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FURTHER RESULTS INVOLVING THE MIT ORDER AND THE IMIT CLASS

Published online by Cambridge University Press:  22 June 2005

I. A. Ahmad ,
M. Kayid  and
F. Pellerey
I. A. Ahmad
Affiliation:
Department of Statistics and Actuarial Science, University of Central Florida, Orlando, Florida 32816-2370
M. Kayid
Affiliation:
Department of Mathematics, Faculty of Education (Suez), Suez Canal University, Suez, Egypt
F. Pellerey
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, 10129 Torino, Italy, E-mail: [email protected]
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Abstract

The purpose of this article is to study several preservation properties of the mean inactivity time order under the reliability operations of convolution, mixture, and shock models. In that context, the increasing mean inactivity time class of lifetime distributions is characterized by means of right spread order and increasing convex order. Some applications in reliability theory are described. Finally, a new test of such a class is discussed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 3 , July 2005 , pp. 377 - 395
Copyright
© 2005 Cambridge University Press

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References

REFERENCES

Ahmad, I.A. (2001). Moments inequalities of ageing families of distributions with hypothesis testing application. Journal of Statistical Planning and Inference 92: 121–132.Google Scholar
Ahmad, I.A. & Mugdadi, A.R. (2004). Further moment inequalities of life distributions with hypothesis testing applications: The IFRA, NBUC, DMRL classes. Journal of Statistical Planning and Inference 120: 1–12.Google Scholar
A-Hameed, M.S. & Proschan, F. (1973). Nonstationary shock models. Stochastic Processes Applications 1: 383–404.Google Scholar
A-Hameed, M.S. & Proschan, F. (1975). Shock models with underlying birth process. Journal of Applied Probability 12: 18–28.Google Scholar
Alzaid, A., Kim, J.S., & Proschan, F. (1991). Laplace ordering and its applications. Journal of Applied Probability 28: 116–130.Google Scholar
Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Silver Spring, MD: To Begin With.
Belzunce, F. (1999). On a characterization of right spread order by the increasing convex order. Statistics and Probability Letters 45: 103–110.Google Scholar
Belzunce, F., Ortega, E., & Ruiz, J.M. (1999). The Laplace order and ordering of residual lives. Statistics and Probability Letters 42: 145–156.Google Scholar
Block, H.W. & Savits, T.H. (1978). Shock models with NBUE survival. Journal of Applied Probability 15: 621–628.Google Scholar
Chandra, N.K. & Roy, D. (2001). Some results on reversed failure rate. Probability in the Engineering and Informational Sciences 15: 95–102.Google Scholar
Di Crescenzo, A. & Longobardi, M. (2002). Entropy-based measure of uncertainty in past lifetime distribution. Journal of Applied Probability 39: 434–440.Google Scholar
Esary, J.D., Marshall, A.W., & Proschan, F. (1973). Shock models and wear processes. Annals of Probability 1: 627–649.Google Scholar
Fagiuoli, E. & Pellerey, F. (1994). Mean residual life and increasing convex comparison of shock models. Statistics and Probability Letters 20: 337–345.Google Scholar
Hu, T., Kundu, A., & Nanda, A.K. (2003). A not on Bayesian imperfect repair model. Technical Report, Department of Statistics and Finance, University of Science and Technology of China, Hefei.
Joag-Dev, K., Kochar, S., & Proschan, F. (1995). A general composition theorem and its applications to certain partial orderings of distributions. Statistics and Probability Letters 22: 111–119.Google Scholar
Karlin, S. (1968). Total positivity, Vol. I. Stanford, CA: Standford University Press.
Kayid, M. & Ahmad, I.A. (2004). On the mean inactivity time ordering with reliability applications. Probability in the Engineering and Informational Sciences 18: 395–409.Google Scholar
Lee, A.J. (1989). U-Statistics. New York: Marcel Dekker.
Li, X. & Lu, J. (2003). Stochastic comparisons on residual life and inactivity time of series and parallel systems. Probability in the Engineering and Informational Sciences 17: 267–275.Google Scholar
Lynch, J., Mimmack, G., & Proschan, F. (1987). Uniform stochastic orderings and total positivity. Canadian Journal of Statistics 15: 63–69.Google Scholar
Mugdadi, A.R. & Ahmad, I.A. (2005). Moments inequalities derived from comparing life with its equilibrium form. Journal of Statistical Planning and Inference (to appear).CrossRef
Nanda, A.K., Singh, H., Misra, N., & Paul, P. (2003). Reliability properties of reversed residual lifetime. Communications in Statistics: Theory & Methods 32: 2031–2041.Google Scholar
Pellerey, F. (1994). Shock models with underlying counting process. Journal of Applied Probability 31: 156–166.Google Scholar
Pellerey, F. & Shaked, M. (1997). Characterizations of the IFR and DFR aging notions by means of the dispersive order. Statistics and Probability Letters 33: 389–393.Google Scholar
Perez-Ocon, R. & Gamiz-Perez, M.L. (1995). Conditions on the arrival process to obtain HNBUE survival using a shock model. Communications in Statistics: Theory & Methods 24: 931–944.Google Scholar
Perez-Ocon, R. & Gamiz-Perez, M.L. (1996). HNBUE property in a shock model with cumulative damage threshold. Communications in Statistics: Theory & Methods 25: 345–360.Google Scholar
Ross, S.M. (1996). Stochastic process, 2nd ed. New York: Wiley.
Ruiz, J.M. & Navarro, J. (1996). Characterizations based on conditional expectations of the double truncated distribution. Annals of the Institute of Statistical Mathematics 48: 563–572.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. New York: Academic Press.
Shaked, M. & Wong, T. (1995). Preservation of stochastic orderings under random mapping by point processes. Probability in the Engineering and Informational Sciences 9: 563–580.Google Scholar