Statistical inference and prediction for the Weibull process with incomplete observations

Computational Statistics and Data Analysis

Volumn 52, Issue 3, 2008, Pages 1587-1603

  Yu, Jun Wu ^a   Tian, Guo Liang ^b   Tang, Man Lai ^c  

^a HUNAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF MARYLAND GREENEBAUM CANCER CENTER   (United States)

^c HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

AMSAA model; Confidence intervals; Goodness of fit test; Nonhomogeneous Poisson process; Prediction limits; Reliability growth; Weibull process

Indexed keywords

AIR CONDITIONING; PARAMETER ESTIMATION; PREDICTIVE CONTROL SYSTEMS; WEIBULL DISTRIBUTION;

AMSAA MODEL; CONFIDENCE INTERVALS; GOODNESS OF FIT TEST; NONHOMOGENEOUS POISSON PROCESS; PREDICTION LIMITS; RELIABILITY GROWTH; WEIBULL PROCESS;

STATISTICAL METHODS;

EID: 35549002651     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.05.003     Document Type: Article

References (22)

1. Abramowitz M., and Stegun I.E. Handbook of Mathematical Functions (1970), National Bureau of Standards, Washington, DC
2. Bain L.J. Statistical Analysis of Reliability and Life-testing Models (1978), Marcel Dekker, New York
3. Bain L.J., and Engelhardt M. Inference on the parameters and current system reliability for a time-truncated Weibull process. Technometrics 22 (1980) 421-426
4. Bar-Lev S.K., Lavi I., and Reiser B. Bayesian inference for the power law process. Ann. Inst. Statist. Math. 44 (1992) 623-639
5. Crow, L. H., 1974. Reliability analysis for complex repairable systems. In: Proschan, F., Serfling, R.J. (Eds.), Reliability and Biometry - Statistical Analysis of Life Length. SIAM, Philadelphia, pp. 379-410.
6. Crow L.H. Confidence interval procedures for the Weibull process with application to reliability growth. Technometrics 24 (1982) 67-72
7. Crow, L.H., Basu, A.P., 1988. Reliability growth estimation with missing data - II. IEEE Proceedings of the Annual Reliability and Maintainability Symposium, pp. 248-253.
8. Crowder M.J., Kimber A.C., Smith R.L., and Sweeting T.J. Statistical Analysis of Reliability (1991), Chapman & Hall, London
9. Dempster A.P., Laird N.M., and Rubin D.B. Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 (1977) 1-38
10. Duane J.T. Learning curve approach to reliability monitoring. IEEE Trans. Aerospace 2 (1964) 563-566
11. Engelhardt M., and Bain L.J. Prediction intervals for the Weibull process. Technometrics 20 (1978) 167-169
12. Huang C.Y., Lyu M.R., and Kuo S.Y. A unified scheme of some nonhomogeneous Poisson process models for software reliability estimation. IEEE Trans. Software Eng. 29 (2003) 261-269
13. IEC TC-56 (Secretariat) 144 (1982). Tests for Validity of a Constant Failure Rate Assumption. IEC TC-56 Standard 605, Part 6.
14. Joe H. Statistical inference for general order statistics and nonhomogeneous Poisson software reliability models. IEEE Trans. Software Eng. 15 (1989) 1485-1490
15. Kuo L., and Yang T.Y. Bayesian computation for nonhomogeneous Poisson process in software reliability. J. Amer. Statist. Assoc. 91 (1996) 763-773
16. Kyparisis, J., Singpurwalla, N.D., 1985. Bayesian inference for the Weibull process with applications to assessing software reliability growth and predicting software failures. In: Billard, L. (Ed.), Computer Science and Statistics. Elsevier Applied Science, London, pp. 57-64.
17. Lee L., and Lee S.K. Some results on inference for the Weibull process. Technometrics 20 (1978) 41-45
18. Patnaik P.B. The non-central chi-square and F distributions and their applications. Biometrika 36 (1949) 202-232
19. Proschan F. Theoretical explanation of observed decreasing failure rate. Technometrics 5 3 (1963) 375-383
20. Ryan K.J. Some flexible families of intensities for nonhomogeneous Poisson process models and their Bayes inference. Qual. Reliab. Eng. Int. 19 2 (2003) 171-181
21. Verma, A.K., Kapur, P.K. (Eds) (2006). Quality, Reliability and Information Technology: Trends and Future Directions. Narosa Publishing House, New Delhi.
22. Zhou Y.Q., Weng Z., and Xi. Reliability Growth (1992), Science Press, Beijing