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Maximum likelihood estimation techniques for concurrent flaw subpopulations

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Abstract

Failure of structural materials is often caused by the presence of two or more types of defect subpopulations. The maximum likelihood estimation technique for evaluating the Weibull parameters of these underlying subpopulations in the case of known fracture origin is presented. The maximum likelihood estimation equations are derived, and solved by means of nonlinear programming. The estimators obtained therefrom are tested for both accuracy and consistency against a series of simulation runs. For data sets containing a relatively small sample size, the advantage of the method of maximum likelihood over two established nonparametric techniques is demonstrated.

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Authors and Affiliations

  1. School of Engineering, University of Massachusetts, Amherst, Massachusetts, USA

    D. Sonderman, K. Jakus, J. E. Ritter Jr, S. Yuhaski Jr & T. H. Service

Authors
  1. D. Sonderman
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  2. K. Jakus
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  3. J. E. Ritter Jr
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  4. S. Yuhaski Jr
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  5. T. H. Service
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Sonderman, D., Jakus, K., Ritter, J.E. et al. Maximum likelihood estimation techniques for concurrent flaw subpopulations. J Mater Sci 20, 207–212 (1985). https://doi.org/10.1007/BF00555914

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  • DOI: https://doi.org/10.1007/BF00555914

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