Calculation of Weibull life expectancy parameters from fracture data using the maximum likelihood criterion and a NeIder-Mead simplex minimisation algorithm

  • Etienne Brauns VITO (Vlaamse Instelling voor Technologisch Onderzoek)
  • Johan Patyn VITO (Vlaamse Instelling voor Technologisch Onderzoek)

Abstract

This paper describes a mathematical technique to calculate the model parameters for a classical Weibull statistic. This type of statistic can be applied in a number of life time expectancy problems. A typical example is the brittle behaviour of components produced from technical ceramics. A NeIder-Mead simplex algorithm is introduced to obtain the Weibull parameters using the maximum likelihood criterion . Program code for a Matlab for Windows environment is presented.


 

Keywords

References

[1] G.J . De Salvo, R.M. Stanchik, J.W. Fisch. Theory and structural design applications of Weibull statistics. WANL-TME-2688, NERVA Research and Development Report, Westinghouse Electric Corporation, Astronuclear Laboratory, Pittsburgh, Pennsylvania, 1970.
[2] N.N. Nemeth, J.N. Manderscheid, J.P. Gyekenyesi. Ceramics analysis and reliability evaluation of structures (CARES). NASA Technical Paper 2916. Lewis Research Center, Cleveland, Ohio, August 1990.
[3] J.A. NeIder, R. Mead. A simplex method for function minimization. Computer Journal, 7: 308-313, 1964.
[4] R. Danzer. Ceramics: Mechanical performance and lifetime prediction. In: R.W. Cahn (ed.), Encyclopedia of Material Science and Engineering, Supplementary Volume 3, 1557-1570. University of Cambridge, Pergamon Press, 1993.
[5] R. Morrell. Advanced technical ceramics - Monolithic ceramics - Mechanical tests at room temperature - Part 5: Statistical analysis. European Pre-standard ENV 843-5. CEN (Comite Europeen de Normalisation), Brussels (to be announced).
Published
Jul 17, 2023
How to Cite
BRAUNS, Etienne; PATYN, Johan. Calculation of Weibull life expectancy parameters from fracture data using the maximum likelihood criterion and a NeIder-Mead simplex minimisation algorithm. Computer Assisted Methods in Engineering and Science, [S.l.], v. 3, n. 1, p. 37-43, july 2023. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1462>. Date accessed: 14 nov. 2024.
Citation Formats
Issue
Vol 3 No 1 (1996)
Section
Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.