Failure Rate Properties of Parallel Systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866908761752338432 |
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| author | Arab, Idir Hadjikyriakou, Milto Oliveira, Paulo Eduardo |
| author_facet | Arab, Idir Hadjikyriakou, Milto Oliveira, Paulo Eduardo |
| contents | We study failure rate monotonicity and generalized convex transform stochastic ordering properties of random variables, with a concern on applications. We are especially interested in the effect of a tail weight iteration procedure to define distributions, which is equivalent to the characterization of moments of the residual lifetime at a given instant. For the monotonicity properties, we are mainly concerned with hereditary properties with respect to the iteration procedure providing counter-examples showing either that the hereditary property does not hold or that inverse implications are not true. For the stochastic ordering, we introduce a new criterium, based on the analysis of the sign variation of a suitable function. This criterium is then applied to prove ageing properties of parallel systems formed with components that have exponentially distributed lifetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_04009 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Failure Rate Properties of Parallel Systems Arab, Idir Hadjikyriakou, Milto Oliveira, Paulo Eduardo Probability 60E15, 60E05, 62N05 We study failure rate monotonicity and generalized convex transform stochastic ordering properties of random variables, with a concern on applications. We are especially interested in the effect of a tail weight iteration procedure to define distributions, which is equivalent to the characterization of moments of the residual lifetime at a given instant. For the monotonicity properties, we are mainly concerned with hereditary properties with respect to the iteration procedure providing counter-examples showing either that the hereditary property does not hold or that inverse implications are not true. For the stochastic ordering, we introduce a new criterium, based on the analysis of the sign variation of a suitable function. This criterium is then applied to prove ageing properties of parallel systems formed with components that have exponentially distributed lifetimes. |
| title | Failure Rate Properties of Parallel Systems |
| topic | Probability 60E15, 60E05, 62N05 |
| url | https://arxiv.org/abs/1809.04009 |