Gumbel Distribution-Maximum Expected Defect

A probability of occurrence, P, is then chosen to which it corresponds a given. Jarea iP). To this value it corresponds a fatigue limit that can be assessed by the Murakami and Endo Eq. (3.5). The procedure is shown in Fig. 4.33 for a cast iron case. The experimental data are plotted on a probability paper using Eq. 4.66 and the fitting line traced. This line indicates that to 99.9 % probability of occurrence it corresponds a value (,yarea) of 3.65 mm to which, in turn, it corresponds an area equivalent to 1,000 specimens (T = 1,000, see Fig. 4.33). Since the area of the section examined was equal to 12 mm it means that in a surface of 12,000 mm a defect of 3.65 mm should be expected. If the probability P is increased to 99.999 % then the maximum size grows to about 5 mm on a surface of 1.200,000 mm.  

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