Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T10:53:36.728Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results on block replacement policies and renewal theory

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Moshe Shaked  and
Haolong Zhu
Moshe Shaked*
Affiliation:
University of Arizona
Haolong Zhu*
Affiliation:
University of Arizona
*
∗ Postal address for both authors: Department of Mathematics, Building #89, University of Arizona, Tucson, AZ 85721, USA.
∗ Postal address for both authors: Department of Mathematics, Building #89, University of Arizona, Tucson, AZ 85721, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Age and block replacement policies are commonly used in order to reduce the number of in-service failures. The focus in this paper is on the block replacement policies, about which relatively less is known than age replacement policies. Several new results which connect the properties of block replacement policies with the properties of the corresponding renewal function and the excess lifetimes are obtained. Some applications and the relationships between these new results and some known results are included.

Keywords

RELIABILITY THEORYIN-SERVICE FAILURESRENEWAL FUNCTIONEXCESS LIFETIMEIFRDFRNBUNWUNBUENWUE

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 932 - 946
Copyright
Copyright © Applied Probability Trust 1992 

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.)

Footnotes

Research supported by the AFOSR Grant AFOSR-90–0201. Reproduction in whole or in part is permitted for any purpose by the United States Government.

References

[1] Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Life Testing: Probability Models. To Begin With, Silver Springs, MD.Google Scholar
[2] Baxter, L. A. (1988) Some criteria for reliability growth. Microelectron. Reliab. 28, 743–750.CrossRefGoogle Scholar
[3] Berman, M. (1978) Regenerative multivariate point processes. Adv. Appl. Prob. 10, 411–430.CrossRefGoogle Scholar
[4] Brown, M. (1980) Bounds, inequalities, and monotonicity properties for some specialized renewal processes. Ann. Prob. 8, 227–240.CrossRefGoogle Scholar
[5] Brown, M. (1981) Further monotonicity properties for specialized renewal processes. Ann. Prob. 9, 891–895.CrossRefGoogle Scholar
[6] Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes, 2nd edn. Academic Press, New York.Google Scholar
[7] Kijima, M. (1992) Further monotonicity properties of renewal processes. Adv. Appl. Prob. 24(3).CrossRefGoogle Scholar
[8] Marshall, A. W. and Proschan, F. (1972) Classes of distributions applicable in replacement with renewal theory implication. Proc. 6th Berkeley Symp. Math. Statist. Prob. 1, 395–415.Google Scholar