The trunsored model and its applications to lifetime analysis: Unified censored and truncated models

IEEE Transactions on Reliability

Volumn 54, Issue 1, 2005, Pages 11-21

  Hirose, Hideo ^a  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Bootstrap; Censored data; Durable population; Exponential distribution; Fragile population; Grouped data; Likelihood ratio test; Limited failure population; Mixture model; Truncated data; Weibull distribution

Indexed keywords

MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; MONTE CARLO METHODS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; WEIBULL DISTRIBUTION;

BOOTSTRAP; CENSORED DATA; DURABLE POPULATION; EXPONENTIAL DISTRIBUTION; FRAGILE POPULATION; LIFETIME ANALYSIS; LIMITED FAILURE POPULATION; MIXTURE MODEL; TRUNCATED DATA; TRUNSORED MODEL;

RELIABILITY THEORY;

EID: 15744395866     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2004.837521     Document Type: Article

References (38)

1. F. J. Anscombe, "Estimating a mixed-exponential response law," J. Am. Statist. Assoc., vol. 56, pp. 493-502, 1961
2. L. J. Bain and D. L. Weeks. "A note on the truncated exponential distribution," Ann. Math. Statist., vol. 35, pp. 1366-1367, 1964.
3. M. S. Bartlett, "Properties of sufficiency and statistical tests," Proc. Royal Statist. Soc. Ser. A, vol. 160, pp. 268-282, 1937.
4. R. A. Betensky and E. C. Martin, "Commentary: failure-rate functions for doubly-truncated random variables," IEEE Trans. Reliab., vol. 52, pp. 7-8, 2003.
5. J. W. Boag, "Maximum likelihood estimates of the proportion of patients cured by cancer therapy," J. Royal Statist. Soc. Ser. B, vol. 11, pp. 11-53, 1948.
6. S. Blumenthal and R. Marcus, "Estimating population size with exponential failure," J. Amer. Statist. Assoc., vol. 70, pp. 913-922, 1975.
7. W. L. Deemer and D. F. Votaw Jr., "Estimation of parameters of truncated or censored exponential distributions,"Ann. Math. Statist. vol. 26, pp. 498-504, 1955.
8. V. Chan and W. Q. Meeker, "A failure-time model for infant-mortality and wearout failure modes," IEEE Trans. Reliab., vol. 48, pp. 377-387, 1999.
9. B. Efron, "Bootstrap methods: another look at the jackknife," Ann. Statist., vol. 7, pp. 1-26, 1979.
10. B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia, PA: Society of Industrial and Applied Mathematics, 1982.
11. V. T. Farewell, "A model for a binary variable with time-censored data," Biometrika, vol. 64, pp. 43-46, 1977.
12. R. E. Glaser, "Weibull accelerated life testing with unreported early failures," IEEE Trans. Reliab., vol. 44, pp. 31-36, 1995.
13. A. I. Goldman, "Survivorship analysis when cure is a possibility: a Monte Carlo study," Statistics in Medicine, vol. 3, pp. 153-167, 1984.
14. L. M. Hegde and R. C. Dahiya, "Estimation of the parameters of a truncated gamma distribution," Communications in Statistics: Theory and Methods, vol. 18, pp. 561-577, 1989.
15. H. Hirose, "Lifetime Estimation of Defective Products From the Imaginal Mixture of Defective and Non-Defective Products: the Trunsored Data Model," Kyushu Institute of Technology, Tech. Rep. CSSE-00-10, August 2, 2000.
16. H. Hirose, "Trunsored data analysis with applications to field data," in Int. Conf. Statistics and Related Fields, Honolulu, Hawaii, June 5-9, 2002.
17. N. L. Johnson et al., Continuous Univariate Distributions, 2nd ed. New York: Wiley, 1994, vol. 1.
18. J. D. Kalbfleisch and D. A. Sprott, "Application of likelihood methods to models involving large numbers of parameters (with discussion)," J. Royal Statist. Soc. Ser. B, vol. 32, pp. 175-208, 1970.
19. J. D. Kalbfleisch and J. F. Lawless, "Estimation of reliability in field performance studies," Technometrics, vol. 30, pp. 365-388, 1988.
20. J. D. Kalbfleisch and J. F. Lawless, "Some useful statistical models for truncated data," J. Qual. Technol., vol. 24, pp. 145-151, 1992.
21. J. P. Klein and M. L. Moeschberger, Survival Analysis. New York. NY: Springer, 1997.
22. Y. Komori and H. Hirose, "Parameter estimation based on grouped or continuous data for truncated exponential distributions," Communications in Statistics: Theory and Method. vol. 31. pp. 889-900, 2002.
23. R. A. Maller and S. Zhou, Survival Analysis With Long-Term Survivors New York, NY: Wiley, 1996.
24. M. D. Maltz and R. McCleary, "The mathematics of behavioral change: recidivism and construct validity," Evaluation Quarterly, vol. 1, pp. 421-438, 1977.
25. W. Q. Meeker and L. A. Escober, Statistical Methods for Reliability Data. New York, NY: Wiley, 1998.
26. W. Q. Meeker, "Limited failure population life tests: application to integrated circuit reliability," Technometrics, vol. 29, pp. 51-65, 1987.
27. M. M. Mittal and R. C. Dahiya, "Estimating the parameters of a truncated Weibull distribution," Communications in Statistics: Theory and Methods, vol. 18, pp. 2027-2042, 1989.
28. G. B. Nath, "Unbiased estimates of reliability for the truncated gamma distribution," Scandinavian Actuarial Journal, pp. 181-186, 1975.
29. J. Navarro, "Failure-rate functions for doubly-truncated random variables," IEEE Trans. Reliab., vol. 45, pp. 685-690, 1996.
30. Y. Peng, K. B. G. Dear, and K. C. Carriere, "Testing for the presence of cured patients: a simulation study," Statistics in Medicine, vol. 20, pp. 1783-1796, 2001.
31. L. Sanathanan, "Estimating the size of a truncated sample," J. Amer. Statist. Assoc., vol. 72, pp. 669-672, 1977.
32. D. Sinha et al., "Modeling accelerated life test data by using a Bayesian approach," J. Royal Statist. Soc. Ser. C - Appl. Statist. vol. 52, pp. 249-259, 2003.
33. W. R. Steinhurst, "Hypothesis tests for limited failure survival distributions," Evaluation Review, vol. 5, pp. 699-711, 1981.
34. L. Q. Sun and X. Zhou, "Survival function and density estimation for dependent data," Statist. Prob. Lett., vol. 52, pp. 47-57, 2001.
35. D. J. Taylor et al., "A mixture model for occupational exposure mean testing with a limit of detection," Biometrics, vol. 57, pp. 681-688, 2001.
36. H. T. V. Vu. R. A. Maller, and X. Zhou, "Asymptotic properties of a class of mixture models for failure data: the interior and boundary cases," Ann. Institute Statist. Math., vol. 50, pp. 627-653, 1998.
37. R. Wallace et al., Reliability. New York: Wiley, 2000.
38. S. Zhou and R. A. Maller, "Likelihood ratio test for the presence of immunes in a censored sample," Statistics, vol. 27, pp. 181-201, 1995.