Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-18T22:13:44.323Z Has data issue: false hasContentIssue false
  • English
  • Français

Repair replacement policies

Part of: Operations research and management science Special processes Survival analysis and censored data Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Henry W. Block ,
Naftali A. Langberg  and
Thomas H. Savits
Henry W. Block*
Affiliation:
University of Pittsburgh
Naftali A. Langberg*
Affiliation:
Haifa University
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗ Postal address: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
∗∗ Postal address: Department of Statistics, Haifa University, Mount Carmel, Haifa, Israel.
∗ Postal address: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we introduce the concept of repair replacement. Repair replacement is a maintenance policy in which items are preventively maintained when a certain time has elapsed since their last repair. This differs from age replacement where a certain amount of time has elapsed since the last replacement. If the last repair was a complete repair, repair replacement is essentially the same as age replacement. It is in the case of minimal repair that these two policies differ. We make comparison between various types of policies in order to determine when and under which condition one type of policy is better than another.

Keywords

AGE REPLACEMENTBLOCK REPLACEMENTMINIMAL REPAIR REPLACEMENTREPAIR REPLACEMENTSTOCHASTIC COMPARISON

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60K10: Applications (reliability, demand theory, etc.) 90B25: Reliability, availability, maintenance, inspection 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 194 - 206
Copyright
Copyright © Applied Probability Trust 1993 

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

Supported by AFOSR Grant No. AFOSR-84-0113, AFOSR-89-0370, and NSA Grant No. MDA-904-90-H-4036.

Partially supported by AFOSR Grant No. AFOSR-84-0113.

References

Assher, H. and Feingold, H. (1984) Repairable Systems Reliability: Modeling, Inference, Misconceptions and their Causes. Marcel Dekker, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1964) Comparison of replacement policies and renewal theory implications. Ann. Math. Statist. 35, 577–589.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing: Probability Models. To Begin With, Silver Springs, MD.Google Scholar
Block, H. W., Langberg, N. A. and Savits, T. H. (1990a) Maintenance comparisons: Block policies. J. Appl. Prob. 29, 649–657.CrossRefGoogle Scholar
Block, H. W., Langberg, N. A. and Savits, T. H. (1990b) Stochastic comparisons of maintenance policies. Topics in Statistical Dependence, ed. Block, H. W., Sampson, A. R. and Savits, T. H. IMS Lecture Notes-Monograph Series. 16, 57–68.CrossRefGoogle Scholar
ÇlInlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Kamae, T., Krengel, U. and O'Brien, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899–912.CrossRefGoogle Scholar
Marsaglia, G. and Tubilla, A. (1975) A note on the ‘lack of memory’ property of the exponential distribution. Ann. Prob. 3, 353–354.CrossRefGoogle Scholar