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PRESERVATION OF RELIABILITY CLASSES UNDER MIXTURES OF RENEWAL PROCESSES

Published online by Cambridge University Press:  18 December 2007

F. G. Badía  and
C. Sangüesa
F. G. Badía
Affiliation:
Departamento de Métodos EstadísticosUniversidad de ZaragozaZaragoza, Spain E-mail:gbadia@unizar.es
C. Sangüesa
Affiliation:
Departamento de Métodos EstadísticosUniversidad de ZaragozaZaragoza, Spain E-mail:gbadia@unizar.es
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Abstract

In this work we provide sufficient conditions for the arrival times of a renewal process so that the number of its events occurring before a randomly distributed time, T, independent of the process preserves the aging properties of T.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 1 , January 2008 , pp. 1 - 17
Copyright
Copyright © Cambridge University Press 2008

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References

1.Barlow, R.E. & Proschan, F. (1965). Mathematical theory of reliability. New York: Wiley.Google Scholar
2.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Reinhart and Winston.Google Scholar
3.Block, H.W. & Savits, T.H. (1980). Laplace transforms for classes of life distributions. The Annals of Probability 8: 465–474.CrossRefGoogle Scholar
4.Block, H.W., Savits, T.H., & Singh, H. (1998). The reversed hazard rate function. Probability in the Engineering and Informational Sciences 12: 69–90.CrossRefGoogle Scholar
5.Chandra, N.K. & Roy, D. (2001). Some results on reversed hazard rate. Probability in the Engineering and Informational Sciences 15: 95–102.CrossRefGoogle Scholar
6.Grandell, J. (1997). Mixed Poisson processes. London: Chapman & Hall.CrossRefGoogle Scholar
7.Esary, J.D., Marshall, W., & Proschan, F. (1973). Shock models and wear processes. The Annals of Probability 4: 627–649.Google Scholar
8.Finkelstein, M.S. (2002). On the reversed hazard rate. Reliability Engineering and System Safety 78: 71–75.CrossRefGoogle Scholar
9.Lai, C.D. & Xie, M. (2006). Stochastic Ageing and Dependendence for Reliability. New York: Springer.Google Scholar
10.Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. Chichester: Wiley.Google Scholar
11.Nanda, A.K. & Sengupta, D. (2005). Discrete life distributions with decreasing reversed hazard. Sankhyā 67: 106–125.Google Scholar
12.Ross, S.M., Shanthikumar, J.G., & Zhu, Z. (2005). On increasing-failure-rate random variables. Journal of Applied Probability 42: 797–809.CrossRefGoogle Scholar
13.Sengupta, D. & Nanda, A.K. (1999). Log-concave and concave distributions in reliability. Naval Research Logistics 46: 419–433.3.0.CO;2-B>CrossRefGoogle Scholar
14.Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. London: Academic Press.Google Scholar
15.Shanthikumar, J.G. & Yao, D.D. (1991). Bivariate characterization of some stochastic order relations. Advances in Applied Probability 23: 642–659.CrossRefGoogle Scholar
16.Sunoj, S.M. & Maya, S.S. (2006) Some properties of weighted distributions in the contex of repairable systems. Communications in Statistics: Theory and Methods 35: 223–228.CrossRefGoogle Scholar
17.Vinogradov, O.P. (1973). The definition of distribution functions with increasing hazard rates in terms of the Laplace transform. Teorija Verojatnosteıˇi ee Primenenija 18: 811–814 (in Russian).Google Scholar