On the exponential formula for reliability

IEEE Transactions on Reliability

Volumn 53, Issue 2, 2004, Pages 265-268

  Finkelstein, Maxim ^a  

^a UNIVERSITY OF THE FREE STATE   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

FAILURE ANALYSIS; MATHEMATICAL MODELS; PERFORMANCE; POISSON DISTRIBUTION; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

EXPONENTIAL FORMULA; EXTERNAL COVARIATES; INTERNAL COVARIATES; OBSERVED FAILURE RATE; SHOCK PROCESS;

RELIABILITY THEORY;

EID: 3142664745     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2004.829164     Document Type: Article

References (15)

1. J. D. Kalbfleisch and R. L. Prentice, The Statistical Analyses of Failure Time Data: John Wiley & Sons, 1980.
2. A. I. Yashin and A. Arjas, "A note on random intensities and conditional survival functions," J. Appl. Prob., vol. 25, pp. 630-635, 1988.
3. T. Aven and U. Jensen, Stochastic Models in Reliability Springer, 1999.
4. N. D. Singpurwalla and S. P. Wilson, "The exponential formula of reliability and survival analysis: Does it always hold?," Lifetime Data Analysis, vol. 1, pp. 187-194, 1995.
5. A. I. Yashin and K. G. Manton, "Effects of unobserved and partially observed covariate processes on system failure: A review of models and estimation strategies," Statistical Science, vol. 12, pp. 20-34, 1997.
6. Y. Kebir, "On hazard rate processes," Naval Res. Log., vol. 38, pp. 865-877, 1991.
7. N. D. Singpurwalla, "Survival in dynamic environment," Statistical Science, vol. 10, pp. 86-103, 1995.
8. M. S. Finkelstein and V. Esaulova, "Modeling a failure rate for a mixture of distribution functions," Probability in the Engineering and Informational Sciences, vol. 15, pp. 383-400, 2001.
9. T. R. Fleming and D. P. Harrington, Counting Processes and Survival Analysis. New York: John Wiley, 1991.
10. D. R. Cox and V. Isham, Point Processes. London: Chapman and Hall, 1980.
11. H. W. Block, T. H. Savits, and W. Borges, "Age dependent minimal repair," J. Appl. Prob., vol. 22, pp. 370-386, 1985.
12. N. J. Lynn and N. D. Singpurwalla, "Comment: Burn-in makes us feel good," Statistical Science, vol. 12, pp. 13-19, 1997.
13. M. S. Finkelstein, "Simple bounds for terminating poisson and renewal processes," Journal of Statistical Planning and Inference, 2003, to be published.
14. M. S. Finkelstein, "Wearing-out of components in a variable environment," Rel. Eng. and System Safety, vol. 66, pp. 235-242, 1999.
15. S. Kotz and N. D. Singpurwalla, "On a bivariate distribution with exponential marginals," Scandinavian Journal of Statistics, vol. 26, pp. 451-64, 1999.