二元相关退化系统可靠性分析及剩余寿命预测

doi:10.3969/j.issn.1001-506X.2020.11.31

Abstract

Abstract:

Degradation dependency and individual difference have a direct influence on the reliability of bivariate degradation system. To solve this problem, based on the degradation process model, the corresponding system reliability and residual life prediction models are developed. Firstly, considering the individual differences of the degradation process and dependency simultaneously, a bivariate dependent degradation model of the system is developed using the Gamma process and the Copula function with random parameters, and to improve the applicability of the model, the assumption of non-conjugate prior distribution is adopted for random parameters. On this basis, the influence of stochastic parameters on system reliability is analyzed, and a residual life prediction method based on the Bayesian theory is proposed. The unknown parameters of the model are estimated by Markov chain Monte Carlo (MCMC) method. The case analysis shows the necessity of considering individual differences in reliability estimation of such systems, and also verifies the accuracy of the residual life prediction method.

Key words: reliability, residual life, bivariate dependent degradation process, Bayesian theory, Copula function

CLC Number:

TB114

Zhiyuan YANG, Jianmin ZHAO, Liying LI, Zhonghua CHENG, Chiming GUO. Reliability analysis and residual life estimation of bivariate dependent degradation system[J]. Systems Engineering and Electronics, 2020, 42(11): 2661-2668.

Figures/Tables 11

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References 23

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Copula函数	AIC值
Gaussian	-1 983.8
Gumbel	-2 042.5
Clayton	-2 057.3
Frank	-2 091.9

变量	分布类型	Weibull分布	正态分布	对数正态分布	Gamma分布
β₁	A_n²	0.924 7	0.684 3	0.484 2	0.537 6
β₁	p值	0.013 6	0.050 5	0.182 5	0.062 6
β₂	A_n²	0.310 6	0.288 0	0.275 4	0.325 7
β₂	p值	0.592 9	0.584 9	0.623 8	0.598 4
θ	A_n²	1.257 3	0.398 6	1.679 0	1.318 5
θ	p值	0.001 5	0.310 3	0.000 5	0.082 8

参数	期望值	标准差	MC误差	2.5%	中位点	97.5%
α₁	10.690	1.235	0.084 45	8.241	10.640	13.250
α₂	9.373	1.089	0.067 54	7.357	9.342	11.570
μ₁	-5.974	0.119	0.007 62	-6.207	-5.974	-5.729
σ₁	0.143	0.043	0.000 59	0.092	0.136	0.194
μ₂	-6.149	0.121	0.006 77	-6.383	-6.150	-5.914
σ₂	0.169	0.032	0.000 72	0.097	0.160	0.234
μ₀	2.355	0.614	0.050 68	1.221	2.419	3.661
σ₀	0.158	0.012	0.002 05	0.096	0.140	0.181
γ₁	1.355	0.023	0.000 82	1.309	1.356	1.403
γ₂	1.254	0.024	0.000 86	1.207	1.254	1.303

参数	α₁	α₂	β₁	β₂	γ₁	γ₂	θ
估计值	7.555	6.947	0.003 3	0.002 8	1.392	1.271	3.481

t_k	X₁(t_k)	X₂(t_k)
1	0.029	0.021
2	0.076	0.058
3	0.146	0.096
4	0.223	0.155
5	0.311	0.207
6	0.374	0.244
7	0.464	0.291
8	0.530	0.327

Reliability analysis and residual life estimation of bivariate dependent degradation system

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Figures/Tables 11

References 23

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t_k	$ {\hat \beta _1^*}$	${\hat \beta _2^*} $	${{{\hat \theta }^*}}$	剩余寿命估计值	剩余寿命真值
4	0.002 99	0.002 63	2.361	5.051	5.65
5	0.003 11	0.002 74	2.356	4.087	4.65
6	0.002 96	0.002 60	2.368	3.236	3.65
7	0.003 04	0.002 58	2.327	2.398	2.65
8	0.002 90	0.002 49	2.318	1.510	1.65

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