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Imperfect repair models with preventive maintenance

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Haijun Li  and
Moshe Shaked
Haijun Li*
Affiliation:
Washington State University
Moshe Shaked*
Affiliation:
University of Arizona
*
∗Postal address: Department of Mathematics, Washington State University, Pullman, WA 99164, USA.
∗∗Postal address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA. Email address: shaked@math.arizona.edu
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Abstract

Brown and Proschan (1983) introduced the imperfect repair model, in which an item, upon failure, is replaced with a new one with probability α, and is minimally repaired with probability 1 − α. In this paper we equip the imperfect repair model with preventive maintenance, and we obtain stochastic maintenance comparisons for the numbers of failures under different policies via a point-process approach. We also obtain some results involving stochastic monotonicity properties of these models with respect to the unplanned complete repair probability α.

Keywords

Block and age replacementstochastic ordercompensator functionNBUIFR

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1043 - 1059
Copyright
Copyright © Applied Probability Trust 2003 

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References

Abdel-Hameed, M. (1987). An imperfect maintenance model with block replacements. Appl. Stoch. Models Data Anal. 3, 63–72.Google Scholar
Barlow, R. E., and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Berg, M. and Cléroux, R. (1982). The block replacement problem with minimal repair and random repair costs. J. Statist. Computation Simulation 15, 1–7.Google Scholar
Block, H. W., Langberg, N. A., and Savits, T. H. (1990a). Comparisons for maintenance policies involving complete and minimal repair. In Topics in Statistical Dependence (IMS Lecture Notes Monogr. 16), eds Block, H. W., Sampson, A. R. and Savits, T. H., Inst. Math. Statist., Hayward, CA, pp. 57-68.CrossRefGoogle Scholar
Block, H. W., Langberg, N. A., and Savits, T. H. (1990b). Maintenance comparisons: block policies. J. Appl. Prob. 27, 649–657.Google Scholar
Brown, M., and Proschan, F. (1983). Imperfect repair. J. Appl. Prob. 20, 851–859.Google Scholar
Fontenot, R. A., and Proschan, F. (1984). Some imperfect maintenance models. In Reliability Theory and Models, eds Abdel-Hameed, M. S., Çinlar, E. and Quinn, J., Academic Press, San Diego, pp. 83–101.Google Scholar
Kijima, M. (1989). Some results for repairable systems. J. Appl. Prob. 26, 194–203.Google Scholar
Kwieciński, A., and Szekli, R. (1991). Compensator conditions for stochastic ordering of point processes. J. Appl. Prob. 28, 751–761.Google Scholar
Last, G., and Szekli, R. (1998). Stochastic comparison of repairable systems by coupling. J. Appl. Prob. 35, 348–370.Google Scholar
Li, H., and Xu, S. (2001). On the Markov block replacement policy in multivariate repairable systems. To appear in Operat. Res.Google Scholar
Pham, H., and Wang, H. (1996). Imperfect maintenance. Europ. J. Operat. Res. 94, 425–438.CrossRefGoogle Scholar
Rolski, T., and Szekli, R. (1991). Stochastic ordering and thinning of point processes. Stoch. Process. Appl. 37, 299–312.CrossRefGoogle Scholar
Shaked, M., and Szekli, R. (1995). Comparison of replacement policies via point processes. Adv. Appl. Prob. 27, 1079–1103.Google Scholar
Wang, H. (2002). A survey of maintenance policies of deteriorating systems. Europ. J. Operat. Res. 139, 469–489.Google Scholar