Shape Casting pp 115-123 | Cite as

On Estimating Largest Defects in Castings

  • Murat TiryakioğluEmail author
  • Irisi Nini
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


The procedure developed by Beretta and Murakami has two issues that were not addressed previously: (i) the selection of the Weibull plotting position formula for linear regression fits to estimate Gumbel distribution parameters and (ii) the untested hypothesis that the estimates for the upper Gumbel percentiles are distributed normally. Monte Carlo simulations were run to determine the plotting position formula that provided the least bias and the distribution of Gumbel percentiles. It was found that among the nine formulas used in this study, the one developed by Hazen had the least bias, whereas the one by Weibull had the highest bias. Moreover, 0.999 percentiles of the Gumbel distribution were found to follow the three-parameter lognormal distribution. Empirical relationships between the estimated parameters of the three-parameter lognormal distribution and sample size are provided in the paper.


Gumbel Beretta–Murakami method Fatigue of cast metals Three-parameter lognormal 


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Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.University of North FloridaJacksonvilleUSA
  2. 2.School of EngineeringUniversity of North FloridaJacksonvilleUSA

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