Joint modeling of degradation and failure time data

Journal of Statistical Planning and Inference

Volumn 139, Issue 5, 2009, Pages 1693-1706

  Lehmann, Axel ^a  

^a LEIPZIG UNIVERSITY OF APPLIED SCIENCES   (Germany)

Author keywords

Covariate process; Degradation process; Degradation threshold shock model; Failure time; Marked point process; Maximum likelihood estimation; Moment estimator; Repairable item

Indexed keywords

EID: 59849084142     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2008.05.027     Document Type: Article

References (32)

1. Aven T., and Jensen U. Stochastic Models in Reliability (1999), Springer, New York
2. Bagdonavičius V. Testing the hypothesis of the additive accumulation of damage. Probab. Theory Appl. 23 (1978) 403-408
3. Bagdonavičius V., and Nikulin M.S. Estimation in degradation models with explanatory variables. Lifetime Data Anal. 7 (2001) 85-103
4. Bagdonavičius V., Bikelis A., and Kazakečius V. Statistical analysis of linear degradation and failure time data with multiple failure modes. Lifetime Data Anal. 10 (2004) 65-81
5. Bagdonavičius V., Bikelis A., Kazakečius V., and Nikulin M. Non-parametric estimation in degradation-renewal-failure models. In: Nikulin M., Commenges D., and Huber C. (Eds). Probability, Statistics and Modelling in Public Health (2006), Springer Science+Business Media, Berlin 23-36
6. Bogdanoff J.L., and Kozin F. Probabilistic Methods of Cumulative Damage (1985), Wiley, New York
7. Cox D.R. Some remarks on failure-times, surrogate markers, degradation, wear and the quality of life. Lifetime Data Anal. 5 (1999) 307-314
8. Doksum K.A., and Normand S.L.T. Gaussian models for degradation processes-part I: methods for the analysis of biomarker data. Lifetime Data Anal. 1 (1995) 131-144
9. Finkelstein M.S. On the exponential formula of reliability. IEEE Trans. Rel. 53 (2004) 265-269
10. Flournoy, N., 1980. On the survivor and hazard functions. Paper read at the 1980 Statistical Meetings, Houston, TX: Abstract published by the American Statistical Association.
11. Kahle W., and Lehmann A. Parameter estimation in damage processes: dependent observations of damage increments and first passage time. In: Kahle W., von Collani E., Franz F., and Jensen U. (Eds). Advances in Stochastic Models for Reliability, Quality and Safety (1998), Birkhauser, Boston 139-152
12. Kalbfleisch J.D., and Prentice R.S. The Statistical Analysis of Failure Time Data (1980), Wiley, New York
13. Kebir Y. On hazard rate processes. Naval Res. Logist. Quart. 38 (1991) 865-876
14. Lehmann A. A Wiener process based model for failure and degradation data in dynamic environments. Dresdner Schriften Mathemat. Stochastik 4 (2001) 35-40
15. Lehmann A. On a degradation-failure model for repairable items. In: Nikulin M., Balakrishnan N., Limnios N., and Mesbah M. (Eds). Semiparametric Models and its Applications for Reliability, Survival Analysis and Quality of Life (2004), Birkhauser, Boston 65-79
16. Lehmann, A., 2005. Joint models for degradation and failure time data. In: Proceedings of the International Workshop on Statistical Modelling and Inference in Life Sciences, September 1-4, Potsdam, pp. 90-94.
17. Lemoine A.L., and Wenocur M.L. On failure modeling. Naval Res. Logist. Quart. 32 (1985) 479-508
18. Lu C.J., and Meeker W.Q. Using degradation measures to estimate a time-to-failure distribution. Technometrics 35 (1993) 161-174
19. Meeker W.Q., and Escobar L.A. Statistical Methods for Reliability Data (1998), Wiley, New York
20. Meeker W.Q., Escobar L.A., and Lu C.J. Accelerated degradation test: modeling and analysis. Technometrics 40 (1998) 89-99
21. Padgett W.J., and Tomlinson M.A. Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Anal. 10 (2004) 191-206
22. Shaked M., and Shantikumar J.G. On the first-passage times of pure jump processes. J. Appl. Probab. 25 (1988) 501-509
23. Singpurwalla N.D. Survival in dynamic environments. Statist. Sci. 10 (1995) 86-103
24. Singpurwalla N.D., and Wilson S.P. The exponential formula of reliability and survival: Does it always hold?. Lifetime Data Anal. 1 (1995) 187-194
25. Singpurwalla N.D., and Youngren M.A. Multivariate distributions induced by dynamic environments. Scand. J. Statist. 20 (1998) 251-261
26. Tsiatis A.A., and Davidian M. Joint modeling of longitudinal and time-to-event data: an overview. Statist. Sinica 14 (2004) 809-834
27. Wenocur M.L. Brownian motion with quadratic killing and some implications. J. Appl. Probab. 23 (1986) 893-903
28. Wenocur M.L. A reliability model based on the gamma process and its analytical theory. Adv. Appl. Probab. 21 (1989) 899-918
29. Whitmore G.A., and Schenkelberg F. Modelling accelerated degradation data using Wiener diffusion with a time scale transformation. Lifetime Data Anal. 3 (1997) 27-45
30. Yashin A.I. Dynamics in survival analysis: conditional Gaussian property versus Cameron-Martin formula. In: Krylov N.V., Liptser R.S., and Novikov A.A. (Eds). Statistics and Control of Stochastic Processes (1985), Springer, New York 466-475
31. Yashin A.I., and Arjas E. A note on random intensities and conditional survival functions. J. Appl. Probab. 25 (1988) 630-635
32. Yashin A.I., and Manton G.M. Effects of unobserved and partially observed covariate processes on system failure: a review of models and estimation strategies. Statist. Sci. 12 (1997) 20-34