双应力恒加试验Weibull分布型产品置信可靠性评估模型

doi:10.3969/j.issn.1001-506X.2020.09.33

系统工程与电子技术 ›› 2020, Vol. 42 ›› Issue (9): 2140-2148.doi: 10.3969/j.issn.1001-506X.2020.09.33

• 可靠性 • 上一篇

双应力恒加试验Weibull分布型产品置信可靠性评估模型

梁红琴¹(), 冯雪峰^2,*(), 唐家银²(), 刘奇锋¹()

1. 西南交通大学机械工程学院, 四川成都 610031
2. 西南交通大学数学学院, 四川成都 611756

收稿日期:2020-01-19 出版日期:2020-08-26 发布日期:2020-08-26
通讯作者: 冯雪峰 E-mail:sugargl@163.com;tongjikaoyan666@163.com;tangjiayin@swjtu.edu.cn;1351524844@qq.com
作者简介:梁红琴(1976-),女,讲师,博士,主要研究方向为可靠性统计、应用概率统计。E-mail:sugargl@163.com|唐家银(1976-),男,副教授,博士研究生导师，博士,主要研究方向为系统可靠性与工程、应用概率统计。E-mail:tangjiayin@swjtu.edu.cn|刘奇锋(1997-),男,硕士研究生,主要研究方向为先进设计制造及自动化。E-mail:1351524844@qq.com
基金资助:
中国铁路总公司科技研究开发计划项目(2017J003-H);中央高校基本科研业务费(2682017ZDPY13);教育部人文社会科学研究规化基金(20XJAZH009)

Confidence reliability evaluation model of dual constant-stress accelerated life test for Weibull distribution product

Hongqin LIANG¹(), Xuefeng FENG^2,*(), Jiayin TANG²(), Qifeng LIU¹()

1. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
2. School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China

Received:2020-01-19 Online:2020-08-26 Published:2020-08-26
Contact: Xuefeng FENG E-mail:sugargl@163.com;tongjikaoyan666@163.com;tangjiayin@swjtu.edu.cn;1351524844@qq.com

摘要/Abstract

摘要：

为了有效快速评估高可靠性长寿命产品在正常应力条件下的可靠性，提出了一种双应力恒加试验Weibull分布型产品置信可靠性评估模型。首先，采用加速寿命试验(accelerated life test，ALT)技术，建立广义Eyring-Weibull可靠性模型，假定试验各应力水平组合下Weibull分布的形状参数相同，且尺度参数与各应力水平组合间呈对数线性关系。其次，给出了Weibull分布定时截尾双应力恒加试验的极大似然估计(maximum likelihood estimation，MLE)方法、与似然函数相关的Fisher信息矩阵以及模型参数的渐近协方差矩阵，构造了模型参数和一些可靠性指标的渐近置信区间。最后，通过仿真算例证明了所提方法的可行性。

关键词: 双应力恒加试验, 加速方程, 可靠性, Weibull分布, Fisher信息矩阵

Abstract:

In order to evaluate the reliability of high reliability and long life products under normal stress conditions effectively and quickly, a confidence reliability evaluation model of dual constant-stress accelerated life test (DCSALT) for Weibull distribution product is proposed. Firstly, the generalized Eyring-Weibull reliability model is established by using the accelerated life test (ALT) technology. In this model, it is assumed that the Weibull distribution has constant shape parameter and a log-linear relation between its scale parameter and each stress level combination. Secondly, a maximum likelihood estimation (MLE) method for DCSALT with fixed time censoring of the Weibull distribution, the Fisher information matrix realted to the likelihood function, and the asymptotic covariance matrix of the model parameters is presented. Furthermore, the asymptotic confidence intervals of the model parameters and some reliability indexs are constructed. Finally, the simulation example demonstrates the feasibility of the proposed method.

Key words: dual constant-stress accelerated life test (DCSALT), acceleration equation, reliability, Weibull distribution, Fisher information matrix

中图分类号:

TB114.3

梁红琴, 冯雪峰, 唐家银, 刘奇锋. 双应力恒加试验Weibull分布型产品置信可靠性评估模型[J]. 系统工程与电子技术, 2020, 42(9): 2140-2148.

Hongqin LIANG, Xuefeng FENG, Jiayin TANG, Qifeng LIU. Confidence reliability evaluation model of dual constant-stress accelerated life test for Weibull distribution product[J]. Systems Engineering and Electronics, 2020, 42(9): 2140-2148.

