Effect of Ranking Selection on the Weibull Modulus Estimation

Abstract

Determination of mechanical properties of materials requires repeatable and consistent results. Therefore, the Weibull statistical distribution is widely used to verify the confidence levels of the test results where probability of failure is predicted. The reliability of results is characterised by Weibull distribution where Weibull parameters are determined and compared with the benchmarks. Recent studies showed that the size of the population and the method chosen to estimate the Weibull modulus play an important role. Therefore, in this study, the effect of ranking selection over the Weibull parameters (alpha-characteristic life, beta-shape parameter, R² and survival probability) was investigated. The data from authors’ recent research were re-evaluated. In addition, randomly generated data with population from 5 to 50 sample sizes were studied. The results showed that the mean rank regression to estimate the failure probability had the highest R² and the lowest shape parameter. It was also found that the results were independent of sample size.

 

Keywords: Estimators, mechanical test, prediction limit, Weibull distribution, Weibull modulus

 

Keywords

• Estimators, mechanical test, prediction limit, Weibull distribution, Weibull modulus

References

1. Weibull, W., “A statistical distribution function of wide Mechanics, 293-297 (September 1951). of Applied
2. Bernard, A. and Bos-Levenbach, E., C., “The plotting of observations on probability paper”, Statistica, 7: 163-173 (1953).
3. Weibull, W., “A statistical study of the strength of materials”, Ing. Vetenskaps Akad. Handl., 151: 1- 45 (1939).
4. Hazen, A., “Flood flows”, New York, John Wiley, (1930).
5. Filliben, J. J., “The probability plot correlation coefficient test for normality” Technometrics, 17(1): 111-117 (1975).
6. Blom, G. J., “Statistical estimates and transformed beta-variables”, John Wiley, (1958).
7. Gringorten, I. I., “A plotting rule for extreme probability paper”, J. Geophys. Res., 68: 813-814 (1963).
8. Dispinar, D. and Campbell, J., “Use of bifilm index as an assessment of liquid metal quality”, International Journal of Cast Metals Research, 19: 5-17 (2006).

9. Kirtay, S., Oktay E., Gunay, V. “Glass strengthening by SiO2-TiO2 organically modified silica coating”, Thin Solid Films, 515(4): 2145- 2152, (2006).