Transform-Resampled Double Bootstrap Percentile with Applications in System Reliability Assessment

Abstract

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.