Reliability analysis using the least squares method in nonlinear mixed-effect degradation models

Statistica Sinica

Volumn 9, Issue 3, 1999, Pages 855-877

  Wu, Shuo Jye ^a   Shao, Jun ^b  

^a TAMKANG UNIVERSITY   (Taiwan)

^b University of Wisconsin Madison   (United States)

Author keywords

Asymptotic covariance matrix; Asymptotic normality; Consistency; Failure time distribution; Percentile

Indexed keywords

EID: 0033460988     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. Boulanger, M. and Escobar, L. A. (1994). Experimental design for a class of accelerated degradation tests. Technometrics 36, 260-272.
2. Carey, M. B. and Koenig, R. H. (1991). Reliability assessment based on accelerated degradation: a case study. IEEE Trans. Reliability R-40, 499-506.
3. Davidian, M. and Giltinan, D. M. (1993). Some simple methods for estimating intraindividual variability in nonlinear mixed effects models. Biometrics 49, 59-73.
4. Doksum, K. A. (1991). Degradation rate models for failure time and survival data. CWI Quarterly 4, 195-203.
5. Gallant, A. R. (1975). Seemingly unrelated nonlinear regressions. J. Econometrics 3, 35-50.
6. Gallant, A. R. (1987). Nonlinear Statistical Models. John Wiley, New York.
7. Graybill, F. A. (1983). Matrices with Applications in Statistics. 2nd edition. Wadsworth, Belmont.
8. Jennrich, R. I. (1969). Asymptotic properties of nonlinear least squares estimators. Ann. Math. Statist. 40, 633-643.
9. Lu, C. J. and Meeker, W. Q. (1993). Using degradation measures to estimate a time-to-failure distribution. Technometrics 35, 161-174.
10. Lu, C. J., Meeker, W. Q. and Escobar, L. A. (1996). A comparison of degradation and failure-time analysis methods for estimating a time-to-failure distribution. Statist. Sinica 6, 531-546.
11. Lu, J.-C., Park, J. and Yang, Q. (1997). Statistical inference of a time-to-failure distribution derived from linear degradation data. Technometrics 39, 391-400.
12. Meeker, W. Q., Escobar, L. A. and Lu, C. J. (1998). Accelerated degradation tests: modeling and analysis. Technometrics 40, 89-99.
13. Nelson, W. (1981). Analysis of performance-degradation data from accelerated tests. IEEE Trans. Reliability R-30, 149-155.
14. Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis. John Wiley, New York.
15. Phillips, P. C. B. (1976). The iterated minimum distance estimator and the quasi-maximum likelihood estimator. Econometrica 44, 449-460.
16. Shao, J. and Chow, S.-C. (1994). Statistical inference in stability analysis. Biometrics 50, 753-763.
17. Tseng, S.-T., Hamada, M. and Chiao, C.-H. (1995). Using degradation data to improve fluorescent, lamp reliability. Journal of Quality Technology 27, 363-369.
18. Wu, C. F. J. (1981). Asymptotic theory of nonlinear least squares estimation. Ann. Statist. 9, 501-513.
19. Wu, S.-J. (1996). Reliability analysis using the least squares method in nonlinear mixed-effect degradation models. Ph. D. dissertation, University of Wisconsin-Madison, Department of Statistics.
20. Zhuang, D. (1994). Degradation failure model and its statistical analysis. Ph.D. dissertation, East China Normal University, Department of Mathematical Statistics.