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The Uncertainty of Estimated Lognormal and Weibull Parameters for Test Data with Small Sample Size
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 08, 2013 by SAE International in United States
Annotation ability available
In this paper, the uncertainty of the estimated parameters of lognormal and Weibull distributions for test data with small sample size is investigated. The confidence intervals of the estimated parameters are determined by solving available analytical equations, and the scatters of the estimated parameters with respect to the true values are estimated by using Monte Carlo simulation approaches. Important parameters such as mean, standard deviation, and design curve are considered. The emphasis is on the interpretation and the implication of the obtained shape parameter β of the Weibull distribution function and the design curve obtained from a lognormal distribution function. Finally, the possible impact of this study on the current engineering practice is discussed.
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CitationWei, Z., Yang, F., Luo, L., and Lin, S., "The Uncertainty of Estimated Lognormal and Weibull Parameters for Test Data with Small Sample Size," SAE Technical Paper 2013-01-0945, 2013, https://doi.org/10.4271/2013-01-0945.
- Dodson , B. The Weibull Analysis Handbook Second ASQ Quality Press Milwaukee, Wisconsin 2006
- Neter , J. , Wasserman , W. , Kutner , M.H. Applied Linear Statistical Models Richards D. Irwin, Inc. Homewood, IL. 1990
- Nelson , W.B. Accelerated Testing: Statistical Models, Test Plans, and Data Analysis Wiley-Interscience 2004
- Cohen , A. C. Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples Technometrics 1965 7 579 588
- Meeker , W.K. Escobar, Statistical Methods for Reliability Data Wiley Series in Probability and Statistics 1998
- Standard practice for statistical analysis of linear or linearized stress-life (S-N) and strain-life fatigue data ASTM, E739-91
- Lieberman , G.J. Tables for one-sided statistical tolerance limits, Technical Report No.34 Applied Mathematics and Statistics Laboratory, Stanford University November 1 1957
- Natrella , M.G. Experimental statistics, Handbook 91 National Bureau of Standards 1966
- Guttman , I. Standard tolerance regions Darien, CT Hafner Publishing Company 1970
- Link , C.L. An equation for one-sided tolerance limits for normal distributions Research paper FPL 458 Madison, WI U.S. Department of Agriculture, Forest Service, Forest Products Laboratory 1 4
- Wei , Z. , Dogan , B. , Luo , L. , Lin , B. , Konson , D. PVP2012-78233, Design curve construction based on tolerance limit concept Proceedings of the ASME 2012 Pressure Vessels & Piping Division Conference July 15 19 2012 Toronto, Canada
- Wei , Z. , Yang , F. , Luo , L. , Avery , K. et al. Fatigue Life Assessment of Welded Structures with the Linear Traction Stress Analysis Approach SAE Int. J. Mater. Manf. 5 1 183 194 2012 10.4271/2012-01-0524
- Box , G.E.P. , Muller , M.E. A note on the generation of random normal deviates The Annals of Mathematical Statistics 1958 29 610 611