Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (4): 971-983.doi: 10.23919/JSEE.2021.000083
• RELIABILITY • Previous Articles Next Articles
Fuqiang SUN1,2,*(), Hongxuan GUO1,2(), Jingcheng LIU3()
Received:
2020-04-12
Online:
2021-08-18
Published:
2021-09-30
Contact:
Fuqiang SUN
E-mail:sunfuqiang@buaa.edu.cn;guohongxuan@buaa.edu.cn;liujjcc@126.com
About author:
Supported by:
Fuqiang SUN, Hongxuan GUO, Jingcheng LIU. Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths[J]. Journal of Systems Engineering and Electronics, 2021, 32(4): 971-983.
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
Table 2
Some common time-varying copulas"
Family | C(x, y) | Θ(θ) |
Normal copula | | |
Gumbel copula | | 1+θ2 |
Clanton copula | | θ2?0.999 |
Frank copula | | θ |
Table 4
Parameter estimation and goodness-of-fit candidate copulas"
Time-varying copula | Parameter’s estimator | AIC | Rank |
Normal | [1.452 9, 0.056 9, ?2.498 9] | ?908.82 | 2 |
Gumbel | [1.236 4, 0.0170, ?3.013 5] | ?1 002.12 | 1 |
Clayton | [?1.381 0, 0.345 3, ?1.880 3] | ?888.27 | 3 |
Frank | [1.467 3 0.929 4, ?4.995 3] | ?480.04 | 4 |
1 | MCPHERSON J W. Reliability physics and engineering: time-to-failure modeling. 2nd ed. Heidelberg, Switzerland: Springer International Publishing Switzerland, 2013. |
2 |
PAN R, CRISPIN T A hierarchical modeling approach to accelerated degradation testing data analysis: a case study. Quality and Reliability Engineering International, 2011, 27 (2): 229- 237.
doi: 10.1002/qre.1100 |
3 |
YE Z S, XIE M Stochastic modelling and analysis of degradation for highly reliable products. Applied Stochastic Models in Business and Industry, 2015, 31 (1): 16- 32.
doi: 10.1002/asmb.2063 |
4 | LEFEVRE H. The fiber-optic gyroscope. 2nd ed. Boston, USA: Artech House, 2014. |
5 | BURET T, RAMECOURT D, HONTHAAS J, et al. Fibre optic gyroscopes for space application. Proc. of the Optical Fiber Sensors Conference, 2006. DOI: 10.1364/OFS.2006.MC4. |
6 |
ZHANG Z X, SI X S, HU C H, et al Degradation data analysis and remaining useful life estimation: a review on Wiener-process-based methods. European Journal of Operational Research, 2018, 271 (3): 775- 796.
doi: 10.1016/j.ejor.2018.02.033 |
7 |
LIU L, LI X Y, JIANG T M, et al Utilizing accelerated degradation and field data for life prediction of highly reliable products. Quality and Reliability Engineering International, 2016, 32 (7): 2281- 2297.
doi: 10.1002/qre.1935 |
8 |
WHITMORE G A, SCHENKELBERG F Modelling accelerated degradation data using Wiener diffusion with a time scale transformation. Lifetime Data Analysis, 1997, 3 (1): 27- 45.
doi: 10.1023/A:1009664101413 |
9 | YE Z S, CHEN N, SHEN Y A new class of Wiener process models for degradation analysis. Reliability Engineering & System Safety, 2015, 139, 58- 67. |
10 |
GEBRAEEL N Z, LAWLEY M A, LI R, et al Residual-life distributions from component degradation signals: a Bayesian approach. IIE Transactions, 2005, 37 (6): 543- 557.
doi: 10.1080/07408170590929018 |
11 |
PARK C, PADGETT W J Stochastic degradation models with several accelerating variables. IEEE Trans. on Reliability, 2006, 55 (2): 379- 390.
doi: 10.1109/TR.2006.874937 |
12 |
ELWANY A, GEBRAEEL N Real-time estimation of mean remaining life using sensor-based degradation models. Journal of Manufacturing Science and Engineering, 2009, 131 (5): 051005.
doi: 10.1115/1.3159045 |
13 |
WANG X, XU D H An inverse gaussian process model for degradation data. Technometrics, 2010, 52 (2): 188- 197.
doi: 10.1198/TECH.2009.08197 |
14 | RODRIGUEZ-PICON L A, RODRIGUEZ-PICON A P, ALVARADO-INIESTA A Degradation modeling of 2 fatigue-crack growth characteristics based on inverse Gaussian processes: a case study. Applied Stochastic Models in Business and Industry, 2018, 35 (3): 504- 521. |
15 |
YE Z S, CHEN L P, TANG L C, et al Accelerated degradation test planning using the inverse gaussian process. IEEE Trans. on Reliability, 2014, 63 (1): 750- 763.
