Product Reliability Evaluation under Multi-stage Stresses Based on Equivalent Time Recurrence and Hierarchical Group Algorithm

SHENG Pei; XIAO Zhicai

doi:10.7643/ issn.1672-9242.2026.01.015

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Equipment Environmental Engineering ›› 2026, Vol. 23 ›› Issue (1) : 130-136. DOI: 10.7643/ issn.1672-9242.2026.01.015

Product Reliability Evaluation under Multi-stage Stresses Based on Equivalent Time Recurrence and Hierarchical Group Algorithm

SHENG Pei, XIAO Zhicai

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Abstract

Aiming at the problem that the variable stress superposition effect is difficult to be quantified in product reliability prediction under multi-stage variable stress environments, a reliability evaluation method integrating equivalent time recurrence and hierarchical group algorithm is proposed. The real time is mapped to equivalent aging time through equivalent time recurrence to quantify the superposition impact of stresses in different stages on product aging. The hierarchical group algorithm is used to construct a fitness function and iteratively fit Weibull parameters. With the three-stage life test of a certain product as an example, the results show that the error of the optimized Weibull parameters is controllable, and the prediction error of failure probability meets engineering requirements. This method can effectively support product reliability evaluation under multi-stage stress scenarios and provide technical support for product life prediction.

Key words

multi-stage stress / reliability evaluation / equivalent time recurrence / hierarchical group algorithm / Weibull parameters / failure probability prediction

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SHENG Pei, XIAO Zhicai. Product Reliability Evaluation under Multi-stage Stresses Based on Equivalent Time Recurrence and Hierarchical Group Algorithm[J]. Equipment Environmental Engineering. 2026, 23(1): 130-136 https://doi.org/10.7643/ issn.1672-9242.2026.01.015

