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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References
W. A. Weibull,Ingenioeruetenskapsahad, Hand. L. No. 141 (1939).
N. R. Mann, R. E. Schaefer, andN. D. Singpurwalla, “Methods for Statistical Analysis of Reliability and Life Data” (Wiley, New York, 1974).
A. De S. Jayatilaka andK. Trustrum,J. Mater. Sci. 12 (1977) 1426.
K. Trustrum andA. De S. Jayatilaka,ibid. 14 (1979) 1080.
R. A. Jeryan, “Ceramics for High Performance Applications”, Vol. II (Brook Hill, Chestnut Hill, Mass., 1978) pp. 35–51.
C. A. Johnson, “Fracture Mechanics of Ceramics”, Vol. 5 (Plenum Press, New York, 1983) pp. 365–86.
T. E. Easler, R. C. Bradt andR. E. Tressler,J. Amer. Ceram. Soc. 64 (1981) c-53.
W. Nelson,Technometrics 14 (4) (1972) 945.
K. Jakus, J. E. Ritter Jr, T. Service andD. Sonderman,J. Amer. Ceram. Soc. 64 (1981) c-174.
L. Johnson, “The Statistical Treatment of Fatigue Experiments” (Elsevier, New York, 1964).
W. Mendenhall, R. Shaeffer andM. Wackerly, “Mathematical Statistics with Applications”, 2nd Edn. (Duxbury Press, Boston, 1981).
J. L. Kuester andJ. H. Mize, “Optimization Techniques with Fortran” (McGraw-Hill, New York, 1973).
C. R. Rao, “Linear Statistical Inference and its Application” (John Wiley, New York, 1965).
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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