Metal fatigue, Wicksell transform and extreme values

Applied Stochastic Models in Business and Industry

Volumn 18, Issue 3, 2002, Pages 301-312

  Takahashi, Rinya ^a   Sibuya, Masaaki ^b  

^a KOBE UNIVERSITY OF MERCANTILE MARINE   (Japan)

^b Takachiho University   (Japan)

Author keywords

Generalized gamma distribution; Gumbel distribution; Non metallic inclusions; Peaks over threshold; Stereology

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; ERROR ANALYSIS; FATIGUE OF MATERIALS; INCLUSIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MAXIMUM LIKELIHOOD ESTIMATION; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; STEEL ANALYSIS; STRESS ANALYSIS;

GENERALIZED GAMMA DISTRIBUTION; GUMBEL DISTRIBUTION; WICKSELL TRANSFORM;

STATISTICAL TESTS;

EID: 0036658549     PISSN: 15241904     EISSN: None     Source Type: Journal    
DOI: 10.1002/asmb.477     Document Type: Article

References (21)

1. Murakami Y, Usuki H. Quantitative evaluation of effects on non-metallic inclusions on fatigue strength of high strength steels, II-Fatique limit evaluation based on statistics for extreme values of inclusion size. International Journal of Fatigue 1989; 11:299-307.
2. Murakami Y. Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions. Yokendo: Tokyo, 1993 (in Japanese).
3. Murakami Y. Inclusion rating by statistics of extreme values and its application to fatigue strength prediction and quality control of materials. Journal of Research of the National Institute of Standards and Technology 1994; 99:345-351.
4. Beretta S. Murakami Y. Statistical analysis of defects for fatigue strength prediction and quality control of materials. Fatigue and Fracture of Engineering Materials and Structures 1998; 21:1049-1065.
5. Murakami Y. Beretta S. Small defects and inhomogeneities in fatigue strength: experiments, models and statistical implications. Extrems 1999; 2:123-147.
6. Bomas H., Mayr P., Linkewitz T. Inclusions size distribution and endurance limit of a hard steel. Extrems 1999; 2:149-164.
7. Svensson T. de Maré J. Random features of the fatigue limit. Extrems 1999; 2:165-176.
8. Wicksell S.D. The corpuscle problem. A mathematical study of a biometric problem. Biometrika 1925; 17:84-99.
9. Stoyan D., Kendall W.S., Mecke J. Stochastic Geometry and its Applications (2nd edn). Wiley: Chichester, 1995.
10. Sibuya M. Wicksell's corpuscle problem. In Encyclopedia of Statistical Sciences, Update, Vol. 3, Kotz S, Read CB, Bankd DL (eds). Wiley: New York, 1999.
11. Takahashi R. Sibuya M. The maximum size of the planar sections of random spheres and its application to metallurgy. Annals of the Institute of Statistical Mathematics 1996; 48:127-144.
12. Takahashi R, Sibuya M. Prediction of the maximum size in Wicksell's corpuscle problem. Annals of the Institute of Statistical Mathematics 1998; 50:361-377.
13. Takahashi R., Sibuya M. Prediction of the maximum size in Wicksell's corpuscle problem, II. Annals of the Institute of Statistical Mathematics 2001; 53:647-660.
14. Galambos J. The Asymptotic Theory of Extreme Order Statistics (2nd edn) Krieger: Florida, 1987.
15. Drees H., Reiss R.D. Tail behavior in Wicksell's corpuscle problem. In Probability Theory and Applications: Essays to the Memory of József Mogyoródi, Galambos J. Katai I (eds), Kluwer: Dordrecht, 1992; 205-220.
16. Asano K., Ohashi T. Nuri Y. The effect of ingot size and capping time on the distribution, composition and type on non-metallic inclusions in large rimming ingots. Tetsu-to-Hagané, The Iron and Steel Institute of Japan 1968; 54:643-672 (in Japanese).
17. nS inclusion in rolled steel detected by ultrasonic testing. Tetsu-to-Hagané, The Iron and Steel Institute of Japan 1985; 71:893-900 (in Japanese).
18. Weissman I. Estimation of parameters and large quantiles based on the k largest observations. Journal of the American Statistical Association 1978; 73:812-815.
19. Smith R.L. Estimating tails of probability distributions. Annals of Statistics 1987; 15:1174-1207.
20. Pickands J. Statistical inference using extreme order statistics. Annals of Statistics 1975; 3:119-131.
21. Takahashi R., Sibuya M. Maximum size prediction in Wicksell's corpuscle problem for the exponential tail data. Extreme Value Analysis-Theory and Practice, International Symposium, Leuven, Belgium, August 2001.