References

[1] 吴帅帅, 王航, 刘永阔.机会维修策略下的核动力装置系统维修决策模型[J].哈尔滨工程大学学报, 2025, 46(11): 2278-2286.
WU S S, WANG H, LIU Y K.Maintenance Decision Optimization Model for Nuclear Propulsion Systems under Opportunistic Maintenance Strategies[J].Journal of Harbin Engineering University, 2025, 46(11): 2278-2286.
[2] 黄惠新, 吴超扬, 辛海鹏.基于威布尔分布的发动机核心部件可靠性调查——以液压机械组件为例[J].航空维修与工程, 2025(7): 55-57.
HUANG H X, WU C Y, XIN H P.Reliability Investigation of Engine Key Components Based on Weibull Distribution—In Case of Hydraulic Mechanical Unit[J].Aviation Maintenance & Engineering, 2025(7): 55-57.
[3] 黄希宇, 彭钟.基于灰狼-粒子群算法的VSG参数自适应控制策略研究[J].机电工程技术, 2025, 54(18): 35-41.
HUANG X Y, PENG Z.Research on VSG Parameter Adaptive Control Strategy Based on Grey Wolf Particle Swarm Optimization[J].Mechanical & Electrical Engineering Technology, 2025, 54(18): 35-41.
[4] 万乡缘.一次性设备加速寿命试验的研究及应用[D].重庆: 重庆理工大学, 2025.
WAN X Y.Research and Application of Accelerated Life Test for One-Shot Device[D].Chongqing: Chongqing University of Technology, 2025.
[5] 陈国庆, 郑波, 黄健豪.基于CPSOGSA算法的威布尔参数估计及其在民机设备可靠性评估中的应用[J].中国民航飞行学院学报, 2023, 34(3): 5-9.
CHEN G Q, ZHENG B, HUANG J H.Weibull Parameter Estimation Based on CPSOGSA Algorithm and Application in Reliability Estimation of Civil Aircraft Equipment[J].Journal of Civil Aviation Flight University of China, 2023, 34(3): 5-9.
[6] 李康乐, 霍文博, 王杰, 等.基于PDC支路参数时变特征的电缆局部老化类型诊断方法[J].高电压技术, 2025, 51(11): 5549-5557.
LI K L, HUO W B, WANG J, et al.Diagnosis Method of the Local Aging Type of Cables Based on Time-Varying Characteristics of PDC Branch Parameters[J].High Voltage Engineering, 2025, 51(11): 5549-5557.
[7] 武磊.浅谈通过威布尔分布模型判别风电机组故障时期的应用[C]//2024年电力行业技术监督专业技术交流研讨会优秀论文集.哈密: 国华(哈密)新能源有限公司, 2024.
WU L.On the Application of Identifying Fault Periods of Wind Turbine Units via Weibull Distribution Model[C]//Excellent Proceedings of the 2024 Professional Technical Exchange Seminar on Technical Supervision in the Power Industry.Hami: Guohua (Hami) New Energy Co., Ltd, 2024.
[8] 杨喆, 冯靖祎.基于威布尔分布的故障预测与诊断方法研究[J].生物医学工程与临床, 2025, 29(2): 256-261.
YANG Z, FENG J Y.Research on Fault Prediction and Diagnosis Method Based on Weibull Distribution[J].Biomedical Engineering and Clinical Medicine, 2025, 29(2): 256-261.
[9] 雷启贵, 李荣, 赵庭, 等.逆威布尔分布下一类多部件应力-强度模型的可靠度估计[J].高师理科学刊, 2025, 45(8): 7-14.
LEI Q G, LI R, ZHAO T, et al.Reliability Estimation of a Class of Multi-Component Stress-Strength Models under Inverse Weibull Distribution[J].Journal of Science of Teachersʹ College and University, 2025, 45(8): 7-14.
[10] 杨柳, 李会葆.竞争失效下Ⅱ型截尾逆威布尔分布恒定应力加速寿命模型的参数估计[J].安庆师范大学学报(自然科学版), 2024, 30(4): 20-24.
YANG L, LI H B.Parameter Estimation of Type-II Censoring Inverse Weibull Distribution Constant Stress Accelerated Life Model under Competitive Failure[J].Journal of Anqing Normal University (Natural Science Edition), 2024, 30(4): 20-24.
[11] 谭诗翰, 石全, 胡起伟, 等.考虑多种故障模式和多阶段故障过程的装备预防性维修策略优化模型[J/OL].系统工程与电子技术, 2025: 1-13.[2025-09-22].https://link.cnki.net/urlid/11.2422.tn.20250611.0934.024.
TAN Shihan, SHI Quan, HU Qiwei, et al.Optimization Model of Equipment Preventive Maintenance Strategy Considering Multiple Failure Modes and Multi-Stage Failure Processes[J/OL].Systems Engineering and Electronics, 2025: 1-13.[2025-09-22].https://link.cnki.net/urlid/11.2422.tn.20250611.0934.024.
[12] 雷星, 王紫钰, 赵秀杰.面向多阶段任务系统的加速退化试验方案[J].工业工程, 2025, 28(4): 89-100.
LEI X, WANG Z Y, ZHAO X J.Accelerated Degradation Test Planning for Multi-Stage Mission Systems[J].Industrial Engineering Journal, 2025, 28(4): 89-100.
[13] 陈卓, 闫明, 金映丽.基于失效概率等效原理的损伤累积概率模型[J].振动与冲击, 2025, 44(14): 132-138.
