Statistical models to analyze failure, wear, fatigue, and degradation data with explanatory variables

Communications in Statistics - Theory and Methods

Volumn 38, Issue 16-17, 2009, Pages 3031-3047

  Bagdonavicius, Vilijandas ^a   Nikulin, Mikhail ^b  

^a VILNIUS UNIVERSITY   (Lithuania)

^b UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

Covariates; Degradation; Failure time regression; Reliability; Wear

Indexed keywords

ACCELERATED LIFE TESTING; COVARIATES; DEGRADATION DATA; DEGRADATION PROCESS; EXPERIMENTAL FACTORS; EXPLANATORY VARIABLES; FAILURE TIME; FAILURE TIME REGRESSION; FAILURE-TIME DISTRIBUTION; REGRESSION MODEL; RELIABILITY INFORMATION; STATISTICAL INFERENCE; STATISTICAL MODELS; WEAR;

DEGRADATION; FAILURE ANALYSIS; REGRESSION ANALYSIS; TESTING;

QUALITY ASSURANCE;

EID: 70249113727     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920902947519     Document Type: Article

References (49)

1. Bagdonavičius, V. (1978). Testing the hyphothesis of the additive accumulation of damages. Probab. Theor. Applic. 23:403-408.
2. Bagdonavičius, V., Nikulin, M. (1999). Modified partial likelihood in generalized Cox model. Lifetime Data Anal. 5:323-344.
3. Bagdonavičius, V., Nikulin, M. (2000). On nonparametric estimation in accelerated experiments with step stresses. Statistics 33:349-365.
4. Bagdonavičius, V., Nikulin, M. (2002a). Accelerated Life Models. Boca Raton, FL: Chapman & Hall/CRC.
5. Bagdonavičius, V., Nikulin, M. (2002b). Estimation in degradation models with explanatory variables. Lifetime Data Anal. 7:85-103.
6. Bagdonavičius, V., Bikelis, A., Kazakevičius, V. (2002). Estimation of tire wear and traumatic failure intensities. Tire Sci. Technol. 30:214-239.
7. Bagdonavičius, V., Hafdi, M. A., Nikulin, M. (2004a). Analysis of survival data with crosseffects of survival functions. Biostatistics 5:415-425.
8. Bagdonavičius, V., Cheminade, O., Nikulin, M. (2004b). Statistical planning and inference in accelerated life testing using the CHSS model. J. Statist. Plann. Infer. 126:535-551.
9. Bagdonavičius, V., Bikelis, A., Kazakevičius, V., Nikulin, M. (2007). Non-parametric estimation from simultaneous renewal-failure- degradation data with competing risks.J. Statist. Plann. Infer. 137:2191-2207.
10. Bagdonavičius, V., Clerjaud, L., Nikulin, M. (2008a). Accelerated life testing when the hazard rate function has cup shape. In: Huber, C., Limnios, N., Mesbah, M., Nikulin, M., eds. Mathematical Methods in Survival Analysis, Reliability and Quality of Life. New York: ISTE and J. Wiley, pp. 203-216.
11. Bagdonavičius, V., Levuliene, R., Nikulin, M. (2008b). Testing absence of hazard rates crossing. Proc. Second Int. Conf. Accelerated Life Testing Reliab. Qual. Control, ALT2008. Guerin, F., Nikulin, M., eds. University Victor Segalen Bordeaux 2, Bordeaux, 9-11 June, pp. 27-31.
12. Bagdonavičius, V., Masiulaityte, I., Nikulin, M. (2008c). Statistical analysis of redundant systems with warm stand-by units. Stochastics Int. J. Probab. Stochastic Process. 80:115-128.
13. Carey, M. B., Koenig, R. H. (1991). Reliability assessment based on accelerated degradation: a case study. IEEE Trans. Reliab. 40:499-506.
14. Ceci, C., Mazliak, L. (2004). Optimal design in nonparametric life testing. Statist. Infer. Stochastical Process. 7:305-325.
15. Cox, D. (1975). Partial likelihood. Biometrika 62:269-276.
16. Dabrowska, D. (2006). Estimation in a class of semi-parametric transformation models. In: Rojo, J., ed. Second Eric L. Lehmann Symposium - Optimality. Institute of Math. Statistics, Lecture Notes and Monograph Series, Vol.49, pp. 166-216.
17. Doksum, K. A., Normand, S. L. T. (1995). Gaussian models for degradation processes - part I: Methods for the analysis of biomarker data. Lifetime Data Anal. 1:131-144.
18. Duchesne, T., Rosenthal, J. S. (2003). On the collapsibility of lifetime regression models. Adv. Appl. Probab. 35:755-772.
19. Harlamov, B. (2004). Inverse gamma-process as a model of wear. In: Antonov, V., Huber, C., Nikulin, M., Politschook, V., eds. Longevity, Aging and Degradation Models in Reliability, Health, Medicine and Biology. St. Petersburg State Polytechnical University, Saint Petersburg, Vol.2, pp. 180-190.
20. Huber, C., Limnios, N., Mesbah, M., Nikulin, M., eds. (2008). Mathematical Methods in Survival Analysis, Reliability and Quality of Life. Hermes(ISTE)/Wiley.
21. Henderson, R. (2007). Discussion on the paper by Zeng and Lin. J. Roy. Statist. Soc. B 69:536-537.
22. Hsieh, F. (2001). On heteroscedastic hazards regression models: theory and application. J. Roy. Statist. Soc. Ser. B 63:63-79.