图/表 6

表1

表2

图1

表3

表4

图2

参考文献 25

1	MEEKER W Q , ESCOBAR L A . Statistical methods for reliability data[M]. New York: Wiley, 1999.
2	NELSON W B . Accelerated testing: statistical models, test plans, and data analysis[M]. New York: Wiley, 2004.
3	NELSON W B . A bibliography of accelerated test plans[J]. IEEE Trans.on Reliability,, 2005, 54 (2): 194- 197. doi: 10.1109/TR.2005.847247
4	NELSON W B . A bibliography of accelerated test plans part Ⅱ-refe-rences[J]. IEEE Trans.on Reliability, 2005, 54 (3): 370- 373. doi: 10.1109/TR.2005.853289
5	WANG W , KECECIOGLU D B . Fitting the Weibull log-linear model to accelerated life-test data[J]. IEEE Trans.on Reliability, 2000, 49 (2): 217- 223. doi: 10.1109/24.877341
6	WATKINS A J , JOHN A M . On constant stress accelerated life tests terminated by type Ⅱ censoring at one of the stress levels[J]. Journal of Statistical Planning and Inference, 2008, 138 (3): 768- 786. doi: 10.1016/j.jspi.2007.02.013
7	ZHENG G Y , SHI Y M . Statistical analysis in constant-stress accelerated life tests for generalized exponential distribution based on adaptive type-Ⅱ progressive hybrid censored data[J]. Chinese Journal of Applied Probability and Statistics, 2013, 29 (4): 363- 380.
8	XU A C , TANG Y C . Statistical analysis of competing failure modes in accelerated life testing based on assumed copulas[J]. Chinese Journal of Applied Probability and Statistics, 2012, 28 (1): 51- 62.
9	CORDEIRO J B , PHAM H . Optimal design of life testing cost model for type-Ⅱ censoring Weibull distribution lifetime units withrespect to unknown parameters[J]. International Journal of System Assurance Engineering and Management, 2017, 8 (1): 28- 32. doi: 10.1007/s13198-016-0511-6
10	WU S J , HUANG S R . Planning two or more level constant-stress accelerated life tests with competing risks[J]. Reliability Engineering & System Safety, 2017, 158, 1- 8.
11	WANG L , SHI Y M . Estimation for constant-stress accelerated life test from generalized half-normal distribution[J]. Journal of Systems Engineering and Electronics, 2017, 28 (4): 810- 816. doi: 10.21629/JSEE.2017.04.21
12	WANG L . Estimation of constant-stress accelerated life test for Weibull distribution with nonconstant shape parameter[J]. Journal of Computational and Applied Mathematics, 2018, 343, 539- 555. doi: 10.1016/j.cam.2018.05.012
13	NASSAR M , DEY S . Different estimation methods for exponentiated Rayleigh distribution under constant-stress accelerated life test[J]. Quality and Reliability Engineering International, 2018, 34 (8): 1633- 1645. doi: 10.1002/qre.2349
14	ISMAIL A A . Statistical analysis of type-Ⅰ progressively hybrid censored data under constant-stress life testing model[J]. Physica A: Statistical Mechanics and its Applications, 2019, 520, 138- 150. doi: 10.1016/j.physa.2019.01.004
15	ZHANG C F , SHI Y M , WU M . Statistical inference for competing risks model in step-stress partially accelerated life tests with progressively type-Ⅰ hybrid censored Weibull life data[J]. Journal of Computational and Applied Mathematics, 2016, 297, 65- 74. doi: 10.1016/j.cam.2015.11.002
16	LIU B , SHI Y M , ZHANG F , et al. Reliability nonparametric Bayesian estimation for the masked data of parallel systems in step-stress accelerated life tests[J]. Journal of Computational and Applied Mathematics, 2017, 311, 375- 386. doi: 10.1016/j.cam.2016.07.029
17	GUAN Q , TANG Y C . Bayesian planning of optimal step-stress accelerated life test for log-location-scale distributions[J]. Acta Mathematicae Applicatae Sinica, English Series, 2018, 34 (1): 51- 64. doi: 10.1007/s10255-018-0725-2
18	LING M H . Optimal design of simple step-stress accelerated life tests for one-shot devices under exponential distributions[J]. Probability in the Engineering and Informational Sciences, 2019, 33 (1): 121- 135. doi: 10.1017/S0269964818000049
19	陈文华, 钱萍, 马子魁, 等. 基于定时测试的综合应力加速寿命试验方案优化设计[J]. 仪器仪表学报, 2009, 30 (12): 2544- 2550. doi: 10.3321/j.issn:0254-3087.2009.12.014
	CHEN W H , QIAN P , MA Z K , et al. Optimum design of multiple stress accelerated life test plan under periodic inspection[J]. Chinese Journal of Scientific Instrument, 2009, 30 (12): 2544- 2550. doi: 10.3321/j.issn:0254-3087.2009.12.014
20	CHEN W H , GAO L , LIU J , et al. Optimal design of multiple stress constant accelerated life test plan on non-rectangle test region[J]. Chinese Journal of Mechanical Engineering, 2012, 25 (6): 1231- 1237. doi: 10.3901/CJME.2012.06.1231
21	BALAKRISHNAN N , LING M H . Best constant-stress acce-lerated life-test plans with multiple stress factors for one-shot device testing under a Weibull distribution[J]. IEEE Trans.on Reliability, 2014, 63 (4): 944- 952. doi: 10.1109/TR.2014.2336391
22	GAO L , CHEN W H , QIAN P , et al. Optimal design of multiple stresses accelerated life test plan based on transforming the multiple stresses to single stress[J]. Chinese Journal of Mechanical Engineering, 2014, 27 (6): 1125- 1132. doi: 10.3901/CJME.2014.0826.141
23	LIN K S , CHEN Y X , XU D . Reliability assessment model considering heterogeneous population in a multiple stresses accelerated test[J]. Reliability Engineering & System Safety, 2017, 165 (C): 134- 143.
24	茆诗松, 王玲玲. 加速寿命试验[M]. 北京: 科学出版社, 1997.
	MAO S S , WANG L L . Accelerated life testing[M]. Beijing: Science Press, 1997.
25	XIE X D , ZHOU K , CHEN B Y , et al. Degradation of oxytetracycline using microporous and mesoporousphotocatalyst composites: uniform design to explore factors[J]. Journal of Environmental Chemical Engineering, 2016, 4 (4): 4453- 4465. doi: 10.1016/j.jece.2016.10.012

