Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-08T07:30:02.966Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE MEAN INACTIVITY TIME ORDERING WITH RELIABILITY APPLICATIONS

Published online by Cambridge University Press:  01 July 2004

M. Kayid  and
I. A. Ahmad
M. Kayid
Affiliation:
Department of Mathematics, Faculty of Education (Suez), Suez Canal University, Suez, Egypt
I. A. Ahmad
Affiliation:
Department of Statistics and Actuarial Science, University of Central Florida, Orlando, FL 32816-2370, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this article is to study several preservation properties of stochastic comparisons based on the mean inactivity time order under the reliability operations of convolution and mixture. Characterizations and relationships with the other well-known orders are given. Some examples of interest in reliability theory are also presented. Finally, testing in the increasing mean inactivity time class is discussed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 3 , July 2004 , pp. 395 - 409
Copyright
© 2004 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. (2001). Moments inequalities of aging families of distributions with hypothesis testing applications. Journal of Statistical Planning and Inference 92: 121–132.Google Scholar
Ahmad, I.A. & Mugdadi, A.R. (2003). 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
Ahmed, A. (1988). Preservation properties for the mean residual life ordering. Statistical Papers 29: 143–150.Google Scholar
Ahmed, A. & Kayid, M. (2004). Preservation properties for the Laplace transform ordering of residual lives. Statistical Papers (to appear).
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. (1999). The Laplace order and ordering of residual lives. Statistics and Probability Letters 42: 145–156.Google Scholar
Block, H., Savits, T., & Singh, H. (1998). The reversed hazard rate function. Probability in the Engineering and Informational Sciences 12: 69–70.Google Scholar
Chandra, N.K. & Roy, D. (2001). Some results on reversed hazard 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
Gao, X., Belzunce, F., Hu, T., & Pellerey, F. (2003). Developments of 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.
Hollander, M. & Proschan, F. (1975). Tests for mean residual life. Biometrika 62: 585–592.Google Scholar
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: Stanford University Press.
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
Mugdadi, A.R. & Ahmad, I.A. (2004). Moment inequalities derived from comparing life with its equilibrium form. Journal of Statistical Planning and Inference (to appear).
Muller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. West Sussex: 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
Ross, S.M. (1996). Stochastic process, 2nd ed. New York: Wiley.
Sengupta, D. & Nanda, A.K. (1999). Log-concave and concave distributions in reliability. Naval Research Logistics 46(4): 419–433.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. New York: Academic Press.
Wand, M.P. & Jones, M.C. (1995). Kernel smoothing. London: Chapman & Hall.