23. Huber-Carol, C., Nikulin, M. (2008). Extended Cox model and accelerated models in reliability, with general censoring and truncation. In: Vonta, F., Nikulin, M., Limnios, N., Huber-Carol, C., eds. Statistical Models and Methods for Biomedical and Technical Systems. Boston: Birkhauser, pp. 3-22.
24. Kahle, W., Lehmann, A. (1998). Parameter estimation in damage processes: dependent observations of damage increments and first passage time. In: Kahle, W., von Collani,E., Franz, F., Jensen, U., eds. Advances in Stochastic Models for Reliability, Quality and Safety. Boston: Birkhauser, pp. 139-152.
25. Kahle, W., Wendt, H. (2006). Statistical analysis of some parametric degradation models. In: Nikulin, M., Commenges, D., Huber, C., eds. Probability, Statistics and Modelling in Public Health. New York: Springer, pp. 266-279.
26. Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. New York: Wiley.
27. Lawless, J., Crowder, M. (2004). Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Anal. 10:213-227.
28. Lehmann, A. (2001). A Wiener process based model for failure and degradation data in dynamic environments. Dresdner Schriften zur Mathemat. Stochastik 4:35-40.
29. Lehmann, A. (2004). On degradation-failure models for repairable items. In: Nikulin, M., Balakrishnan, N., Mesbah, M., Limnios, N., eds. Parametric and Semiparametric Models with Applications to Reliability, Survival Analysis, and Quality of Life. Boston: Birkhauser, pp. 65-80.
30. Lehmann, A. (2005). Joint models for degradation and failure time data. Proc. Int. Workshop Statist. Model. Infer. Life Sci., September 1-4, Potsdam, pp. 90-94.
31. Lehmann, A. (2006). Degradation-threshold-shock models. In: Nikulin, M., Commenges, D., Huber, C., eds. Probability, Statistics and Modelling in Public Health. New York: Springer, pp. 286-298.
32. Lin, D. Y., Ying, Z. (1995). Semiparametric inference for accelerated life model with time dependent covariates. J. Statist. Plann. Infer. 44:47-63.
33. Martinussen, T., Scheike, Th. H. (2006). Dynamic Regression Models for Survival Data. New York: Springer.
34. Meeker, W., Escobar, L. (1998). Statistical Methods for Reliability Data. New York: Wiley.
35. Nelson, W. (2004). Accelerated Life Testing: Statistical Models, Test Plans, and Data Analysis. New York: Wiley-Interscience.
36. Padgett, W. J., Tomlinson, M. A. (2004). Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Anal. 10:191-206.
37. Padgett, W. J., Tomlinson, M. A. (2005). Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Anal. 11:511-527.
38. Sedyakin, N. M. (1966). On a physical principle in reliability theory (in Russian). Techn. Cybernetics 3:80-87.
39. Singpurwalla, N. (1971). Inference from accelerated life tests when observations are obtained from censored data. Technometrics 13:161-170.
40. Singpurwalla, N. (1995). Survival in dynamic environments. Statist. Sci. 1:86-103.
41. Scheike, T. H. (2006). A flexible semiparametric transformation model for survival data. Lifetime Data Anal. 12:461-480.
42. Sundara-Rajan, K. (2002). Accelerated Testing - An Electrical Perspective. Course INDE 526, Internet.
43. Viertl, R. (1988). Statistical Methods in Accelerated Life Testing. Goettingen: Vandenhoeck and Ruprecht.
44. Vonta, F., Nikulin, M., Limnios, N., Huber-Carol, C., eds. (2008). Statistical Models and Methods for Biomedical and Technical Systems. Boston: Birkhauser.
45. Wendt, H., Kahle, W. (2004). On parametric estimation for a position-dependent marking of a doubly stochastic poisson process. In: Nikulin, M., Balakrishnan, N., Mesbah, M., Limnios, N., eds. Parametric and Semiparametric Models with Applications to Reliability, Survival Analysis, and Quality of Life. Boston: Birkhauser, pp. 473-486.
46. Yashin, A. I. (2004). Semiparametric models in the studies of aging and longevity. In: Nikulin, M., Balakrishnan, N., Limnios, N., Mesbah, M., eds. Parametric and Semiparametric Models with Applications for Reliability, Survival Analysis, and Quality of Life. Boston: Birkhauser, pp. 149-166.
47. Zacks, Sh. (1992). Introduction to Reliability Analysis. New York: Springer-Verlag.
48. Zacks, Sh. (2004). Failure distributions associated with general compound renewal damage processes. In: Antonov, V., Huber, C., Nikulin, M., Polischook, V., eds. Longevity, Aging and Degradation Models in Reliability, Public Health, Medicine and Biology. St. Petersburg: St. Petersburg State Polytechnical University, Vol.2, pp. 336-344.
49. Zeng, D., Lin, D. Y. (2007). Maximum likelihood estimation in semiparametric regression models with censored data. J. Roy. Statist. Soc. Ser. B 69:509-564.