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Discrete Replacement Models

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Stochastic Models in Reliability Theory

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 235))

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Abstract

This chapter considers seven models with discrete variables where a unit is replaced preventively after a specified number N of uses, failures, faults, preventive maintenances and shocks have occured. Optimal policies to minimize the expected cost rates are discussed. Each optimal number N* is given by a unique solution of equation. Further, two discrete problems of a parallel redundant system which determine the total number of failed units and the number of units are considered. Finally, extended models with continuous and discrete variables are introduced.

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References

  1. R.E. Barlow and F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965.

    MATH  Google Scholar 

  2. J.D. Esary, A.W. Marshall and F. Proschan, “Shock models and wear processes,” Ann. of Prob., vol. 1(4), August 1973, pp. 627–649.

    Article  MathSciNet  MATH  Google Scholar 

  3. N. Kaio and S. Osaki, “Discrete-time ordering policies,” IEEE Trans. Rel., vol. R-28(5), December 1979, pp. 405–406.

    Article  MathSciNet  Google Scholar 

  4. H. Mine, H. Kawai and Y. Fukushima, “Preventive replacement of an intermittently-used system,” IEEE Trans. Rel., vol. R-30(4), October 1981, pp. 391–392.

    Article  Google Scholar 

  5. H. Morimura, “On some prevetive maintenance policies for IPR,” J. Operations Res. Soc. Japan, vol. 12(1), April 1970, pp. 94–124.

    MathSciNet  MATH  Google Scholar 

  6. T. Nakagawa, “On a replacement problem of a cumulative damage model,” Operational Res. Quart., vol. 27(4.i), December 1976, pp. 895–900.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Nakagawa, “Replacement problem of a parallel system in random environment,” J. Appl. Prob., vol. 16(1), March 1979, pp. 203–205.

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Nakagawa, “Further results of replacement problem of a parallel system in random environment,” J. Appl. Prob., vol. 16, 1979, pp. 923–926.

    Article  MathSciNet  MATH  Google Scholar 

  9. T. Nakagawa, “A summary of imperfect preventive maintenance polcies with minimal repair,” R.A.I.R.O., vol. 14(3), August 1980, 249–255.

    MathSciNet  MATH  Google Scholar 

  10. T. Nakagawa, “A summary of periodic replacement with minimal repair at failure,” J. Operations Res. Soc. Japan, vol. 24(3), September 1981, pp. 213–227.

    MathSciNet  MATH  Google Scholar 

  11. T. Nakagawa, “Generalized models for determining optimal number of minimal repairs before replacement,” J. Operations Res. Soc. Japan, vol. 24(4), December 1981, pp. 213–227.

    MathSciNet  MATH  Google Scholar 

  12. T. Nakagawa, “Optimal number of units for a parallel system,” J. Appl. Prob., vol. 21(2), June 1984, pp. 000–000.

    Article  MathSciNet  Google Scholar 

  13. T. Nakagawa, “A summary of discrete replacement policies,” Euro. J. of Operations Res., vol. 13(3), 1984, pp. 000–000.

    MathSciNet  Google Scholar 

  14. T. Nakagawa and S. Osaki, “The discrete Weibull distribution,” IEEE Trans. Rel., vol. R-24(5), December 1975, pp. 300–301.

    Article  Google Scholar 

  15. T. Nakagawa and S. Osaki, “Discrete time age replacement policies,” Operational Res. Quart., vol. 28(4.i), 1977, pp. 881–885.

    Article  MATH  Google Scholar 

  16. T. Nakagawa, K. Yasui and S. Osaki, “Optimum maintenance policies for a computer system with restart,” FTCS-11, June 1981, pp. 148-150.

    Google Scholar 

  17. K.S. Park, “Optimal number of minimal repairs before replacement,” IEEE Trans. Rel., vol. R-28(2), June 1979, pp. 137–140.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Meijo University, Nagoya 468, Japan

    Toshio Nakagawa

Authors
  1. Toshio Nakagawa
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Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering Faculty of Engineering, Hiroshima University, Higashi-Hiroshima 724, Japan

    Shunji Osaki

  2. Faculty of Business Administration, Senshu University, Kawasaki 214, Japan

    Yukio Hatoyama

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© 1984 Springer-Verlag Berlin Heidelberg

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Nakagawa, T. (1984). Discrete Replacement Models. In: Osaki, S., Hatoyama, Y. (eds) Stochastic Models in Reliability Theory. Lecture Notes in Economics and Mathematical Systems, vol 235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45587-2_4

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  • DOI: https://doi.org/10.1007/978-3-642-45587-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13888-4

  • Online ISBN: 978-3-642-45587-2

  • eBook Packages: Springer Book Archive

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