection between the new aging classes and other aging classes well-known from the literature. Reliability properties of the new classes are studied. Formally, we derive the preservation property under monotonic transformations. Some Rother characterization and implications are studied.
Rocznik
Strony
727--737
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Department of Statistics, University of Birjand, Iran
autor
  • Department of Statistics, University of Birjand, Iran
Bibliografia
  • 1. Ahmad, I.A., Kayid, M. and Li, X. (2005) The NBUT class of life distributions. IEEE Transactions on Reliability 54(3), 396–401.
  • 2. Ahmad, I.A. and Mugdadi, A.R. (2010) Higher Order Equilibrium Life Distributions. IEEE Transactions on Reliability 59(1), 66–73.
  • 3. Asadi, M. and Berred, A. (2012) Properties and estimation of the mean past lifetime. Statistics 46(3), 405–417.
  • 4. Bryson, M.C. and Siddiqui, M.M. (1969) Some criteria for aging. Journal of American Statistical Association 64(328), 1472–1483.
  • 5. Deshpande, J.V., Kochar, S.C. and Singh, H. (1986) Aspects of positive aging. J. Appl. Probab 23,(3), 748–758.
  • 6. Elbatal, I. (2007) Some aging classes of life distributions at specific age. International Mathematical Forum 2(29), 1445–1456.
  • 7. Eryilmaz, S. (2010) Mean Residual and Mean Past Lifetime of Multi-State Systems With Identical Components. IEEE Transactions on Reliability 59(4), 644–649.
  • 8. Hollander, R.M., Park, D.H. and Proschan, F. (1986) A class of life distributions for aging. Journal of American Statistical Association 81(393), 91–95.
  • 9. Izadkhah, S. and Kayid, M. (2013) Reliability analysis of the harmonicmean inactivity time order. IEEE Transactions on Reliability 62(2), 329–337, DOI: 10.1109/TR.2013.2255793.
  • 10. Kayid, M. and Ahmad, I.A. (2004) On the mean inactivity time ordering with reliability applications. Probability in the Engineering and Informational Sciences 18(3), 395–409.
  • 11. Kayid, M. (2007) A general family of NBU classes of life distributions. Statistical Methodology 4(2), 185–195.
  • 12. Kayid, M., Diab, L.S., Alzughaibi, A. and Ahmad, I.A. (2011) Starshaped ordering of life distributions and its aging properties. IEEE Transactions on Reliability 60(1), 257–262.
  • 13. Knopik, L. (2006) Characterization of a class of lifetime distributions. Control and Cybernetics 35(2), 407–414.
  • 14. Li, X. and Xu, M. (2006) Some results aboutMIT order and IMIT class of life distributions. Probability in the Engineering and Informational Sciences 20(3), 481–496.
  • 15. Li, X. and Xu, M. (2007) A new aging notion based upon the reversed hazard rate order. Southeast Asian Bulletin of Mathematics 31(1), 95–109.
  • 16. Li, X. and Xu, M. (2008) Reversed hazard rate order of equilibrium distributions and a related aging notion. Statistical Papers 49(4), 749–767.
  • 17. Marshall, A.W. and Proschan, F. (1972) Classes of life distributions applicable in replacement with renewal theory implications. Sixth Berkeley Symposium on Mathematical Statistics and Probability 1, 395–415.
  • 18. Nanda, A.K., Singh, H., Misra, N. and Paul, P. (2003) Reliability properties of reversed residual lifetime. Communications in Statistics-Theory and Methods 32(10), 2031–2042.
  • 19. Nanda, A.K., Bhattacharjee, S. and Alam, S.S. (2006) On upshifted reversed mean residual life order. Communications in Statistics-Theory and Methods 35(8), 1513–1523.
  • 20. Pellerey, F. and Petakos, K. (2002) On closure property of the NBUC class under formation of parallel systems. IEEE Transactions on Reliability 51(4), 452–454.
  • 21. Poursaeed, M.H. and Nematollahi, A.R. (2010) Some aspects of the mean past lifetime of a parallel system under double regularly checking. Statistics 44(5), 505–515.
  • 22. Shaked, M. and Shanthikumar, J.G. (2007) Stochastic Orders. Springer Verlag, New York.
  • 23. Zhang, S. and Cheng, H. (2010) Testing for increasing mean inactivity time. Statistics 44(5), 467–476.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7bcaa62a-d65b-4876-83d5-63d1c082603a
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