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1. 北京航空航天大学 可靠性与系统工程学院, 北京 100191;
2. 可靠性与环境工程技术重点实验室, 北京 100191

Evaluation method for accelerated degradation testing with interval analysis
LIU Le1,2, LI Xiaoyang1,2 , JIANG Tongmin1
1. School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China
Abstract: Traditional evaluation methods of accelerated degradation testing (ADT) are based on precise degradation data to conduct reliability and lifetime assessment. However, with interfere of the uncertainties from human factors, the test data can be imprecise represented by interval rather than precise data. Under this consideration, an interval analysis method for ADT evaluation was proposed based on Wiener process, which included possibility and necessity models. Interval regression method was firstly used to transfer the problems of modeling interval degradation data under different accelerated stress levels into quadratic programming problems. The interval drift coefficients under different stress levels with possibility model and diffusion coefficient were obtained. Then the interval drift coefficients were extrapolated to normal stress condition with accelerated model under necessity model, and further to analyze the relationship between measurement uncertainty and reliability and lifetime evaluation results. Finally, the numerical study was used to present and verify the proposed methodology, and conduct uncertainty sensitivity analysis. The results show that both reliability and lifetime evaluation results are effected by epistemic uncertainty of measurement, and their correctness can be ensured with decreasing epistemic uncertainty.
Key words: accelerated degradation testing (ADT)     interval analysis     reliability     life evaluation     epistemic uncertainty     sensitivity analysis
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1 退化模型及区间分析方法 1.1 退化模型

1.2 区间回归分析

2 区间型加速退化试验分析 2.1 基于区间回归分析方法的加速退化建模

 图 1 区间型加速退化试验分析流程 Fig. 1 Flowchart of interval accelerated degradation testing analysis

1) 获取各加速应力条件下漂移系数[μijij]和扩散系数σ.

2) 外推正常应力条件下漂移系数[μ00].

2.2 可靠性与寿命指标分析

3 数值案例 3.1 加速退化试验信息

 应力编号 加速载荷/g 样品数 测量时间/h 1 10 4 2,5,10,20,50,100,200,500 2 50 4 2,5,10,20,50,100,200,500 3 100 4 2,5,10,20,50,100,200,500

 图 2 3种加载条件下的加速磨损退化试验数据 Fig. 2 Degradation data for accelerated wear testing under three applied weights

1) 随机从正态分布中抽取Δi满足:Δi~N(m,ζm),m为均值,ζ为收缩系数.简单起见,设ζ=0.02表示多人参与情况,ζ=0表示单人参与情况.

2) 第i个原始测量值±|Δi|作为该测量点的实际记录值,即区间退化数据.

 图 3 3种加载条件下的漂移系数μ Fig. 3 Draft coefficient μ under three applied weights

 图 4 当m=0.5 μm时的区间可靠度曲线 Fig. 4 Interval reliability curves when m=0.5 μm
3.2 测量不确定性对可靠性和寿命的影响分析

1) 多人参与加速试验测试的情况(认知水平存在不同).

2) 单人参与测试的情况(认知水平单一).

 图 5 两种情况下不同m值对应的漂移系数 中心值和半径 Fig. 5 Center and radius of draft coefficients under different m values in two cases

 图 6 两种情况下不同m值对应的扩散系数 Fig. 6 Diffusion coefficients under different m values in two cases

 图 7 两种情况下不同m值对应的可靠度R=0.9的 可靠寿命中心值和半径 Fig. 7 Center and radius of reliable lifetimes when R=0.9 under different m values in two cases

4 结 论

1) 退化数据测量由于人为因素和设备等原因,存在主观认知不确定性和系统随机不确定性,在实际加速试验中应尽量减少人员参与,尽可能地消除测量中存在的认知不确定性.

2) 数值案例表明:与寿命评估有关的模型参数,即漂移系数μ0和扩散系数σ均受测量不确定性的影响,降低不确定性水平能够使得模型参数更为可信.

3) 加速试验的寿命评估结果受测量不确定性的影响,且随着认知不确定性的降低,评估结果的不确定性也随之降低.因此,在试验过程和结果处理中需考虑和消除此影响.

#### 文章信息

LIU Le, LI Xiaoyang, JIANG Tongmin

Evaluation method for accelerated degradation testing with interval analysis

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(12): 2225-2231.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0790