Replacement Policies with a Random Threshold Number of Faults

  • Xufeng Zhao
  • Mingchih Chen
  • Kazunori Iwata
  • Syouji Nakamura
  • Toshio Nakagawa
Conference paper


Most systems fail when a certain amount of reliability quantities have exceeded their threshold levels. The typical example is cumulative damage model in which a system is subjected to shocks and suffers some damage due to shocks, and fails when the total damage has exceeded a failure level K. This paper proposes the following reliability model: Faults occur at a nonhomogeneous Poisson process and the system fails when N faults have occurred, which could be applied to optimization problems in computer systems with fault tolerance, and we suppose that the system is replaced before failure at a planned time T. Two cases where the threshold fault number N is constantly given and is a random variable are considered, we obtain the expected cost rates and discuss their optimal policies.


Replacement Constant threshold Random threshold Faults 



This work is partially supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science under Grant No. 22500897 and No. 24530371; National Science Council of Taiwan NSC 100-2628-E-0330-002.


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Copyright information

© Springer Science+Business Media Singapore 2013

Authors and Affiliations

  • Xufeng Zhao
    • 1
  • Mingchih Chen
    • 2
  • Kazunori Iwata
    • 3
  • Syouji Nakamura
    • 4
  • Toshio Nakagawa
    • 1
  1. 1.Aichi Institute of TechnologyToyotaJapan
  2. 2.Fu Jen Catholic UniversityNew TaipeiTaiwan
  3. 3.Aichi UniversityNagoyaJapan
  4. 4.Kinjo Gakuin UniversityNagoyaJapan

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