Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T02:57:06.579Z Has data issue: false hasContentIssue false
  • English
  • Français

SOME RESULTS ABOUT MIT ORDER AND IMIT CLASS OF LIFE DISTRIBUTIONS

Published online by Cambridge University Press:  01 June 2006

Xiaohu Li  and
Maochao Xu
Xiaohu Li
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China, E-mail: [email protected]
Maochao Xu
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate some new properties of mean inactivity time (MIT) order and increasing MIT (IMIT) class of life distributions. The preservation property of MIT order under increasing and concave transformations, reversed preservation properties of MIT order, and IMIT class of life distributions under the taking of maximum are developed. Based on the residual life at a random time and the excess lifetime in a renewal process, stochastic comparisons of both IMIT and decreasing mean residual life distributions are conducted as well.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 3 , July 2006 , pp. 481 - 496
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahmad, I.A., Kayid, M., & Pellerey, F. (2005). Further results involving the MIT order and the IMIT class, Probability in the Engineering and Informational Sciences 19(3): 377–395.Google Scholar
Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Silver Spring, MD: To begin with.
Belzunce, F., Ortega, E., & Ruiz, J. (2001). A note on stochastic comparisons of excess lifetimes of renewal processes. Journal of Applied Probability 38: 1–7.Google Scholar
Block, H., Savits, T., & Singh, H. (1998). The reversed hazard rate function. Probability in the Engineering and Informational Science 12: 69–90.Google Scholar
Brown, M. (1980). Bounds, inequalities, and monotonicity properties for some specialized renewal processes. Annals of Probability 8: 227–240.Google Scholar
Chen, Y. (1994). Classes of life distributions and renewal counting process. Journal of Applied Probability 31: 1110–1115.Google Scholar
Gao, X., Belzunce, F., Hu, T., & Pellerey, F. (2002). Developments on some preservation properties of the Laplace transform order of residual lives. 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 & Probability Letters 22: 111–119.Google Scholar
Kayid, M. & Ahmad, I.A. (2004). On the mean inactivity time ordering with reliability applications. Probability in the Engineering and Informational Sciences 18(3): 395–409.Google Scholar
Karlin, S. & Taylor, H.M. (1975). A first course in stochastic process. 2nd ed. New York: Academic Press.
Li, X. (2004). Some properties of aging notions based upon the moment generating function order. Journal of Applied Probability 41(3): 927–934.Google Scholar
Li, X. & Kochar, S. C. (2001). Some new results involving NBU(2) class of life distributions. Statistics & Probability Letters 46: 229–237.Google Scholar
Li, X., Li, Z., & Jing, B. (2000). Some results about NBUC class of life distributions. Statistics & Probability Letters 46: 229–237.Google Scholar
Li, X. & Lu, J. (2003). Stochastic comparisons on residual life and inactivity time of series and parallel systems. Probability in Engineering and Informational Sciences 17: 267–276.Google Scholar
Li, X. & Zuo, M. (2004). Stochastic comparison of residual life and inactivity time at a random time. Stochastic Models 20(2): 229–235.Google Scholar
Marshall, K.T. (1968). Some inequalities in queuing. Operation Research 16: 651–665.Google Scholar
Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. New York: Wiley.
Nanda, A.K., Singh, H., Misra, N., & Paul, P. (2003). Reliability properties of reversed residual lifetime. Communications in Statistics: Theory and Methods 32(10): 2031–2042.Google Scholar
Ruiz, J.M. & Navarro, J. (1996). Characterization based on conditional expectations of the double truncated distributions. Annals of the Institute of Statistics and Mathematics 48: 563–572.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. San Diego: Academic Press.
Shaked, M. & Zhu, H. (1992). Some results on block replacement policies and renewal theory. Journal of Applied Probability 29: 932–946.Google Scholar
Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: Wiley.
Yue, D. & Cao, J. (2000). Some results on the residual life at random time. Acta Mathematicae Applicatae Sinica 16: 436–443.Google Scholar
Yue, D. & Cao, J. (2001). The NBUL class of life distribution and replacement policy comparisons. Naval Research Logistics 48: 578–591.Google Scholar