Reliability Analysis based on Inverse Gauss Degradation Process and Evidence Theory

doi:10.23940/ijpe.19.02.p1.353361

Abstract

Abstract:

The degradation analysis of products has been demonstrated as a significant toolkit for reliability analysis.Datafrom the same batch of products in different working environments cannot be directly used to analyze product reliability. In this paper, motivated by this circumstance, we first assume that degradation data sets from different working environments are subject to different inverse Gaussian process models, and maximum likelihood estimation is used to obtain multiple model parameters. Secondly, we construct evidence by quantifying different information ofproducts, apply the evidence theory to fuse model parameters, and then analyze the reliability of products from the same batch. Finally, we use performance degradation data of the laser to illustrate the method.

Key words: degenerate modeling, inverse Gaussian process, evidence theory, data fusion, reliability analysis

Yuwei Wang and Hailin Feng . Reliability Analysis based on Inverse Gauss Degradation Process and Evidence Theory [J]. Int J Performability Eng, 2019, 15(2): 353-361.

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References 17

1	X. R.Cheng and J. Y. Li, “Remaining Lifetime Prediction of Blowout Preventer Valve based on Fusion of Lifetime Data and Degradation Data, ”in Proceedings of Journal of Shandong University of Science andTechnology, Vol. 36, No. 5, pp.23-28, 2017
2	L. S.Khanh and F. A. B. Mitra, “Remaining Useful Lifetime Estimation and Noisy Gamma Deterioration Process, ”in Proceedings of Reliability Engineering and System Safety, Vol. 149, pp.76-87, 2016 doi: 10.1016/j.ress.2015.12.016
3	Z. S.Ye and N. Chen, “The Inverse Gaussian Process as a Degradation Model, ” Proceedings of Technometrics, Vol. 56, No. 3, pp.302-311, 2014 doi: 10.1080/00401706.2013.830074
4	F. Duanand G.Wang, “Reliability Modeling of Two-Phase Inverse Gaussian Degradation Process, ”in Proceedings of the Second International Conference on Reliability Systems Engineering, IEEE, pp.1-6, 2017 doi: 10.1109/ICRSE.2017.8030736
5	H. Guo, T. Zhang, L. Y. Ping, E. S. Pan, “Research on Competing Failure Modeling based on the Inverse Gaussian Process, ”in Proceedings of Industrial Engineering and Management, Vol. 22, No. 1, pp. 89-94, 2017
6	J. B. Liu, D. H. Pan, J.Cao, “Remaining Useful Life Estimation using an Inverse Gaussian Degradation Model, ”Neurocomputing, Vol. 185, pp.64-72, 2016 doi: 10.1016/j.neucom.2015.12.041
7	Y. Zhou, L. V. Wei-Min, and Y. Sun, “Fusion Prediction Method for the Life of MEMS Accelerometer based on Inverse Gaussian Process, ” Journal of Chinese Inertial Technology, 2017
8	W. Peng, Y. J. Yang, J. Mi and H. Z. Huang, “Bayesian Degradation Analysis with Inverse Gaussian Process Models under Time Varying Degradation Rates, ”IEEE Transactions on Reliability, No. 99, pp.1-13, 2017 doi: 10.1109/TR.2016.2635149
9	X. Zhang, Y. Li, X. Wang, “Maintenance Strategy of Corroded Oil-Gas Pipeline based on Inverse Gaussian Process, ”in Proceedings of Acta Petrolei Sinica, Vol. 38, No. 3, pp.356-362, 2017
10	W. Peng, Y. F. Li, Y. J. Yang, S. P. Zhu, H. G. Huang, “Bivariate Analysis of Incomplete Degradation Observations based on Inverse Gaussian Processes and Copulas, ”IEEE Transactions on Reliability, Vol.65, No. 2, pp. 624-639, 2016 doi: 10.1109/TR.2015.2513038
11	F. Ye, J. Chen, and Y.Li, “Improvement of D-S Evidence Theory for Multi-Sensor Conflicting Information, ” Symmetry, 2017
12	J. B.Yang and M. G. Singh, “An Evidential Reasoning Approach for Multiple Attribute Decision Making with Uncertainty, ” IEEE Transactions on Systems Man and Cybernetics, Vol. 22, No. 1, pp. 1-18, 1994 doi: 10.1109/21.259681
13	Z. Zhang, C. Jiang, X. X. Ruan, and F. J. Guan, “A Novel Evidence Theory Model Dealing with Correlated Variables and the Corresponding Structural Reliability Analysis Method, ”Structural & Multidisciplinary Optimization, No. 1- 3, pp.1-16, 2017 doi: 10.1007/s00158-017-1843-9
14	L. F. Ming, C. H. Hu, Z. J. Zhou, P. Wang, “A degradation Modeling Method based on Inverse Gaussian Process and Evidential Reasoning, ”in Proceedings of Electronics Optics & Control, Vol. 22, No. 1, pp. 92-96, 2015 doi: 10.3969/j.issn.1671-637X.2015.01.021
15	L. Liang, Y. Shen, Q . Cai, and Y. Gu, “A Reliability Data Fusion Method based on Improved D-S Evidence Theory, ”in Proceedings of International Conference on Reliability, Maintainability and Safety, IEEE, pp.1-6, 2017 doi: 10.1109/ICRMS.2016.8050147
16	H. Wang, G. J. Wang, F. J. Duan, “Planning of Step-Stress Accelerated Degradation Test based on the Inverse Gaussian Process, ”Reliability Engineering & System Safety, Vol. 154, pp.97-105, 2016
17	D. Dubois and H. Prade, “A Survey of Belief Revision and Updating Rules in Various Uncertainty Models, ” Hoboken, John Wiley & Sons, 1994 doi: 10.1002/int.4550090105

	Time (h)
	500	1000	1500	2000	2500	3000
Sample1	1.07	1.77	2.40	3.02	3.75	4.76
Sample2	0.61	1.77	2.58	3.88	4.63	5.62
Sample3	0.93	1.96	3.29	4.11	4.91	5.84
Sample4	1	1.96	2.84	4.01

Parameters	Sample1	Sample2	Sample3	Sample4
$\Lambda (t)\text{=}\mu t$	0.790$t$	0.930$t$	0.973$t$	1.002$t$
$\lambda $	0.051	0.050	0.028	0.011

	Evidence
	Sample size	Mean deviation	Expert experience	After fusion
Sample1parameter	0.265	0.04	0.2	0.02
Sample2 parameter	0.265	0.8	0.4	0.87
Sampe3Parameter	0.265	0.11	0.3	0.09
Sample4 parameter	0.205	0.05	0.1	0.02

	Evidence
	Sample size	Mean deviation	Expert experience	After fusion
Sample1 parameter	0.265	0.20	0.2	0.15
Sample2 parameter	0.265	0.21	0.4	0.31
Sample3 parameter	0.265	0.46	0.3	0.50
Sample4 parameter	0.205	0.13	0.1	0.04

	Time (h)
	500	1000	1500	2000	2500	3000
New data	0.74	1.85	3	3.8	4.3	5.6
Infusion evidence	0.8	1.82	2.68	3.4	4.0	4.8
Fusion evidence	0.7	1.81	2.8	3.7	4.4	5.7