基于最大信息熵的长寿命产品可靠度置信区间Bootstrap估计方法

doi:10.12305/j.issn.1001-506X.2023.06.33

摘要/Abstract

摘要：

针对当前无失效数据可靠性评估方法估计精度低, 难以同时得到参数的点估计和置信区间估计且难以避免结果不一致的问题, 考虑无失效数据的情况, 提出了一种基于最大信息熵和模拟退火算法并结合参数Bootstrap法的可靠度点估计和置信区间估计方法。首先考虑威布尔分布的失效概率次序特性, 在Bayes理论下通过失效概率的取值范围和最大化先验分布的信息熵构建超参数优化模型; 然后，采用模拟退火算法求解优化模型避免陷入局部最优解; 再利用加权最小二乘法得到可靠度的点估计; 最后，以参数Bootstrap法实现新样本的重新抽取, 进而得到可靠度的置信区间估计。通过仿真算例与谐波减速器无失效数据实际算例, 验证了所提方法不仅能够提高可靠度点估计和区间估计的精度, 还能够提高评估结果的可信度。

关键词: 可靠性评估, 无失效数据, Bayes理论, 最大信息熵, 参数Bootstrap法

Abstract:

In the reliability assessment method of zero-failure data, the current method has low estimation accuracy and it is difficult to obtain the point estimation and the confidence interval estimation of the parameters at the same time and avoid inconsistent results. In the state of zero-failure data, a point estimation and confidence interval estimation of reliability method is proposed based on maximum information entropy and simulated annealing algorithm which are combined with the parametric Bootstrap method. Firstly, the order of failure probability of Weibull distribution is considered and a hyperparameter optimization model is constructed by using the value range of failure probability and maximizing the information entropy of prior distribution under Bayes theory. Secondly, the simulated annealing algorithm is used to solve the optimization model to avoid falling into the local optimal solution. Thirdly, the weighted least squares method is used to obtain the point estimation of reliability is obtained. Finally, the parametric Bootstrap method is used to re-extract new samples, and then the confidence interval estimation of reliability is obtained. It is verified that the proposed method can not only improve the accuracy of reliability point estimation and interval estimation, but also improve the credibility of evaluation results through simulation examples and actual examples of harmonic reducer with zero-failure data.

Key words: reliability assessment, zero-failure data, Bayes theory, maximum information entropy, parametric Bootstrap method

中图分类号:

O231.2

何燕秋, 王有元, 何俐萍. 基于最大信息熵的长寿命产品可靠度置信区间Bootstrap估计方法[J]. 系统工程与电子技术, 2023, 45(6): 1880-1892.

Yanqiu HE, Youyuan WANG, Liping HE. Bootstrap estimation method of confidence interval for long-life product reliability based on maximum information entropy[J]. Systems Engineering and Electronics, 2023, 45(6): 1880-1892.

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序号i	截尾时间T_i	第i组样品数	未失效数s_i
1	T₁	n₁	s₁
2	T₂	n₂	s₂
⋮	⋮	⋮	⋮
k	T_k	n_k	s_k

序号	失效时间	序号	失效时间	序号	失效时间
1	611.6	11	783.8	21	812.6
2	882.0	12	1249.6	22	1295.1
3	1359.8	13	1498.6	23	1582.1
4	1595.1	14	2088.8	24	2195.7
5	2256.9	15	2320.6	25	2329.4
6	2387.5	16	2594.7	26	2949.2
7	3066.9	17	3073.9	27	3357.2
8	3494.3	18	3510.5	28	3526.7
9	3565.5	19	3826.2	29	4137.2
10	4217.1	20	4817.7	30	5126.1

序号i	截尾时间t_i	样本数量n_i	未失效样本量s_i
1	610	3	30
2	880	3	27
3	1 350	3	24
4	1 590	3	21
5	2 250	3	18
6	2 380	3	15
7	3 060	3	12
8	3 490	3	9
9	3 560	3	6
10	4 210	3	3

序号i	T_i/h	a_i	b_i	p_i
1	610	1	1	0.031 3
2	880	1.474 0	0.857 5	0.050 3
3	1 350	3.179 6	0.873 7	0.113 3
4	1 590	4.462 3	0.875 8	0.169 4
5	2 250	11.394 9	0.957 0	0.375 4
6	2 380	13.307 6	0.953 0	0.454 8
7	3 060	28.295 9	0.900 6	0.686 9
8	3 490	47.784 8	0.921 5	0.828 1
9	3 560	53.210 9	0.946 1	0.884 5
10	4 210	84.964 1	0.714 8	0.958 1

方法	$\hat{m} $	$ \hat{\eta}$	$\mathrm{MRE}_{\hat{m}} $	$ \mathrm{MRE}_{\hat{\eta}}$
文献[21]方法	1.827 5	3 834.8	0.086 3	0.278 3
E-Bayes方法	0.779 3	7 657.0	0.610 4	1.552 3
多层Bayes方法	0.744 7	9 742.0	0.627 7	2.247 3
本文方法	2.384 4	2 843.3	0.192 2	0.052 2