Degradation modeling applied to residual lifetime prediction using functional data analysis

Annals of Applied Statistics

Volumn 5, Issue 2 B, 2011, Pages 1586-1610

  Zhou, Rensheng R ^a   Serban, Nicoleta ^a   Gebraeel, Nagi ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Condition monitoring; Functional principal component analysis; Nonparametric estimation; Residual life distribution; Sparse degradation signal

Indexed keywords

EID: 84862896155     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/10-AOAS448     Document Type: Article

References (26)

1. Bogdanoff, J. L. and Kozin, F. (1985). Probabilistic Models of Cummulative Damage. Wiley, New York.
2. Cross, R. J., Makeev, A. and Armanios, E. (2006). A comparison of predictions from probabilistic crack growth models inferred from Virkler's data. J. ASTM International 3. DOI: 101520/JAI100574.
3. Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge Series in Statistical and Probabilistic Mathematics 1. Cambridge Univ. Press, Cambridge. Mathematical Reviews (MathSciNet): MR1478673 Zentralblatt MATH: 0886.62001
4. Doksum, K. A. and Hoyland, A. (1992). Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution. Technometrics 34 74-82.
5. Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability 57. Chapman and Hall, New York. Mathematical Reviews (MathSciNet): MR1270903 Zentralblatt MATH: 0835.62038
6. Fan, J. and Yao, Q. (2003). Nonlinear Time Series: Nonparametric and Parametric Methods. Springer, New York. Mathematical Reviews (MathSciNet): MR1964455
7. Gebraeel, N. (2006). Sensory updated residual life distribution for components with exponential degradation patterns. IEEE Transactions on Automation Science and Engineering 3 382-393.
8. Gebraeel, N., Lawley, M., Li, R. and Ryan, J. (2005). Residual-life distributions from component degradation signals: A Bayesian approach. IIE Transactions 37 543-557.
9. James, G. M., Hastie, T. J. and Sugar, C. A. (2000). Principal component models for sparse functional data. Biometrika 87 587-602. Mathematical Reviews (MathSciNet): MR1789811 Zentralblatt MATH: 0962.62056 Digital Object Identifier: doi:10.1093/biomet/87.3.587
10. Karhunen, K. (1947). Über lineare Methoden in der Wahrscheinlichkeitsrechnung. Suomalainen Tiedeakatemia, Finland. Mathematical Reviews (MathSciNet): MR23013
11. Kotulski, Z. A. (1998). On efficiency of identification of a stochastic crack propagation model based on Virkler experimental data. Archives of Mechanics 5 829-847.
12. Liao, C. M. and Tseng, S. T. (2006). Optimal design for step-stress accelerated degradation tests. IEEE Transactions on Reliability 55.
13. Loève, M. (1945). Functions aleatoire de second order. Comptes Rendus Acad. Sci. 220.
14. Lu, C. J. and Meeker, W. Q. (1993). Using degradation measures to estimate a time-to-failure distribution. Technometrics 35 161-174. Mathematical Reviews (MathSciNet): MR1225093 Digital Object Identifier: doi:10.1080/00401706.1993.10485038
15. Müller, H.-G. and Zhang, Y. (2005). Time-varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories. Biometrics 61 1064-1075. Mathematical Reviews (MathSciNet): MR2216200 Digital Object Identifier: doi:10.1111/j.1541-0420.2005.00378.x
16. Nelson, W. (1990). Accelerated Testing Statistical Models, Test Plans and Data Analysis. Wiley, New York.
17. Padgett, W. J. and Tomlinson, M. A. (2004). Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Anal. 10 191-206. Mathematical Reviews (MathSciNet): MR2081721 Digital Object Identifier: doi:10.1023/B:LIDA.0000030203.49001.b6
18. Park, C. and Padgett, W. J. (2006). Stochastic degradation models with several accelerating variables. IEEE Transactions on Reliability 55 379-390.
19. Pettit, L. I. and Young, K. D. S. (1999). Bayesian analysis for inverse Gaussian lifetime data with measures of degradation. J. Statist. Comput. Simulation 63 217-234. Mathematical Reviews (MathSciNet): MR1703821 Zentralblatt MATH: 0939.62026 Digital Object Identifier: doi:10.1080/00949659908811954
20. Ramsay, J. O. and Silverman, B. W. (1997). Functional Data Analysis. Springer, New York. Mathematical Reviews (MathSciNet): MR2168993
21. Rice, J. A. and Silverman, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. J. Roy. Statist. Soc. Ser. B 53 233-243. Mathematical Reviews (MathSciNet): MR1094283
22. Tseng, S. T. and Peng, C. Y. (2007). Stochastic diffusion modeling of degradation data. J. Data Sci. 5 315-333.
23. Virkler, D. A., Hillberry, B. M. and Goel, P. K. (1979). The statistical nature of fatigue crack propagation. J. Eng. Mater. Technol. 101 148-153.
24. Yao, F., Müller, H.-G. and Wang, J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 577-590. Mathematical Reviews (MathSciNet): MR2160561 Zentralblatt MATH: 1117.62451 Digital Object Identifier: doi:10.1198/016214504000001745
25. Yu, H. F. and Tseng, S. T. (1998). On-line procedure for terminating an accelerated degradation test. Statist. Sinica 8 207-220.
26. Zhou, R. R., Serban, N. and Gebraeel, N. (2010). Supplement to "Degradation modeling applied to residual lifetime prediction using functional data analysis." Ann. Appl. Statist. DOI: 10.1214/10-AOAS448SUPP.