Data Scatter and Statistical Considerations



If five specimens of the same material, size and surface finish were subjected to the same traction or fatigue test five different results are likely to be obtained. If the test pieces were ten, then ten different results are likely to be obtained. Increasing the number of specimens will not change this general outcome, but will probably yield some new lower or higher value, as well. Therefore, also the spread between the maximum and the minimum value will increase, albeit most values will appear closely-spaced. But the search of the reasonably lower value when not of the lowest possible, which indeed is the target of the designer, cannot be done by just increasing over and over the number of test specimens. The problem of inferring what might be the target value in the fatigue analysis can be solved with the available limited number of data using statistical analysis. This chapter provides the most used and recent statistical tools today available to that purpose.


Fatigue Life Weibull Distribution Work Piece Fatigue Limit Stress Amplitude 
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  1. 1.
    Härkegård, G.: Fatigue assessment based on weakest-link Theory. Vortragim rahmendes kolloquiums fuer technische wissenshaftenundess seminars in mechanik, 44, ETH Zürich 18 (2007)Google Scholar
  2. 2.
    Hutchinson, T.P.: Essential of Statistical Methods. Rumbsby Scientific Publishing, Sidney (1993)Google Scholar
  3. 3.
    Gosset, W.S.: The probable error of a mean. Biometrica 6, 1–25 (1908)Google Scholar
  4. 4.
    Beyer, W.: Handbook of Tables for Probability an Statistics. CRC Press, Boca Raton (1966)Google Scholar
  5. 5.
    Lieberman, G.J.: Tables for one-sided statistical tolerance limits. Indust. Qual. Contr. 14(10), 7–9 (1958)Google Scholar
  6. 6.
    Williams, C.R., Lee, Y., Rilly, J.T.: A practical method for statistical analysis of strain life fatigue data. Int. J. Fatigue 25(5), 446–448 (2003)CrossRefGoogle Scholar
  7. 7.
    Weibull, W.: Ingeniors vetenskapf akademien handlingar. Stockolm 151, 1–45 (1939)Google Scholar
  8. 8.
    Milella, P.P., Bonora, N.: On the dependence of the Weibull exponent on geometry and loading conditions and its implications on the fracture toughness probability curve using a local approach criterion. Int. J. Fract. 104, 71–87 (2000)CrossRefGoogle Scholar
  9. 9.
    Troshehenko, V.T.: Some comments to the construction of probabilistic models of structural integrity. NEA workshop on probabilistic structure integrity analysis and its relationship to deterministic analysis, report OECD/GD(96)124, pp. 29–43, Stockholm, Sweden, 28 February-1 March (1996)Google Scholar
  10. 10.
    Gumbel, E.J.: Statistic of Extremes. Columbia University Press, New York (1957)Google Scholar
  11. 11.
    Sinclair, G.M., Dolan, T.J.: Effect of stress amplitude on statistical variability of 75S-T6 aluminum alloy. ASME Trans. 75, 687–872 (1973) Google Scholar
  12. 12.
    Murakami, Y., Usuki, H.: Quantitative evaluation of effects of non-metallic inclusions on fatigue strength of high strength steel. Int. J. Fatigue 11(5), 299–307 (1989)CrossRefGoogle Scholar
  13. 13.
    Murakami, Y., Toriyama, T., Coudert, E.M.: Instruction for a new method of inclusion rating and correlation with the fatigue limit. J. Test. Eval. 22(4), 318–326 (1994)CrossRefGoogle Scholar
  14. 14.
    Murakami, Y.: Inclusion rating by statistic of extreme values and its application to fatigue strength prediction and quality control of materials. J. Res. Natl. Inst. Stand. Technol. 99, 345–348 (1994)CrossRefGoogle Scholar

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© Springer-Verlag Italia 2013

Authors and Affiliations

  1. 1.Department of Civil and Mechanical EngineeringUniversity of CassinoCassinoItaly

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