Bayesian estimation and prediction of the intensity of the Power Law Process

Journal of Statistical Computation and Simulation

Volumn 72, Issue 8, 2002, Pages 613-631

  Sen, Ananda ^a  

^a OAKLAND UNIVERSITY   (United States)

Author keywords

Aggregated data; Bayesian inference; Intensity function; Markov chain Monte Carlo; Power Law Process; Repairable systems

Indexed keywords

EID: 0036375653     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949650213742     Document Type: Article

References (31)

1. Bain, L. J. and Engelhardt, M (1980) Inferences on the parameters and current system reliability for a time truncated Weibull process, Technometrics, 22, 421-426.
2. Bar-lev, S K., Lavi, I and Reiser, B. (1992) Bayesian inference for the power law process, Annals of Institute of Statistical Mathematics, 44, 623-639.
3. Beiser, J A and Rigdon, S. (1997) Bayes prediction for the number of failures of a repairable system, IEEE Transactions on Reliability; 46, 291-295
4. Bhattacharya, G. K. and Ghosh, J. K. (1991) Asymptotic properties of estimators in a binomial reliability growth model and its continuous-time analog, Journal of Statistical Planning and Inference, 29, 43-53.
5. Calabria, R., Guida, M. and Pulcini, G. (1988) Some modified maximum likelihood estimators for the Weibull process. Reliability Engineering and System Safety, 23, 51-58
6. Calabria, R., Guida, M. and Pulcini, G. (1990) Bayes estimation of prediction intervals for a power law process, Communications in Statistics Theory and Methods, 19, 3023-3035.
7. Calabria, R. and Pulcini, G. (1996) Maximum likelihood and Bayes prediction of current system lifetime, Communications in Statistics- Theory and Methods, 25, 2297-2309
8. Crow, L. H. (1974) Reliability analysis for complex repairable systems. In: Proschan, F. and Serfling, R J. (Eds.), Reliability and Biometry pp. 379-410.
9. Crow, L. H. (1982) Confidence interval procedures for the Weibull process with applications to reliability growth, Technometrics, 24, 67-72.
10. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm. Journal of Royal Statistical Society. Series B, 39, 1-38.
11. Duane, J. T. (1964) Learning curve approach to reliability monitoring, IEEE Transactions on Aerospace, 2, 563-566.
12. Gelfand, A E. and Smith, A. F. M. (1990) Sampling-based approaches to calculating marginal densities, Journal of the American Statistical Association, 85, 398-409.
13. Ghosh, M and Sen, P. K (1991) Bayesian Pitman closeness, Communications in Statistics - Theory and Methods. 20, 3729-3750.
14. Gilks, W. R. and Wild P. (1992) Adaptive rejection sampling for Gibbs sampling, Applied Statistics, 41, 337348.
15. Guida, M., Calabria, R. and Pulcini, G. (1989) Bayes inference for a non-homogeneous Poisson process with power intensity law, IEEE Transactions on Reliability, 38, 603-609.
16. Higgins, J. J. and Tsokos, C. P (1981) A quasi-Bayes estimate of the failure intensity of a reliability growth model. IEEE Transactions on Reliability R-30, 471-475.
17. Kuo, L. and Yang, T. Y. (1996) Bayesian computation for nonhomogeneous Poisson processes in software reliability, Journal of the American Statistical Association, 91, 763-773.
18. Kyparisis, J. and Singpurwalla, N. (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: the Interface pp. 57-64.
19. Lee, L. and Lee, S. K. (1978) Some results on inference for the Weibull process, Technometrics, 20, 41-45.
20. Lingham, R. T. and Sivaganesan, S. (1997) Testing hypotheses about the power law process under failure truncation using intrinsic Bayes factors, Annals of Institute of Statistical Mathematics, 49, 693-710.
21. Qiao, H. and Tsokos, C. P. (1998) Best efficient estimates of the intensity function of the power law process, Journal of Applied Statistics, 25, 111-120.
22. Rigdon, S, E. and Basu, A. P. (1988) Estimating the intensity function of a Weibull process at the current time: failure truncated case, Journal of Statistical Computation and Simulation, 30, 17-38.
23. Rigdon, S. E. and Basu, A. P. (1990) Estimating the intensity function of a power law process at the current time: time truncated case, Communications in Statistics Simulation, 19, 1079-1104.
24. Rigdon, S. E. and Basu, A. P. (2000) Statistical Methods for the Reliability of Repairable Systems, New York, John Wiley and Sons.
25. Sen, A. and Khattree, R. (1998) On estimating the current intensity of failure for the power-law process, Journal of Statistical Planning and Inference, 74, 253-272.
26. Sinha, B. K. and Ghosh, M. (1987) Inadmissibility of the best equivanant estimators of the variance-covariance matrix and the generalized variance under entropy loss, Statistics and Decisions, 5, 201-227.
27. Smith, A. F. M. and Gelfand, A. E. (1992) Bayesian statistics without tears: a sampling-resampling perspective, The American Statistician, 46, 84-88.
28. Sweeting, T. J. and Phillips, M. J. (1995) An application of nonstandard asymptotics to the analysis of repairable-systems data, Technometrics, 37, 428-435.
29. Triner, D. A. and Phillips, M. J. (1986) The reliability of equipment fitted to a fleet of ships. In: Proceedings of the 9th Advances in Reliability Technology Symposium, Bradford, Warrington, UK, Atomic Energy Authority.
30. Varian, H. R. (1975) A Bayesian approach to real estate assessment. In: Fienberg, E. and Zelner, A. (Eds.), Studies in Bayesian Econometrics and Statistics, in Honor of L. J. Savage, Amsterdam, North-Holland, pp. 195-208.
31. Zellner, A. (1986) Bayesian estimation and prediction using asymmetric loss functions, Journal of the American Statistical Association, 81, 446-451.