doi: 10.1109/TR.2014.2315773 |
16 |
PENG W, LI Y F, YANG Y J, et al Bayesian degradation analysis with inverse gaussian process models under time-varying degradation rates. IEEE Trans. on Reliability, 2017, 66 (1): 84- 96.
doi: 10.1109/TR.2016.2635149 |
17 | ZHOU W, XIANG W, HONG H P Sensitivity of system reliability of corroding pipelines to modeling of stochastic growth of corrosion defects. Reliability Engineering & System Safety, 2017, 167, 428- 438. |
18 | LI X, HU Y, ZHOU J, et al Bayesian step stress accelerated degradation testing design: a multi-objective Pareto-optimal approach. Reliability Engineering & System Safety, 2018, 171, 9- 17. |
19 | LIU D, WANG S P, ZHANG C, et al Bayesian model averaging based reliability analysis method for monotonic degradation dataset based on inverse Gaussian process and Gamma process. Reliability Engineering & System Safety, 2018, 180, 25- 38. |
20 |
CHAO D H, MA J, CHEN S Y Assessment of storage reliability for FOGs by multivariate degradation data. Optics and Precision Engineering, 2011, 19 (1): 35- 40.
doi: 10.3788/OPE.20111901.0035 |
21 | MAO D H, DONG J L, WANG L X, et al Comprehensive assessment of fog storage life based on multivariate degradation data. Computer Measurement & Control, 2014, 22 (2): 446- 449. |
22 |
KAT H M The dangers of using correlation to measure dependence. Journal of Alternative Investments, 2003, 6 (2): 54- 58.
doi: 10.3905/jai.2003.319091 |
23 |
SARI J K, NEWBY M J, BROMBACHER A C, et al Bivariate constant stress degradation model: LED lighting system reliability estimation with two-stage modelling. Quality and Reliability Engineering International, 2009, 25 (8): 1067- 1084.
doi: 10.1002/qre.1022 |
24 | PAN Z Q, BALAKRISHNAN N, SUN Q Bivariate constant-stress accelerated degradation model and inference. Communications in Statistics-Simulation and Computation, 2011, 40 (2): 259- 269. |
25 |
PENG W W, LI Y F, YANG Y J, et al Bivariate analysis of incomplete degradation observations based on inverse gaussian processes and copulas. IEEE Trans. on Reliability, 2016, 65 (2): 624- 639.
doi: 10.1109/TR.2015.2513038 |
26 | FANG G Q, PAN R, HONG Y L Copula-based reliability analysis of degrading systems with dependent failures. Reliability Engineering & System Safety, 2020, 193, 106618. |
27 |
SUN F Q, LIU L, LI X Y, et al Stochastic modeling and analysis of multiple nonlinear accelerated degradation processes through information fusion. Sensors, 2016, 16 (8): 1242.
doi: 10.3390/s16081242 |
28 |
PATTON A J Modelling asymmetric exchange rate dependence. International Economic Review, 2006, 47 (2): 527- 556.
doi: 10.1111/j.1468-2354.2006.00387.x |
29 |
WANG Y P, PHAM H Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas. IEEE Trans. on Reliability, 2012, 61 (1): 13- 22.
doi: 10.1109/TR.2011.2170253 |
30 | SUN F Q, WANG N, LI X Y, et al A time-varying copula-based prognostics method for bivariate accelerated degradation testing. Journal of Intelligent & Fuzzy Systems, 2018, 34 (6): 3707- 3718. |
31 | PAN J, BAI G H, CHEN W H. Lifetime estimation of nitrile butadiene rubber O-rings under storage conditions using time-varying copula. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2018, 232(6): 635−646. |
32 | ESCOBAR L A, MEEKER W Q A review of accelerated test models. Statistical Science, 2006, 21 (4): 552- 577. |
33 |
LIM H, YUM B J Optimal design of accelerated degradation tests based on Wiener process models. Journal of Applied Statistics, 2011, 38 (2): 309- 325.
doi: 10.1080/02664760903406488 |
34 |
FOLKS J L, CHHIKARA R S The inverse Gaussian distribution and its statistical application—a review. Journal of the Royal Statistical Society: Series B (Methodological), 1978, 40 (3): 263- 275.
doi: 10.1111/j.2517-6161.1978.tb01039.x |
35 |
BHATTACHARYYA G K, FRIES A Fatigue failure models—Birnbaum-saunders vs. inverse Gaussian. IEEE Trans. on Reliability, 1982, R-31 (5): 439- 441.
doi: 10.1109/TR.1982.5221421 |
36 |
LI X Y, HU Y Q, SUN F Q, et al A Bayesian optimal design for sequential accelerated degradation testing. Entropy, 2017, 19 (7): 325.
doi: 10.3390/e19070325 |
37 |
PENG W W, LIU Y, LI Y F, et al A Bayesian optimal design for degradation tests based on the inverse Gaussian process. Journal of Mechanical Science and Technology, 2014, 28 (10): 3937- 3946.
