Inference based on type-II hybrid censored data from a Weibull distribution

IEEE Transactions on Reliability

Volumn 57, Issue 2, 2008, Pages 369-378

  Banerjee, Aveek ^a,b   Kundu, Debasis ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

^b Accenture Services Pvt Ltd India   (India)

Author keywords

Approximate maximum likelihood estimators; Asymptotic distribution; Bayes estimators; Hybrid censoring; Markov chain Monte Carlo; Maximum likelihood estimators; Optimum censoring scheme; Type I censoring; Type II censoring

Indexed keywords

ADMINISTRATIVE DATA PROCESSING; APPROXIMATION THEORY; BLOCK CODES; COSMIC RAY DETECTORS; DISTRIBUTION FUNCTIONS; ESTIMATION; FINANCIAL DATA PROCESSING; MARKOV PROCESSES; MAXIMUM LIKELIHOOD; PARAMETER ESTIMATION; WEIBULL DISTRIBUTION;

ASYMPTOTIC DISTRIBUTIONS; BAYES ESTIMATES; CENSORED DATA; CONFIDENCE INTERVAL (CI); CREDIBLE INTERVALS; DATA SETS; INFORMATION MEASURES; MARKOV CHAIN MONTE CARLO TECHNIQUES; MAXIMUM LIKELIHOOD (ML) ESTIMATORS; MONTE CARLO SIMULATION (MCS); STATISTICAL INFERENCES; UNKNOWN PARAMETERS; WEIBULL; WEIBULL PARAMETERS;

MONTE CARLO METHODS;

EID: 45549092903     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2008.916890     Document Type: Article

References (24)

1. B. Arnold, B. N. Balakrishnan, and H. N. Nagaraja, A First Course in Order Statistics. New York: Wiley, 1992.
2. M. G. Badar and A. M. Priest, "Statistical aspects of fiber and bundle strength in hybrids composites," in Progress in Science and Engineering Composites, T. Hayashi, K. Kawata, and S. Umekawa, Eds. Tokyo:, 1982, pp. 1129-1136, ICCM-IV.
3. U. Balasooriya and N. Balakrishnan, "Reliability sampling plans for log-normal distribution, based on progressively-censored samples," IEEE Trans. Reliability, vol. 49, pp. 199-203, 2000.
4. J. O. Berger and D. Sun, "Bayesian analysis for the Poly-Weibull distribution," Journal of the American Statistical Association, vol. 88, pp. 1412-1418, 1993.
5. S. Chen and G. K. Bhattacharya, "Exact confidence bounds for an exponential parameter under hybrid censoring," Communications in Statistics - Theory and Methods, vol. 17, pp. 1857-1870, 1988.
6. A. Childs, B. Chandrasekhar, N. Balakrishnan, and D. Kundu, "Exact likelihood inference based on type-I and type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, vol. 55, pp. 319-330, 2003.
7. L. Devroye, "A simple algorithm for generating random variates with a log-concave density," Computing, vol. 33, pp. 247-257, 1984.
8. N. Draper and I. Guttman, "Bayesian analysis of hybrid life tests with exponential failure times," Annals of the Institute of Statistical Mathematics, vol. 39, pp. 219-225, 1987.
9. N. Ebrahimi, "Estimating the parameter of an exponential distribution from hybrid life test," Journal of Statistical Planning and Inference, vol. 14, pp. 255-261, 1986.
10. N. Ebrahimi, "Prediction intervals for future failures in exponential distribution under hybrid censoring," IEEE Trans. Reliability, vol. 41, pp. 127-132, 1992.
11. B. Epstein, "Truncated life tests in the exponential case," Annals of Mathematical Statistics, vol. 25, pp. 555-564, 1954.
12. K. Fairbanks, R. Madison, and R. Dykstra, "A confidence interval for an exponential parameter from a hybrid life test," Journal of the American Statistical Association, vol. 77, pp. 137-140, 1982.
13. S. Geman and A. Geman, "Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 721-740, 1984.
14. R. D. Gupta and D. Kundu, "Hybrid censoring schemes with exponential failure distribution," Communications in Statistics - Theory and Methods, vol. 27, pp. 3065-3083, 1988.
15. R. D. Gupta and D. Kundu, "On the comparison of Fisher information matrices of the Weibull and generalized exponential distributions," Journal of Statistical Planning and Inference, vol. 136, pp. 3130-3144, 2006.
16. H. S. Jeong, J. I. Park, and B. J. Yum, "Development of (r, T) hybrid sampling plans for exponential lifetime distributions," Journal of Applied Statistics, vol. 23, pp. 601-607, 1996.
17. M. P. Kandinsky and V. V. Krivtsov, "A simple procedure for Bayesian estimation of the Weibull distribution," IEEE Trans. Reliability Analysis, vol. 54, no. 4, pp. 612-616, 2005.
18. D. Kundu, "On hybrid censoring Weibull distribution," Journal of Statistical Planning and Inference, vol. 137, pp. 2127-2142, 2007.
19. D. Kundu and R. D. Gupta, "Estimation of P(Y < X) for Weibull distribution," IEEE Trans. Reliability, vol. 55, no. 2, pp. 270-280, 2006.
20. D. V. Lindley, "Approximate Bayesian method," Trabojos de Estadistica, vol. 31, pp. 223-237, 1980.
21. Reliability Design Qualifications and Production Acceptance Test, Exponential Distribution, MIL-STD-781- C, U.S. Government Printing Office, Washington, DC, (1977).
22. S. J. Press, The subjectivity of scientists and the Bayesian approach New York: Wiley, 2001.
23. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of ScAentific Computing. UK:Cambridge University Press, 1991.
24. Y. Zhang and W. Q. Meeker, "Bayesian life test planning for the Weibull distribution with given shape parameter," Metrika, vol. 61, pp. 237-249, 2005.