基于Weibull分布的两阶段加速寿命试验模型

doi:10.12305/j.issn.1001-506X.2025.06.22

摘要/Abstract

摘要：

航空航天产品在寿命周期内会经历多个任务阶段, 而现有加速寿命试验模型主要针对单个任务阶段, 难以建立不同阶段应力下产品失效分布之间的联系。对此, 提出一种基于Weibull分布的两阶段加速寿命试验模型。在加速寿命试验的两阶段, 假定产品寿命均服从Weibull分布且具有不同的形状参数和尺度参数, 在损伤失效率模型的基础上, 引入灵活失效率思想, 构建两阶段加速寿命试验模型, 连接不同阶段、不同应力下产品的失效分布。基于极大似然估计理论分析定时截尾下模型的参数估计, 得到模型参数的极大似然估计、渐近置信区间与Bootstrap置信区间。采用蒙特卡罗仿真和电连接器的两阶段加速寿命试验数据进行验证, 结果表明所提模型能够有效描述两阶段加速寿命试验中产品的寿命分布, 反映第一阶段试验对第二阶段试验的影响, 其寿命预测精度较单阶段加速寿命试验模型更高。该模型为分任务阶段产品的加速寿命试验研究提供一种新思路。

关键词: 加速寿命试验, 两阶段模型, Weibull分布, 失效率, 极大似然估计

Abstract:

Aerospace products will go through multiple task stages in their life cycle. The existing accelerated life test (ALT) models are mainly aimed at a single task stage, so it is difficult to establish a relationship between the failure distribution of products under different stages. In this paper, two-stage ALT model with Weibull distribution is proposed. Assuming that the product life follows the Weibull distribution with different shape parameters and scale parameters in the two stages of ALT. On the basis of the tamper failure rate model, a flexible failure rate idea is introduced and two-stage ALT model is constructed to connect the failure distribution of products under different stresses. The model parameter estimation analysis is carried out based on the maximum likelihood estimation (MLE) theory under time censoring. The MLE, asymptotic confidence interval and Bootstrap confidence interval of the model parameters are obtained. The Monte Carlo simulation and the two-stage ALT data of a certain type of electrical connector are used to verify the model. The results show that the proposed model can effectively describe the life distribution of products in the two-stage ALT, reflecting the influence of the first stage test on the second stage test, whose life prediction accuracy is higher than that of the single-stage ALT model. The proposed model provides a new idea for the ALT research of products containing multiple task stages.

Key words: accelerated life test (ALT), two-stage model, Weibull distribution, failure rate, maximum likelihood estimation (MLE)

中图分类号:

刘晓娣, 韩建立, 张建军, 吴一乔, 马天兆. 基于Weibull分布的两阶段加速寿命试验模型[J]. 系统工程与电子技术, 2025, 47(6): 1941-1949.

Xiaodi LIU, Jianli HAN, Jianjun ZHANG, Yiqiao WU, Tianzhao MA. Two-stage accelerated life test model based on Weibull distribution[J]. Systems Engineering and Electronics, 2025, 47(6): 1941-1949.

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应力组合	第一阶段振动/(g²/Hz)	第二阶段温度/℃	第二阶段拔插次数
SC1	0.2	130	13
SC2	0.4	158	11
SC3	0.6	120	9
SC4	0.8	140	7

参数	真值
r₁₀	-2
r₁₁	-1.5
σ₁	0.5
r₂₀	-3
r₂₁	2
r₂₂	-0.2
σ₂	0.4

τ	参数	MLE		Asym-CIs		Boot-CIs
τ	参数	Bias	MSE	CP	AL	CP	AL
10	r₁₀	0.005 9	0.059 5	0.960 8	1.019 2	0.951 9	0.928 6
	r₁₁	0.012 7	0.051 3	0.984 0	0.926 0	0.987 6	0.900 0
	σ₁	0.004 4	0.012 1	0.954 8	0.443 5	0.976 5	0.426 0
	r₂₀	0.043 2	0.214 4	0.998 7	8.643 9	0.985 5	0.906 7
	r₂₁	0.050 6	0.049 4	0.999 2	3.369 4	0.987 2	0.720 1
	r₂₂	0.018 0	0.000 8	0.969 9	0.178 2	0.973 2	0.072 4
	σ₂	0.028 8	0.003 4	0.996 0	0.302 0	0.991 6	0.182 1
15	r₁₀	0.005 1	0.036 6	0.981 2	0.760 9	0.973 6	0.813 7
	r₁₁	0.001 5	0.026 8	0.981 2	0.598 0	0.984 2	0.631 2
	σ₁	0.003 7	0.006 9	0.969 0	0.280 9	0.972 1	0.330 8
	r₂₀	0.071 2	0.226 9	0.998 1	9.998 8	0.984 6	0.961 6
	r₂₁	0.088 3	0.063 0	0.993 2	5.845 0	0.986 5	0.755 1
	r₂₂	0.028 4	0.001 9	0.998 9	0.553 4	0.973 2	0.100 0
	σ₂	0.033 9	0.004 1	0.997 8	0.612 2	0.974 1	0.188 8

τ	参数	MLE		Asym-CIs		Boot-CIs
τ	参数	Bias	MSE	CP	AL	CP	AL
10	r₁₀	0.005 2	0.037 5	0.971 0	0.791 6	0.962 6	0.823 9
	r₁₁	0.001 5	0.032 5	0.986 0	0.710 2	0.984 2	0.734 5
	σ₁	0.004 2	0.007 5	0.965 0	0.345 7	0.973 6	0.334 1
	r₂₀	0.041 8	0.206 9	0.999 2	6.645 4	0.986 1	0.850 0
	r₂₁	0.032 4	0.039 7	0.999 8	2.591 1	0.991 5	0.610 4
	r₂₂	0.013 0	0.000 5	0.986 0	0.140 6	0.981 2	0.058 2
	σ₂	0.021 6	0.002 3	0.980 0	0.234 4	0.973 2	0.171 3
15	r₁₀	0.004 9	0.016 2	0.976 6	0.492 6	0.964 7	0.488 5
	r₁₁	0.001 4	0.0163	0.9838	0.4975	0.9832	0.480 2
	σ₁	0.002 1	0.003 9	0.964 9	0.235 8	0.975 4	0.243 5
	r₂₀	0.054 2	0.217 7	0.998 9	8.086 9	0.987 2	0.915 0
	r₂₁	0.075 0	0.056 1	0.995 4	4.238 3	0.981 6	0.746 4
	r₂₂	0.026 8	0.001 7	0.999 0	0.410 4	0.971 9	0.096 4
	σ₂	0.031 2	0.003 2	0.996 9	0.449 2	0.975 4	0.178 9

应力组合	第一阶段振动/(g²/Hz)	第一阶段截尾时间/h	第二阶段温度/℃	第二阶段拔插次数	样本数
SC1	0.2	5.41	130	7	5
SC2	0.4	2.74	158	4	5
SC3	0.6	1.84	120	6	5
SC4	0.8	1.39	140	2	5