A note on ‘curable’ shock processes |
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Authors: | Ji Hwan Cha Maxim Finkelstein |
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Affiliation: | 1. Department of Statistics, Ewha Womans University, Seoul 120-750, Korea;2. Department of Mathematical Statistics, University of the Free State, 339 Bloemfontein 9300, South Africa;3. Max Planck Institute for Demographic Research, Rostock, Germany |
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Abstract: | In most conventional shock models, the events caused by an external shock are initiated at the moments of its occurrence. Recently, Cha and Finkelstein (2012) had considered the case when each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in the classical shock models, but with delay of some random time. In this paper, we suggest the new type of shock models, where each delayed failure can be cured (repaired) with certain probabilities. These shock processes have not been considered in the literature before. We derive and analyze the corresponding survival and failure rate functions and consider a meaningful reliability example of the stress–strength model. |
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Keywords: | Shock model Cumulative shock model Nonhomogeneous Poisson process Delayed failure Cure models |
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