Inference for a step-stress model with competing risks for failure from the generalized exponential distribution under type-I censoring

IEEE Transactions on Reliability

Volumn 64, Issue 1, 2015, Pages 31-43

  Han, David ^a   Kundu, Debasis ^b  

^a UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Accelerated life testing; competing risks; confidence interval; cumulative damage model; generalized exponential distribution; maximum likelihood estimation; step stress model; type I censoring

Indexed keywords

ELECTRON EMISSION; FINANCIAL DATA PROCESSING; INTELLIGENT SYSTEMS; MAXIMUM LIKELIHOOD; MONTE CARLO METHODS; RISK PERCEPTION; STATISTICAL METHODS; STATISTICAL TESTS;

ACCELERATED LIFE TESTING; COMPETING RISKS; CONFIDENCE INTERVAL; CUMULATIVE DAMAGE MODELS; GENERALIZED EXPONENTIAL DISTRIBUTION; STEP-STRESS MODELS; TYPE-I CENSORING;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 85027920156     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2014.2336392     Document Type: Article

References (29)

1. V. Bagdonavicius, "Testing the hypothesis of additive accumulation of damages," Probab. Theory Applicat., vol. 23, pp. 403-408, 1978.
2. W. Nelson, "Accelerated life testing: Step-stress models and data analysis,"IEEE Trans. Rel., vol. 29, pp. 103-108, 1980.
3. R. Miller and W. Nelson, "Optimum simple step-stress plans for accelerated life testing," IEEE Trans. Rel., vol. R-32, pp. 59-65, 1983.
4. D. S. Bai, M. S. Kim, and S. H. Lee, "Optimum simple step-stress accelerated life tests with censoring," IEEE Trans. Rel., vol. 38, pp. 528-532, 1989.
5. D. S. Bai and Y. R. Chun, "Optimum simple step-stress accelerated life-tests with competing causes of failure," IEEE Trans. Rel., vol. 40, pp. 622-627, 1991.
6. X. Liu and W. S. Qiu, "Modeling and planning of step-stress accelerated life tests with independent competing risks," IEEE Trans. Rel., vol. 60, pp. 712-720, 2011.
7. J. R. van Dorp, T. A. Mazzuchi, G. E. Fornell, and L. R. Pollock, "A Bayes approach to step-stress accelerated life testing," IEEE Trans. Rel., vol. 45, pp. 491-498, 1996.
8. T. Yuan, X. Liu, and W. Kuo, "Planning simple step-stress accelerated life tests using Bayesian methods," IEEE Trans. Rel., vol. 61, pp. 254-263, 2012.
9. N. Balakrishnan and D. Han, "Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring," J. Statist. Plan. Inference, vol. 138, pp. 4172-4186, 2008.
10. D. Han and N. Balakrishnan, "Inference for a simple step-stress model with competing risks for failure from the exponential distribution under time constraint," Comput. Statist. Data Anal., vol. 54, pp. 2066-2081, 2010.
11. E. Gouno, A. Sen, and N. Balakrishnan, "Optimal step-stress test under progressive Type-I censoring," IEEE Trans. Rel., vol. 53, pp. 383-393, 2004.
12. N. Balakrishnan and D. Han, "Optimal step-stress testing for progressively Type-I censored data from exponential distribution," J. Statist. Plan. Inference, vol. 139, pp. 1782-1798, 2009.
13. D. Han, N. Balakrishnan, A. Sen, and E. Gouno, "Corrections on optimal step-stress test under progressive Type-I censoring," IEEE Trans. Rel., vol. 55, pp. 613-614, 2006.
14. D. Han and H. K. T. Ng, "Asymptotic comparison between constantstress testing and step-stress testing for Type-I censored data from exponential distribution," Comm. Statist. Theory Methods, vol. 43, pp. 2384-2394, 2014.
15. M. J. Crowder, "On the identifiability crises in competing risks analysis,"Scand. J. Statist., vol. 18, pp. 223-233, 1991.
16. J. D. Kalbfleisch and R. L. Prentice, The Statistical Analysis of Failure Time Data, 2nd ed. New York, NY, USA: Wiley, 2002.
17. R. L. Prentice, J. D. Kalbfleisch, A. V. Peterson, Jr., N. Flournoy, V. T. Farewell, and N. E. Breslow, "The analysis of failure times in the presence of competing risks," Biometrics, vol. 34, pp. 541-554, 1978.
18. J. Berkson and L. Elveback, "Competing exponential risks with particular inference to the study of smoking lung cancer," J. Amer. Statist. Assoc., vol. 55, pp. 415-428, 1960.
19. D. R. Cox, "The analysis of exponentially distributed lifetimes with two types of failures," J. R. Statist. Soc. Ser. B Statist. Methodol., vol. 21, pp. 411-421, 1959.
20. M. J. Crowder, Classical Competing Risks. Boca Raton, FL, USA: Chapman & Hall, 2001.
21. C. Park, "Parameter estimation of incomplete data in competing risks using the EM algorithm," IEEE Trans. Rel., vol. 54, pp. 282-290, 2005.
22. G. S. Mudholkar and D. K. Srivastava, "Exponentiated Weibull family for analyzing bathtub failure data," IEEE Trans. Rel., vol. 42, pp. 299-302, 1993.
23. R. D. Gupta and D. Kundu, "Generalized exponential distribution: Different method of estimations," J. Statist. Comput. Simul., vol. 69, pp. 315-337, 2001.
24. D. G. Chen and Y. L. Lio, "Parameter estimations for generalized exponential distribution under progressive Type-I interval censoring,"Comput. Statist. Data Anal., vol. 54, pp. 1581-1591, 2010.
25. R. D. Gupta and D. Kundu, "Generalized exponential distribution: Existing results and some recent developments," J. Statist. Plan. Inference, vol. 137, pp. 3537-3547, 2007.
26. J. D. Kalbfleisch, Probability and Statistical Inference II. New York, NY, USA: Springer, 1985.
27. B. Efron and R. Tibshirani, An Introduction to the Bootstrap. New York, NY, USA: Chapman & Hall, 1993.
28. P. Hall, "Theoretical comparison of bootstrap confidence intervals,"Ann. Statist., vol. 16, pp. 927-953, 1988.
29. D. Kundu, N. Kannan, and N. Balakrishnan, "Analysis of progressively censored competing risks data," in Handbook of Statistics 23: Advances in Survival Analysis, N. Balakrishnan and C. R. Rao, Eds. New York, NY, USA: Elsevier, 2003, pp. 331-348.