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Multivariate imperfect repair

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Shey-Huei Sheu  and
William S. Griffith
Shey-Huei Sheu*
Affiliation:
National Taiwan Institute of Technology
William S. Griffith*
Affiliation:
University of Kentucky
*
∗ Postal address: Department of Industrial Management, National Taiwan Institute of Technology, Taipei, Taiwan, ROC.
∗∗ Postal address: Department of Statistics, 817 Patterson Office Tower, Lexington, KY 40506–0027, USA.
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Abstract

We consider models of systems of components with dependent life-lengths having certain multivariate distributions. Upon failure, components are repaired. Two types of repair are possible. After perfect repair, a unit has the same life distribution as a new item. After imperfect repair, a unit has the life distribution of an item which is of the same age but has never failed. Different sources of failure are distinguished and affect the probabilities of perfect and imperfect repair.

Keywords

IFRIFRANBUNON-HOMOGENEOUS POISSON PROCESS

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 947 - 956
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Partially supported by NSF Grant RII-8610671 and the Commonwealth of Kentucky through the Kentucky EPSCoR Program.

References

Ascher, H. and Feingold, H. (1979) Comments on ‘Models for reliability of repaired equipment’. IEEE Trans. Reliability 19, 119.CrossRefGoogle Scholar
Balaban, H. S. and Singpurwalla, N. D. (1984) Stochastic properties of a sequence of interfailure times under minimal repair and survival. In Reliability Theory and Models, ed Abdel-Hameed, M. A., Çlinlar, E. and Quinn, J., pp. 65–80. Academic Press, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing Probability Models. Holt, Rinehart, and Winston, New York.Google Scholar
Berg, M. and Cleroux, R. (1982) A marginal cost analysis for an age replacement policy with minimal repair. Infor 20, 258–263.Google Scholar
Block, H. W., Borges, W. S. and Savits, T. H. (1985) Age dependent minimal repair. J. Appl. Prob. 22, 370–385.Google Scholar
Blumenthal, S., 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
Brown, M. and Proschan, F. (1983) Imperfect repair. J. Appl. Prob. 20, 851–859.Google Scholar
Brown, M. (1980) Bounds, inequalities and monotonicity properties for some specialized renewal processes. Ann. Prob. 8, 227–240.Google Scholar
Cleroux, R., Dubuc, S. and Tilquin, C. (1979) The age replacement problem with minimal repair and random repair cost. Operat. Res. 27, 1158–1167.Google Scholar
Marshall, A. W. and Olkin, I. (1967) A multivariate exponential distribution. J. Amer. Statist. Assoc. 62, 30–44.Google Scholar
Natvig, B. (1990) On information based minimal repair and the reduction in remaining system lifetime due to the failure of a specific module. J. Appl. Prob. 27, 365–375.CrossRefGoogle Scholar
Neveu, J. (1965) Mathematical Foundations of the Calculus of Probability. Holden Day, San Francisco.Google Scholar
Shaked, M. and Shanthikumar, J. G. (1986) Multivariate imperfect repair. Operat. Res. 34, 437–448.Google Scholar