Abstract
Maximum likelihood estimates, confidence limits and tests of hypotheses are derived for the parameters of a Weibull process when some of the early failure times are censored. In some cases the resulting tests are found to be uniformly most powerful unbiased tests.
Keywords
- Poisson Process
- Failure Time
- Intensity Function
- Repairable System
- Conditional Test
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References
Abramowitz, M. and Stegun, I. E. (1970). Handbook of Mathematical Functions. National Bureau of Standards, Washington, D. C.
Ascher, H. and Feingold, H. (1984). Repairable Systems Reliability. Marcel Dekker, New York.
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.
Bain, L. J. and Engelhardt, M. (1991). Statistical Analysis of Reliability and Life-Testing Models. Marcel Dekker, New York.
Bain, L. J. and Weeks, D. L. (1964). A note on the truncated exponential distribution. Annals of Mathematical Statistics 35, 1366–1367.
Bartholomew, D. J. (1963). The sampling distribution of an estimate arising in life-testing. Technometrics 5, 361–374.
Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.
Cox, D. R. and Hinkley, D. V. (1974). Theoretical Statistics. Chapman and Hall, London.
Crow, L. (1974). Reliability analysis of complex, repairable systems. In Reliability and Biometry (F. Proschan and R. J. Serfling, Eds.), Siam, New York, 379–410.
Crow, L. (1982). Confidence interval procedures for the weibull process with applications to reliability growth. Technometrics 24, 67–72.
Engelhardt, M. (1988). Encyclopedia of Statistical Sciences. (N. L. Johnson and S. Kotz, Eds.), John Wiley and Sons, New York.
Lehmann, E. L. (1959). Testing of Statistical Hypotheses. John Wiley and Sons, New York.
Miller, S. K. (1976). The Rasch-Weibull Process. Scandinavian Journal of Statistics 3, 107–115.
Ross, S. M. (1983). Stochastic Processes. John Wiley and Sons, New York.
Yeoman, A. (1987). Forecasting Building Maintenance Using the Weibull Process. M. S. Thesis, University of Missouri-Rolla.
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© 1992 Springer Science+Business Media Dordrecht
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Engelhardt, M., Bain, L.J., Blumenthal, S. (1992). Statistical Analysis Of a Weibull Process With Left- Censored Data. In: Klein, J.P., Goel, P.K. (eds) Survival Analysis: State of the Art. Nato Science, vol 211. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7983-4_11
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DOI: https://doi.org/10.1007/978-94-015-7983-4_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4133-3
Online ISBN: 978-94-015-7983-4
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