水平组合	温度S¹/℃	振动S²/(g²/Hz)	转化温度	转化振动
1	116.0	0.215	2.569	-1.535
2	129.1	1.00	2.486	0.000
3	143.0	0.100	2.403	-2.303
4	158.0	0.464	2.319	-0.768

方案	样本量与截尾时间		水平组合	失效时间t_ij/month
方案	(n₁, n₂, n₃, n₄)	(τ₁, τ₂, τ₃, τ₄)	水平组合	失效时间t_ij/month
1	(12, 12, 8, 8)	(50, 50, 50, 50)	1	14.2, 22.2, 25.7, 27.6, 27.9, 29.6, 31.1, 33.9, 33.9, 35.0, 35.4, 41.6
			2	9.1, 14.7, 19.2, 20.2, 20.8, 21.3, 22.3, 22.9, 23.0, 24.6, 28.5, 29.9
			3	11.3, 12.8, 12.9, 16.7, 18.5, 19.8, 20.2, 24.9
			4	6.3, 6.7, 10.2, 11.2, 11.9, 12.1, 13.2, 15.1
2	(15, 10, 8, 8)	(40, 30, 25, 20)	1	14.5, 21.2, 23.5, 24.2, 25.3, 27.5, 29.9, 30.4, 32.4, 33.1, 35.1, 35.6, 37.2, 38.0, 41.9
			2	9.8, 13.9, 14.2, 14.7, 18.1, 18.8, 19.9, 20.3, 22.9, 23.2
			3	13.4, 13.6, 16.2, 20.2, 21.7, 22.9, 23.4, 26.6
			4	8.3, 9.5, 11.2, 11.6, 12.4, 12.8, 14.1, 18.8
3	(15, 12, 12, 8)	(50, 30, 30, 20)	1	18.0, 18.4, 20.6, 24.4, 24.6, 27.2, 27.4, 28.3, 30.0, 31.1, 32.6, 36.5, 38.4, 38.7, 42.4
			2	8.2, 8.5, 10.9, 11.9, 13.6, 14.4, 16.6, 16.8, 18.8, 19.1, 20.2, 23.7
			3	13.5, 14.2, 14.3, 16.6, 19.3, 22.4, 23.6, 24.2, 25.9, 26.4, 26.9, 27.3
			4	6.2, 11.2, 11.7, 12.0, 12.6, 12.9, 13.9, 16.4
4	(20, 15, 15, 10)	(50, 40, 30, 20)	1	14.2, 18.0, 20.2, 22.2, 25.2, 25.2, 26.0, 26.2, 27.1, 28.4, 31.5, 31.6, 31.9, 32.1, 33.3, 36.1, 37.2, 37.6, 38.6
			2	14.7, 15.0, 15.3, 15.9, 15.9, 15.9, 18.8, 19.3, 20.6, 23.9, 24.2, 24.7, 26.8, 28.2, 28.5
			3	8.6, 11.4, 13.0, 13.3, 13.6, 13.9, 16.0, 16.2, 17.3, 18.0, 19.7, 22.6, 23.6, 24.5, 26.1
			4	7.3, 9.1, 9.3, 10.3, 11.5, 11.7, 11.7, 12.2, 14.9, 14.9

