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Some results for repairable systems with general repair

  • Masaaki Kijima (a1)
Abstract

In this paper, we develop general repair models for a repairable system by using the idea of the virtual age process of the system. If the system has the virtual age Vn – 1 = y immediately after the (n – l)th repair, the nth failure-time Xn is assumed to have the survival function where is the survival function of the failure-time of a new system. A general repair is represented as a sequence of random variables An taking a value between 0 and 1, where An denotes the degree of the nth repair. For the extremal values 0 and 1, An = 1 means a minimal repair and An= 0 a perfect repair. Two models are constructed depending on how the repair affects the virtual age process: Vn = Vn – 1 + AnXn as Model 1 and Vn = An (Vn – 1 + Xn ) as Model II. Various monotonicity properties of the process with respect to stochastic orderings of general repairs are obtained. Using a result, an upper bound for E[Sn ] when a general repair is used is derived.

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Corresponding author
Postal address: Department of Information Sciences, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan.
References
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[1] Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover, New York.
[2] Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.
[3] Block, H. W., Borges, W. S. and Savits, T. H. (1985) Age-dependent minimal repair. J. Appl. Prob. 22, 370385.
[4] Brown, M. and Proschan, F. (1983) Imperfect repair. J. Appl. Prob. 20, 851859.
[5] Crow, E. L. (1974), 379410 in Reliability and Biometry , ed. Proschan, F. and Serfling, R. SIAM, Philadelphia.
[6] Kijima, M. and Sumita, U. (1986) A useful generalization of renewal theory: counting process governed by nonnegative Markovian increments. J. Appl. Prob. 23, 7188.
[7] Kijima, M., Morimura, H. and Suzuki, Y. (1988) Periodical replacement problem without assuming minimal repair. Europ. J. Operat. Res. 37, 194203.
[8] Shaked, M. and Shanthikumar, J. G. (1986) Multivariate imperfect repair. Operat. Res. 34, 437448.
[9] Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.
[10] Uematsu, K. and Nishida, T. (1987) One unit system with a failure rate depending upon the degree of repair. Math. Japonica , 32, 139147.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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