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

Abstract

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

CLC Number:

TB114.3

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.

Figures/Tables 6

Table 1

Table 2

Fig.1

Table 3

Table 4

Fig.2

References 25

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

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