方案	样本量与截尾时间		θ_i	$ \hat \theta $_i	var($ \hat \theta $_i)	置信度为90%的ACI	ACI长度
方案	(n₁, n₂, n₃, n₄)	(τ₁, τ₂, τ₃, τ₄)	θ_i	$ \hat \theta $_i	var($ \hat \theta $_i)	置信度为90%的ACI	ACI长度
1	(12, 12, 8, 8)	(50, 50, 50, 50)	β₀	-6.25	8.29×10^-1	[-7.74, -4.75]	2.99
			β₁	3.77	1.36×10^-1	[3.16, 4.38]	1.22
			β₂	-0.04	1.58×10^-3	[-0.11, 0.02]	0.09
			σ	0.21	7.0×10^-4	[0.17, 0.26]	0.09
2	(15, 10, 8, 8)	(40, 30, 25, 20)	β₀	-4.67	8.75×10^-1	[-6.21, -3.13]	3.08
			β₁	3.07	1.44×10^-1	[2.44, 3.70]	1.26
			β₂	-0.19	1.80×10^-3	[-0.26, -0.11]	0.15
			σ	0.22	8.63×10^-4	[0.17, 0.27]	0.10
3	(15, 12, 12, 8)	(50, 30, 30, 20)	β₀	-4.44	7.93×10^-1	[-5.91, -2.98]	2.93
			β₁	2.94	1.29×10^-1	2.35, 3.53]	1.18
			β₂	-0.23	1.45×10^-3	-0.29, -0.16]	0.13
			σ	0.22	6.63×10^-4	0.18, 0.27]	0.09
4	(20, 15, 15, 10)	(50, 40, 30, 20)	β₀	-5.49	6.06×10^-1	[-6.77, -4.21]	2.56
			β₁	3.45	9.92×10^-2	[2.93, 3.97]	1.04
			β₂	-0.06	1.12×10^-3	[-0.12, -0.01]	0.11
			σ	0.22	4.99×10^-4	[0.18, 0.26]	0.08

方案	样本量与截尾时间		参数	MLE	置信度为90%的ACI	ACI长度
方案	(n₁, n₂, n₃, n₄) (τ₁, τ₂, τ₃, τ₄)		参数	MLE	置信度为90%的ACI	ACI长度
1	(12, 12, 8, 8)	(50, 50, 50, 50)	m	4.66	[3.87, 5.85]	1.98
			η₀₀	80.81	[63.77, 102.41]	38.64
			t_{0.9, 00}	96.65	[76.27, 122.48]	46.21
2	(15, 10, 8, 8)	(40, 30, 25, 20)	m	4.50	[3.69, 5.75]	2.06
			η₀₀	83.39	[65.84, 105.61]	39.77
			t_{0.9, 00}	100.37	[78.95, 127.61]	48.66
3	(15, 12, 12, 8)	(50, 30, 30, 20)	m	4.48	[3.76, 5.53]	1.77
			η₀₀	82.03	[65.34, 103.05]	37.71
			t_{0.9, 00}	98.82	[78.65, 124.15]	45.5
4	(20, 15, 15, 10)	(50, 40, 30, 20)	m	4.51	[3.87, 5.41]	1.54
			η₀₀	74.40	[61.01, 90.73]	29.72
			t_{0.9, 00}	89.51	[73.41, 109.15]	35.74

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双应力恒加试验Weibull分布型产品置信可靠性评估模型

Confidence reliability evaluation model of dual constant-stress accelerated life test for Weibull distribution product

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