Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas

IEEE Transactions on Reliability

Volumn 61, Issue 1, 2012, Pages 13-22

  Wang, Yaping ^a   Pham, Hoang ^a  

^a DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING   (United States)

Author keywords

Copula method; dependent competing risks; fatal shocks; multiple degradation

Indexed keywords

COMPARISON RESULT; COMPETING RISKS; COPULA METHOD; COVARIATES; DEGRADATION PROCESS; DEGRADATION RATE; DEPENDENT RELATIONSHIP; FATAL SHOCKS; JOINT DISTRIBUTIONS; KENDALL'S TAU; NUMERICAL EXAMPLE; RANDOM SHOCKS; SPEARMAN'S RHO; SYSTEM RELIABILITY; TIME VARYING;

RISK ASSESSMENT;

DEGRADATION;

EID: 84858152533     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2011.2170253     Document Type: Article

References (25)

1. W. Li and H. Pham, "An inspection-maintenance model for systems with multiple competing processes," IEEE Trans. Rel., vol. 54, no. 2, pp. 318-327, 2005.
2. H. Pham, A. Suprasad, and R. B. Misra, "Availability and mean life time prediction of multistage degraded system with partial repairs," Reliability Engineering and System Safety, vol. 56, no. 2, pp. 169-173, 1997.
3. W. Li and H. Pham, "Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks," IEEE Trans. Rel., vol. 54, no. 2, pp. 297-303, 2005.
4. P.Wang, "System reliability prediction based on degradation modeling considering field-operating stress scenarios," Ph.D. dissertation, Rutgers University,2003.
5. A. J. Gross, "A competing risk model: A one organ subsystem plus a two organ subsystem," IEEE Trans. Rel., vol. 22, no. 1, pp. 24-27, 1973.
6. M. Finkelstein, "On damage accumulation and biological aging," Journal of Statistical Planning and Inference, vol. 139, no. 5, pp. 1643-1648, 2009.
7. J. M. van Noortwijk, J. A. M. van der Weide, M. J. Kallen, and M. D. Pandey, "Gamma processes and peaks-over-threshold distributions for time-dependent reliability," Reliability Engineering & System Safety, vol. 92, no. 12, pp. 1651-1658, 2007.
8. A. Lehmann, "Joint modeling of degradation and failure time data," Journal of Statistical Planning and Inference, vol. 139, no. 5, pp. 1693-1706, 2009.
9. Z. S. Ye, L. C. Tang, and H. Y. Xu, "A distribution-based systems reliability model under extreme shocks and natural degradation," IEEE Trans. Rel., vol. 60, no. 1, pp. 246-256, 2011.
10. Y.Wang and H. Pham, "Multi-objective optimization of imperfect preventive maintenance policy for dependent competing risk system with hidden failure," IEEE Trans. Rel., vol. 60, no. 3, Sep. 2011, (to appear).
11. B. Saassouh, L. Dieulle, and A. Grall, "Online maintenance policy for a deteriorating system with random change of mode," Reliability Engineering & System Safety, vol. 92, no. 12, pp. 1677-1685, 2007.
12. J. K. Sari, M. J. Newby, A. C. Brombacher, and L. C. Tang, "Bivariate constant stress degradation model: LED lighting system reliability estimation with two-stage modeling," Quality and Reliability Engineering International, vol. 25, no. 8, pp. 1067-1084, 2009.
13. Z. Q. Pan and N. Balakrishnan, "Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes," Reliability Engineering & System Safety, 2011, (In Press).
14. H. Cossette, E. Marceau, and F. Marri, "On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel- Morgenstern Copula," Insurance: Mathematics and Economics, vol. 43, no. 3, pp. 444-455, 2008.
15. M. Ram and S. B. Singh, "Availability and Cost analysis of a parallel redundant complex system with two types of failure under preemptive- resume repair discipline using Gumbel-Hougaard Family Copula in repair," International Journal of Reliability, Quality and Safety Engineering, vol. 15, no. 4, pp. 341-365, 2008.
16. S. M. S. Lo and R. A.Wilke, "A copula model for dependent competing risks," Journal of the Royal Statistical Society: Series C (Applied Statistics), vol. 59, no. 2, pp. 359-376, 2010.
17. B. Miladinovic and C. P. Tsokos, "Sensitivity of the Bayesian reliability estimates for the modified Gumbel failure model," International Journal of Reliability, Quality and Safety Engineering, vol. 16, no. 4, pp. 331-342, 2009.
18. V. K. Kaishev, D. S. Dimitrova, and S. Haverman, "Modeling the Joint distribution of competing risks survival times using Copula functions," Insurance, Mathematics and Economics, vol. 41, no. 3, pp. 339-361, 2007.
19. S. J. Bae and P. H. Kvam, "A nonlinear random coefficients model for degradation testing," Technometrics, vol. 46, no. 4, pp. 460-469, 2004.
20. S. J. Bae, W. Kuo, and P. H. Kvam, "Degradation models and implied lifetime distributions," Reliability Engineering & System Safety, vol. 92, no. 5, pp. 601-608, 2007.
21. H. Pham, A. Suprasad, and R. B. Misra, "Reliability and MTTF prediction of k-out-of-n complex systems with components subjected to multiple stages of degradation," International Journal of Systems Science, vol. 27, no. 10, pp. 995-1000, 1996.
22. R. B. Nelsen, An Introduction to Copulas, 2nd ed. New York: Springer, 2006.
23. R. B. Nelsen, J. J. Quesada-Molina, J. A. Rodriguez-Lallena, and M. Ubeda-Flores, "Bounds on bivariate distribution functions with given margins and measures of association," Commun. Statist. -Theory Meth., vol. 30, no. 6, pp. 1155-1162, 2001.
24. H. Pham, System Software Reliability. Berlin, Germany: Springer- Verlag, 2006.
25. S. Zhang, F.-B. Sun, and R. Gough, "Application of an empirical growth model and multiple imputation in hard disk drive field return prediction," International Journal of Reliability, Quality and Safety Engineering, vol. 17, no. 6, pp. 565-578, 2010.