doi: 10.1007/s12206-014-0904-x |
38 | NELSEN R B. An introduction to copulas. 2nd ed. New York, USA: Springer Science & Business Media, 2007. |
39 | KIM D, KIM J M, LIAO S M, et al Mixture of D-vine copulas for modeling dependence. Computational Statistics & Data Analysis, 2013, 64, 1- 19. |
40 |
NELSEN R B, QUESADA-MOLINA J J, RODRIIGUEZ-LALLENA J A, et al Bounds on bivariate distribution functions with given margins and measures of association. Communications in Statistics-Theory and Methods, 2001, 30 (6): 1055- 1062.
doi: 10.1081/STA-100104355 |
41 |
JOE H Asymptotic efficiency of the two-stage estimation method for copula-based models. Journal of Multivariate Analysis, 2005, 94 (2): 401- 419.
doi: 10.1016/j.jmva.2004.06.003 |
[1] | Liang WANG, Jin'ge MA, Yimin SHI. Dependence Rayleigh competing risks model with generalized censored data [J]. Journal of Systems Engineering and Electronics, 2020, 31(4): 852-858. |
[2] | Zezhou WANG, Yunxiang CHEN, Zhongyi CAI, Yangjun GAO, Lili WANG. Methods for predicting the remaining useful life of equipment in consideration of the random failure threshold [J]. Journal of Systems Engineering and Electronics, 2020, 31(2): 415-431. |
[3] | Zhongyi CAI, Zezhou WANG, Yunxiang CHEN, Jiansheng GUO, Huachun XIANG. Remaining useful lifetime prediction for equipment based on nonlinear implicit degradation modeling [J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 194-205. |
[4] | Tingting HUANG, Bo PENG, Yuepu ZHAO, Zixuan YU. Reliability assessment considering stress drift and shock damage caused by stress transition shocks in a dynamic environment [J]. Journal of Systems Engineering and Electronics, 2019, 30(5): 1025-1034. |
[5] | Liang WANG, Huanyu LI, Jin'ge MA. Inference for dependence competing risks from bivariate exponential model under generalized progressive hybrid censoring with partially observed failure causes [J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 201-208. |
[6] | Zhongyi CAI, Yunxiang CHEN, Jiansheng GUO, Qiang ZHANG, Huachun XIANG. Remaining lifetime prediction for nonlinear degradation device with random effect [J]. Journal of Systems Engineering and Electronics, 2018, 29(5): 1101-1110. |
[7] | Guijie LI, Chaoyang XIE, Fayuan WEI, Fengjun WANG. Moment-independence global sensitivity analysis for the system with fuzzy failure state and its Kriging method [J]. Journal of Systems Engineering and Electronics, 2018, 29(3): 658-666. |
[8] | Jing Cai, Xin Li, and Xi Chen. Joint optimization of maintenance inspection and spare provisioning for aircraft deteriorating parts#br# [J]. Journal of Systems Engineering and Electronics, 2017, 28(6): 1133-1140. |
[9] | Wenlong Lu, Junwei Xie, Heming Wang, and Chuan Sheng. Cognate pulse sorting method based on beam missions characteristics [J]. Journal of Systems Engineering and Electronics, 2016, 27(6): 1183-1190. |
[10] | Junbao Geng, Michael Azarian, and Michael Pecht. Opportunistic maintenance for multi-component systems considering structural dependence and economic dependence [J]. Systems Engineering and Electronics, 2015, 26(3): 493-501. |
[11] | Ying Zhang, Aiguo Wu, and Guangren Duan. Extended parameter-dependent H∞ filtering for uncertain continuous-time state-delayed systems [J]. Journal of Systems Engineering and Electronics, 2014, 25(1): 122-128. |
[12] | Zhijun Cheng, Zheng Yang, and Bo Guo. Optimal opportunistic maintenance model of multi-unit systems [J]. Journal of Systems Engineering and Electronics, 2013, 24(5): 811-817. |
[13] | Mingmin Zhu, Sanyang Liu, Youlong Yang, and Kui Liu. Using junction trees for structural learning of Bayesian networks [J]. Journal of Systems Engineering and Electronics, 2012, 23(2): 286-292. |
[14] | Chunhong Hua, Zhang Ren, and Minhu Zhang. Filtering of long-term dependent fractal noise in fiber optic gyroscope [J]. Journal of Systems Engineering and Electronics, 2010, 21(6): 1041-1045. |
[15] | Zhou Houyong, Huang Shunliang & Shi Kaiquan. Hiding dependence-discovery of F-hiding laws and system laws [J]. Journal of Systems Engineering and Electronics, 2009, 20(3): 543-550. |
Viewed | ||||||
Full text |
|
|||||
Abstract |
|
|||||