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On Estimating Largest Defects in Castings

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Shape Casting

Part of the book series: The Minerals, Metals & Materials Series ((MMMS))

Abstract

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.

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Author information

Authors and Affiliations

  1. University of North Florida, Jacksonville, FL, 32224, USA

    Murat Tiryakioğlu

  2. School of Engineering, University of North Florida, Jacksonville, FL, 32224, USA

    Irisi Nini

Authors
  1. Murat Tiryakioğlu
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  2. Irisi Nini
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Corresponding author

Correspondence to Murat Tiryakioğlu .

Editor information

Editors and Affiliations

  1. University of North Florida, Jacksonville, FL, USA

    Murat Tiryakioğlu

  2. University of Birmingham, Birmingham, UK

    William Griffiths

  3. Cranfield University, Cranfield, UK

    Mark Jolly

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© 2019 The Minerals, Metals & Materials Society

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Tiryakioğlu, M., Nini, I. (2019). On Estimating Largest Defects in Castings. In: Tiryakioğlu, M., Griffiths, W., Jolly, M. (eds) Shape Casting. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-030-06034-3_11

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