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Is perfect repair always perfect?

Abstract

Most often, perfect repair is conventionally understood as a replacement of the failed item by the new one. However, contrary to the common perception, new does not mean automatically that the distribution to the next failure is identical to that on the previous cycle. First, it can be different due to dynamic environment and, secondly, due to heterogeneity of items for replacement. Both of these causes that affect the failure mechanism of items are studied. Environment is modeled by the non-homogeneous Poisson shock process. Two models for the failure mechanism defined by the extreme shock model and the cumulative shock model are considered. Examples illustrating our findings are presented.

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Acknowledgements

The authors thank the referees for valuable comments and constructive suggestions. The work of the first author was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211). The work of the second author was supported by the NRF (National Research Foundation of South Africa) Grant IFR2011040500026.

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Correspondence to Ji Hwan Cha.

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Cha, J.H., Finkelstein, M. Is perfect repair always perfect?. TEST 29, 90–104 (2020). https://doi.org/10.1007/s11749-019-00645-7

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Keywords

  • Statistical perfect repair
  • Information-based perfect repair
  • Shock environment
  • Stochastic intensity

Mathematics Subject Classification

  • 62P30