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Maintenance comparisons: block policies

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.
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Abstract

Complete repair and minimal repair models with a block maintenance policy are considered. Each of these models gives rise to a counting process, and these processes are compared stochastically. This contrasts with most previous work on maintenance policies where only univariate marginal comparisons were made. Also a more general block schedule is considered than is customary.

Keywords

STOCHASTIC COMPARISONBLOCK MAINTENANCE POLICYMINIMAL REPAIRNBU
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 649 - 657
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Supported by AFOSR Grant No. AFOSR-84-0113 and ONR Contract N00014-84-K-0084.

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

References

Asher, 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.Google Scholar
Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing: Probability Models. To Begin With, Silver Spring, MD.Google Scholar
Block, H. W., Langberg, N. A. and Savits, T. H. (1988) Stochastic comparisons: block policies. University of Pittsburgh, Technical Report No. 88-06.Google Scholar
Blumenthal, S. J., Greenwood, J. A. and Herbach, L. H. (1976) A comparison of the bad as old and superimposed renewal models. Management Sci. 23, 280–285.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
Langberg, N. A. (1988) Comparisons of replacement policies. J. Appl. Prob. 25, 780–788.CrossRefGoogle Scholar
Marshall, A. W. and Proschan, F. (1972) Classes of distribution applied in replacement, with renewal theory implications. Proc. 6th Berkeley Symp. Math. Statist. Prob. 1, 395–415.Google Scholar
Shared, M. and Shanthikumar, G. (1989) Some replacement policies in a random environment. Prob. Eng. Inf. Sci. 3, 117–134.Google Scholar
Whitt, W. (1981) Comparing counting processes and queues. Adv. Appl. Prob. 13, 207–220.CrossRefGoogle Scholar