CHEN Z, YAN M, JIN Y L.Damage Accumulation Probability Model Based on the Equivalent Principle of Failure Probability[J].Journal of Vibration and Shock, 2025, 44(14): 132-138.
[14] 裴彥青, 李建锋, 赵宇飞, 等.砂砾石料颗粒级配参数的多维威布尔分布模型[J].水利规划与设计, 2022(12): 11-16.
PEI Y Q, LI J F, ZHAO Y F, et al.Multidimensional Weibull Distribution Model for Grading Parameters of Sand Gravel[J].Water Resources Planning and Design, 2022(12): 11-16.
[15] 赵宇飞, 王毅, 亚森钠斯尔, 等.基于多维概率分布的砂砾石坝填料级配研究[J].岩土工程学报, 2022, 44(11): 2007-2016.
ZHAO Y F, WANG Y, YA S, et al.Gradation of Filling Materials of Sand-Gravel Dams Based on Multi-Dimensional Probability Distribution[J].Chinese Journal of Geotechnical Engineering, 2022, 44(11): 2007-2016.
[16] 徐东, 贾旭杰, 姚兆胜, 等.基于马尔可夫更新过程的多阶段冲击退化系统可靠性分析[J].运筹与管理, 2022, 31(5): 107-111.
XU D, JIA X J, YAO Z S, et al.Reliability Analysis of Multi-Stage Shock and Degradation Model Based on Markov Renewal Process[J].Operations Research and Management Science, 2022, 31(5): 107-111.
[17] 徐东.基于马尔可夫更新过程的多阶段冲击退化及自愈系统可靠性分析[D].北京: 中央民族大学, 2021.
XU D.Reliability Analysis of Multi-Stage Shock Deterioration and Self-Healing Systems Based on Markov Renewal Processes[D].Beijing: Central University for Nationalities, 2021.
[18] 蔡江讯.多环境应力下的光栅编码器加速退化可靠性评估[D].长春: 吉林大学, 2025.
CAI J X.Reliability Assessment of an Encoder for Accelerated Degradation under Multi-Environmental Stresses[D].Changchun: Jilin University, 2025.
[19] 张帆, 田润操, 王鹏, 等.考虑广义耦合的多应力加速寿命评估方法[J].系统工程与电子技术, 2023, 45(10): 3350-3361.
ZHANG F, TIAN R C, WANG P, et al.Multi-Stress Accelerated Life Evaluation Method Considering Generalized Coupling[J].Systems Engineering and Electronics, 2023, 45(10): 3350-3361.
[20] 杨朝霞, 方健文, 李佳蓉, 等.粒子群优化算法在多参数拟合中的应用[J].浙江师范大学学报(自然科学版), 2008, 31(2): 173-177.
YANG Z X, FANG J W, LI J R, et al.Application of Particle Swarm Optimization to Multiparameters Fitting[J].Journal of Zhejiang Normal University (Natural Sciences), 2008, 31(2): 173-177.
[21] 邢燕祯, 王东辉.一种基于收敛因子改进的灰狼优化算法[J].网络新媒体技术, 2020, 9(3): 28-34.
XING Y Z, WANG D H.An Improved Grey Wolf Optimization Algorithm Based on Convergence Factor[J].Journal of Network New Media, 2020, 9(3): 28-34.
[22] 张爱琳, 王凯, 丁超, 等.基于形状分布-平均绝对误差法的历史建筑数字孪生模型更新方法[J].科学技术与工程, 2025, 25(12): 5058-5065.
ZHANG A L, WANG K, DING C, et al.Updating Methods of Digital Twin Models for Historical Buildings Based on Shape Distribution-Mean Absolute Error Method[J].Science Technology and Engineering, 2025, 25(12): 5058-5065.
[23] 丁毓晋, 单泉, 陈砚, 等.改进粒子群算法在装配序列规划中的应用研究[J/OL].机械设计与制造, 2025: 1-8.[2025-09-22].https://doi.org/10.19356/j.cnki.1001-3997.20250919.027.
DING Y J, SHAN Q, CHEN Y, et al.Research on Application of Improved Particle Swarm Optimization Algorithm in Assembly Sequence Planning[J/OL].Machinery Design & Manufacture, 2025: 1-8.[2025-09-22].https://doi.org/10.19356/j.cnki.1001-3997.20250919.027.
[24] 马晨杰, 鲁文其, 林军华, 等.基于改进粒子群算法的伺服系统摩擦参数辨识及前馈补偿[J].组合机床与自动化加工技术, 2025(9): 80-87.
MA C J, LU W Q, LIN J H, et al.Friction Parameter Identification and Feedforward Compensation of Servo System Based on Improved Particle Swarm Optimization[J].Modular Machine Tool & Automatic Manufacturing Technique, 2025(9): 80-87.
[25] 杨智勇, 陈宏伟, 徐显金, 等.改进粒子群优化的烟具加热元件温度模糊控制[J/OL].机械设计与制造, 2025: 1-8.[2025-09-22].https://doi.org/10.19356/j.cnki.1001-3997.20250918.001.
YANG Z Y, CHEN H W, XU X J, et al.Fuzzy Temperature Control of Heating Elements in Tobacco Sets Based on Improved Particle Swarm Optimization[J/OL].Machinery Design & Manufacture, 2025: 1-8.[2025-09-22].https://doi.org/10.19356/j.cnki.1001-3997.20250918.001.