Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T20:38:17.310Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Replacement Policies in a Random Environment

Published online by Cambridge University Press:  27 July 2009

Moshe Shaked  and
J. George Shanthikumar
Moshe Shaked
Affiliation:
Department of MathematicsUniversity of Arizona Tucson, Arizona 85721
J. George Shanthikumar
Affiliation:
School of Business AdministrationUniversity of California, Berkeley Berkeley, California 94720
Get access Rights & Permissions [Opens in a new window]

Abstract

Several models of maintenance of repairable multicomponent systems, subjected to a random environment, are introduced in this paper. For each model, it is shown how various probabilistic quantities of interest are “monotone” as a function of the probability law of the environment or as a function of other parameters of the model. Also, conditions are given which imply the positive dependence of the failure times, or of the counters of the number of failures, in these models.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 1 , January 1989 , pp. 117 - 134
Copyright
Copyright © Cambridge University Press 1989

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

Ahmed, A.N., Leon, R. & Proschan, R. (1981). Generalized association, with applications in multivariate statistics. Annals of Statistics 9: 168–176.CrossRefGoogle Scholar
Arjas, E. & Norros, I. (1984). Life lengths and association: a dynamic approach. Mathematics of Operations Research 9: 151–158.Google Scholar
Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing: probability models. New York: Holt, Rinehart and Winston.Google Scholar
Barlow, R.E. & Proschan, F. (1976). Theory of maintained systems: distribution of time to first system failure. Mathematics of Operations Research 1: 32–42.CrossRefGoogle Scholar
Cinlar, E. & Özekici, S. (1987). Reliability of complex devices in random environments. Probability in the Engineering and Informational Sciences 1: 97–115.CrossRefGoogle Scholar
Cinlar, E., Shaked, M. & Shanthikumar, J.G. (1987). On lifetimes influenced by a common environment. Technical Report, Department of Mathematics, University of Arizona.CrossRefGoogle Scholar
Esary, J.D., Proschan, F. & Walkup, D.W. (1967). Association of random variables, with applications. Annals of Mathematical Statistics 38: 1466–1474.Google Scholar
Harris, T.E. (1977). A correlation inequality for Markov processes in partially ordered state spaces. Annals of Probability 5: 451–454.CrossRefGoogle Scholar
Kamae, T., Krengel, U. & O'Brien, G.L. (1977). Stochastic inequalities on partially ordered spaces. Annals of Probability 5: 899–912.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1987). The multivariate hazard construction. Stochastic Processes and Their Applications 24: 241–258.CrossRefGoogle Scholar