Comparison of Probability and Possibility for Design Against Catastrophic Failure Under Uncertainty

[+] Author and Article Information
Efstratios Nikolaidis

Mechanical, Industrial and Manufacturing Engineering Department, The University of Toledo, Toledo, OH 43606

Sophie Chen

Aerospace and Ocean Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

Harley Cudney

Applied Research Associates Inc., 415 Waterman Road, South Royalton, VT 05068

Raphael T. Haftka, Raluca Rosca

Department of Aerospace Engineering, Mechanics and Engineering Science, The University of Florida, Gainesville, FL 32611-6250

J. Mech. Des 126(3), 386-394 (Sep 01, 2003) (9 pages) doi:10.1115/1.1701878 History: Received December 01, 2000; Revised September 01, 2003
Copyright © 2004 by ASME
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Thurston,  D. L., 1991, “A Formal Method for Subjective Design Evaluation with Multiple Attributes,” Res. Eng. Des., 3(2), pp. 105–122.
Diaz,  A., 1988, “Goal Aggregation in Design Optimization,” Eng. Optimiz., 13, pp. 257–273.
Wood,  K. L., and Antonsson,  E. K., 1990, “Modeling Imprecision and Uncertainty in Preliminary Engineering Design,” Mech. Mach. Theory, 25(3), pp. 305–324.
Carnahan,  J. V., Thurston,  D. L., and Liu,  T., 1994, “Fuzzying Ratings for Multiattribute Decision-Making,” ASME J. Mech. Des., 116, pp. 511–521.
Wood,  K. L., Antonsson,  E. K., and Beck,  J. L., 1990, “Representing Imprecision in Engineering Design: Comparing Fuzzy and Probability Calculus,” Res. Eng. Des., 1, pp. 187–203.
Keeney, R. L., and Raiffa, H., 1993, Decisions with Multiple Objectives, Cambridge University Press, Cambridge, United Kingdom.
Otto, K. N., and Antonsson, E. K., 1993, “The Method of Imprecision Compared to Utility Theory for Design Selection Problems,” Proceedings of the ASME Design Theory and Methodology Conference.
Thurston,  D. L., and Carnahan,  J. V., 1992, “Fuzzy Ratings and Utility Analysis in Preliminary Design Evaluation of Multiple Attributes,” ASME J. Mech. Des., 114, December.
Maglaras,  G., Nikolaidis,  E., Haftka,  R. T., and Cudney,  H. H., 1997, “Analytical-Experimental Comparison of Probabilistic Methods and Fuzzy Set Based Methods for Designing Under Uncertainty,” Struct. Optim., 13(2/3), April pp. 69–80.
Savage, L. J., 1972, The Foundations of Statistics, 2nd rev. ed., Dover, New York.
Berger, J. O., 1985, Decision Theory and Bayesian Analysis, Springer-Verlag, New York, pp. 109–113.
Ben-Haim, Y., and Elishakoff, I., 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier, Amsterdam.
Melchers, R. E., 1987, Structural Reliability, Analysis and Prediction, Ellis Horwood Limited, West Sussex, England.
Langley,  R. S., 2000, “Unified Approach to Probabilistic and Possibilistic Analysis of Uncertain Systems,” J. Eng. Mech., 126(11), pp. 1163–1172.
Oberkampf, W. L., DeLand, S. M., Rutherford, B. M., Diegert, K. V., and Alvin, K. F., 2000, “Estimation of Total Uncertainty in Modeling and Simulation,” Sandia Report SAND2000-0824, April 2000, Albuquerque, NM.
Chen, S., 2000, “Comparing Probabilistic and Fuzzy Set Approaches for Designing in the Presence of Uncertainties,” Ph.D. thesis, Aerospace and Ocean Engineering Department, Virginia Tech.
Zadeh, L. A., 1978, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems, 1, pp. 3–28. Reprinted in Fuzzy Sets and Applications: Selected Papers by L. A. Zadeh.
Klir, G., and Yuan, G., 1995, Fuzzy Sets and Fuzzy Logic, Prentice Hall, Upper Saddle River, New Jersey.
Shafer, G., 1976, A Mathematical Theory of Evidence, Princeton University Press, Princeton.
Giles, R., 1982, Foundations for a Theory of Possibility, Fuzzy Information and Decision Processes, North-Holland Publishing Company.
Zimmermann, H. J., 1996, Fuzzy Set Theory, Kluwer Academic Publishers, Norwell, Massachusetts.
Sugeno, M., 1977, Fuzzy Measures and Fuzzy Intervals: A Survey, Fuzzy Automata and Decision Processes, Gupta, M. M., Saridis, G. N., and Gaines, B. R., eds., North-Holland, Amsterdam and New York, pp. 89–102.
Nataf,  A., 1962, “Determination des Distribution dont les Marges sont Donnees,” Comptes Rendus de l’Academie des Sciences, 225, pp. 42–43.
Der Kiureghian,  A., and Liu,  P.-L., 1986, “Structural Reliability Under Incomplete Information,” J. Eng. Mech., 112(1), pp. 85–104.
Der Kiureghian, A., and Liu, P-L., 1985, “Structural Reliability Under Incomplete Probability Information,” Division of Structural Engineering and Mechanics, University of California at Berkeley, Report No. CEE-8205049.
Dong,  W., and Shah,  H. C., 1987, “Vertex Method for Computing Functions of Fuzzy Variables,” Fuzzy Sets Syst., 24, pp. 65–78.
Ochi, M. K., 1990, Applied Probability and Stochastic Processes in Engineering and Physical Sciences, Wiley, New York.
Ben-Haim, Y., 1996, Robust Reliability in the Mechanical Sciences, Springer-Verlag, Berlin.
Chen, S., Nikolaidis, E., Cudney, H. H., Rosca, R., and Haftka, R. T., 1999, “Comparison of Probabilistic and Possibility-Based Methods for Design Under Uncertainty,” 40th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, San Louis, Missouri.


Grahic Jump Location
Probability density of X, for the statement “X is between 8 and 12” and possibility distribution of X
Grahic Jump Location
Comparison of possibility distribution function and probability density function
Grahic Jump Location
The probabilistic model with the inflated range of frequencies underestimates the probability of failure
Grahic Jump Location
Exemplification of the differences in design philosophies of possibility and probability theory
Grahic Jump Location
Comparison of ten probabilistic designs (black) and ten possibility-based designs (gray). Models of uncertainties were constructed from three samples.




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