Transform-Resampled Double Bootstrap Percentile with Applications in System Reliability Assessment
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916780805455872 |
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| author | Gong, Junpeng He, Xu Li, Zhaohui |
| author_facet | Gong, Junpeng He, Xu Li, Zhaohui |
| contents | System reliability assessment(SRA) is a challenging task due to the limited experimental data and the complex nature of the system structures. Despite a long history dating back to \cite{buehler1957confidence}, exact methods have only been applied to SRA for simple systems. High-order asymptotic methods, such as the Cornish-Fisher expansion, have become popular for balancing computational efficiency with improved accuracy when data are limited, but frequently encounter the "bend-back" problem in high-reliability scenarios and require complex analytical computations. To overcome these limitations, we propose a novel method for SRA by modifying the double bootstrap framework, termed the double bootstrap percentile with transformed resamples. In particular, we design a nested resampling process for log-location-scale lifetime models, eliminating the computational burden caused by the iterative resampling process involved in the conventional double bootstrap. We prove that the proposed method maintains the high-order convergence property, thus providing a highly accurate yet computationally efficient confidence limit for system reliability. Moreover, the proposed procedure is straightforward to implement, involving only a simple resampling operation and efficient moment estimation steps. Numerical studies further demonstrate that our approach outperforms the state-of-the-art SRA methods and, at the same time, is much less susceptible to the bend-back issue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transform-Resampled Double Bootstrap Percentile with Applications in System Reliability Assessment Gong, Junpeng He, Xu Li, Zhaohui Methodology System reliability assessment(SRA) is a challenging task due to the limited experimental data and the complex nature of the system structures. Despite a long history dating back to \cite{buehler1957confidence}, exact methods have only been applied to SRA for simple systems. High-order asymptotic methods, such as the Cornish-Fisher expansion, have become popular for balancing computational efficiency with improved accuracy when data are limited, but frequently encounter the "bend-back" problem in high-reliability scenarios and require complex analytical computations. To overcome these limitations, we propose a novel method for SRA by modifying the double bootstrap framework, termed the double bootstrap percentile with transformed resamples. In particular, we design a nested resampling process for log-location-scale lifetime models, eliminating the computational burden caused by the iterative resampling process involved in the conventional double bootstrap. We prove that the proposed method maintains the high-order convergence property, thus providing a highly accurate yet computationally efficient confidence limit for system reliability. Moreover, the proposed procedure is straightforward to implement, involving only a simple resampling operation and efficient moment estimation steps. Numerical studies further demonstrate that our approach outperforms the state-of-the-art SRA methods and, at the same time, is much less susceptible to the bend-back issue. |
| title | Transform-Resampled Double Bootstrap Percentile with Applications in System Reliability Assessment |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.04573 |