System Reliability Assessment of Solid Rocket Motors Based on Modified Bootstrap Method Under Small-sample Conditions

DU Minglong; WAN Jun; WANG Baoxin; JIA Xinyu; FENG Hao; SONG Jun; LI Jizhen

doi:10.12382/bgxb.2025.0239

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System Reliability Assessment of Solid Rocket Motors Based on Modified Bootstrap Method Under Small-sample Conditions

更新时间：2026-07-20

- System Reliability Assessment of Solid Rocket Motors Based on Modified Bootstrap Method Under Small-sample Conditions
- Acta Armamentarii (2026)
- 作者机构：
  
  1. 西安交通大学机械工程学院,陕西,西安,710049
  2. 重庆长安汽车股份有限公司,重庆,400000
  3. 中车青岛四方机车车辆股份有限公司,山东,青岛,266111
  4. 西安现代控制技术研究所,陕西,西安,710065
  5. 西安近代化学研究所,陕西,西安,710065
- 作者简介：
- 基金信息：
- DOI：10.12382/bgxb.2025.0239
  CLC： TJ763
- Received：03 April 2025，
  
  Online First：20 July 2026，
- 稿件说明：
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杜明龙，万鋆，王保鑫，等. 基于改进Bootstrap方法的固体火箭发动机小样本系统可靠性评估[J/OL]. 兵工学报, 2026(2026-07-20). https://doi.org/10.12382/bgxb.2025.0239.

DU M L, WAN J, WANG B X, et al. System reliability assessment of solid rocket motors based on modified bootstrap method under small-sample conditions[J/OL]. Acta Armamentarii, 2026(2026-07-20). https://doi.org/10.12382/bgxb.2025.0239. (in Chinese)
杜明龙，万鋆，王保鑫，等. 基于改进Bootstrap方法的固体火箭发动机小样本系统可靠性评估[J/OL]. 兵工学报, 2026(2026-07-20). https://doi.org/10.12382/bgxb.2025.0239. DOI：

DU M L, WAN J, WANG B X, et al. System reliability assessment of solid rocket motors based on modified bootstrap method under small-sample conditions[J/OL]. Acta Armamentarii, 2026(2026-07-20). https://doi.org/10.12382/bgxb.2025.0239. (in Chinese) DOI：

摘要

为了解决小样本条件下固体火箭发动机系统的可靠性评估难题，提出基于改进Bootstrap方法的可靠度评估框架。通过发动机组件分解建立串联系统可靠性模型，分别处理成败型单元（二项分布）和寿命型单元（指数/威布尔/正态分布）。采用B-样条函数重构经验分布函数，结合

-means聚类剔除Bootstrap重采样中的异值点，实现寿命型单元参数估计误差率较传统方法降低60%（

=15时误差小于等于±5%）。建立发动机子系统置信下限与系统可靠度的联合约束模型，通过实例验证表明：系统可靠度置信下限可达0.8493（置信度0.95），较LM（列文伯格-马夸尔特）方法提升15.4%。该方法可有效解决小样本、多失效模式下串联系统的可靠性评估问题，为固体火箭发动机的可靠性提升提供理论支撑。

Abstract

A reliabilityassessmentframework based on an improved Bootstrap method is proposed to address the reliability assessment challenges of solid rocket engine systems under small-sample conditions.Aseries system reliability model is establishedby decomposingtheengine components

which separately handles the success-failure units characterized by binomial distribution and the lifetime units characterized by exponential

Weibull or normal distributions.Anempirical distribution functionisreconstructedusing a B-spline function

andtheoutliers in Bootstrap resamplingare eliminatedutilizing k-means clustering

thusreducingthe parameter estimation error for lifetime units by 60% (with error less than or equal to ±5% when

=15)compared to traditional methods. A joint constraint modelfor theconfidence limitsofengine subsystemandthesystem reliability is developed. Thevalidationthrough examples showsthat thelower bound ofsystem reliability confidence can reach 0.8493witha confidence levelof0.95

which is15.4%higher than that oftheLevenberg-Marquardt method. The proposed methodeffectively resolvesthereliability assessment problems for series systems with small samples and multiple failure modes

providing theoretical support for enhancingthereliabilityofsolid rocketmotor.

关键词

Keywords

references

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