This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
Probability Bounds Analysis as a General Approach to Sensitivity Analysis in Decision Making Under Uncertainty
Technical Paper
2007-01-1480
ISSN: 0148-7191, e-ISSN: 2688-3627
Annotation ability available
Sector:
Language:
English
Abstract
Engineers often perform sensitivity analyses to explore how changes in the inputs of a physical process or a model affect the outputs. This type of exploration is also important for the decision-making process. Specifically, engineers may want to explore whether the available information is sufficient to make a robust decision, or whether there exists sufficient uncertainty-i.e., lack of information-that the optimal solution to the decision problem is unclear, in which case it can be said to be sensitive to information state. In this paper, it is shown that an existing method for modeling and propagating uncertainty, called Probability Bounds Analysis (PBA), actually provides a general approach for exploring the global sensitivity of a decision problem that involves both probabilistic and imprecise information. Specifically, it is shown that PBA conceptually generalizes an approach to sensitivity analysis suggested in the area of decision analysis. The global nature of the analysis theoretically guarantees that the decision maker will identify any sensitivity in the formulated problem and information state. However, a tradeoff is made in the numerical implementation of PBA; a particular existing implementation that preserves the guarantee of identifying existing sensitivity is overly conservative and can result in “false alarms.” The use of interval arithmetic in sensitivity analysis is discussed, and additional advantages and limitations of PBA as a sensitivity analysis tool are identified.
Authors
Citation
Aughenbaugh, J. and Paredis, C., "Probability Bounds Analysis as a General Approach to Sensitivity Analysis in Decision Making Under Uncertainty," SAE Technical Paper 2007-01-1480, 2007, https://doi.org/10.4271/2007-01-1480.Also In
Reliability and Robust Design in Automotive Engineering, 2007
Number: SP-2119; Published: 2007-04-16
Number: SP-2119; Published: 2007-04-16
SAE 2007 Transactions Journal of Passenger Cars: Mechanical Systems
Number: V116-6; Published: 2008-08-15
Number: V116-6; Published: 2008-08-15
References
- Ferson, S. Donald, S. 1998 “Probability Bounds Analysis,” Probabilistic Safety Assessment and Management Mosleh, A. Bari, R. A. Springer-Verlag New York, NY 1203 1208
- Howard, R. A. 1968 “Foundations of Decision Analysis,” IEEE Transactions on Systems Science and Cybernetics 211 219
- Clemen, R. T. 1996 Making Hard Decisions: An Introduction to Decision Analysis Second Duxbury Press New York
- Howard, R. A. 1988 “Decision Analysis: Practice and Promise,” Management Science 34 6 679 695
- Matheson, J. E. Howard, R. A. 1988 “An Introduction to Decision Analysis,” Readings on the Principles and Applications of Decision Analysis Howard, R. A. Matheson, J. E. Strategic Decisions Group I 17 55
- Ferson, S. Tucker, W. T. 2006 “Sensitivity Analysis Using Probability Bounding,” Reliability Engineering & System Safety 91 10-11 1435 1442
- Ferson, S. Tucker, W. T. 2006 “Sensitivity in Risk Analyses with Uncertain Numbers,” Sandia National Laboratories Albuquerque, NM http://www.ramas.com/sensanal.pdf
- Aughenbaugh, J. M. Duncan, S. Paredis, C. J. J. Bras, B. A. 2006 “A Comparison of Probability Bounds Analysis and Sensitivity Analysis in Environmentally Benign Design and Manufacture,” ASME 2006 International Design Engineering Technical Conferences, Design Automation Conference ASME Philadelphia, PA
- Nikolaidis, E. 2005 “Types of Uncertainty in Design Decision Making,” Engineering Design Reliability Handbook Nikolaidis, E. Ghiocel, D. M. Singhal, S. CRC Press New York
- Aughenbaugh, J. M. Paredis, C. J. J. 2006 “Why Are Intervals and Imprecision Important in Engineering Design?” Reliable Engineering Computing Workshop Savannah, GA, USA
- Aughenbaugh, J. M. Paredis, C. J. J. 2006 “The Value of Using Imprecise Probabilities in Engineering Design,” Journal of Mechanical Design 128 4 969 979
- Walley, P. 1991 Statistical Reasoning with Imprecise Probabilities Chapman and Hall New York
- Shafer, G. 1976 A Mathematical Theory of Evidence Princeton University Press Princeton, NJ
- Hart, A. G. 1942 “Risk, Uncertainty and the Unprofitability of Compounding Probabilities,” Studies in Mathematical Economics and Econometrics Lange, O. Mcintyre, F. Yntema, T. O. University of Chicago Press Chicago
- Levi, I. 1974 “On Indeterminate Probabilities,” Journal of Philosophy 71 391 418
- Tintner, G. 1941 “The Theory of Choice under Subjective Risk and Uncertainty,” Econometrica 9 298 304
- Good, I. J. 1983 Good Thinking: The Foundations of Probability and Its Applications University of Minnesota Press Minneapolis
- Kyburg, H. E. 1987 “Objective Probabilities,” IJCAI-87 902 904
- Sarin, R. K. 1978 “Elicitation of Subjective Probabilities in the Context of Decision-Making,” Decision Sciences 9 37 48
- Weichselberger, K. 2000 “The Theory of Interval-Probability as a Unifying Concept for Uncertainty,” International Journal of Approximate Reasoning 24 2-3 149 170
- Berleant, D. 1993 “Automatically Verified Reasoning with Both Intervals and Probability Density,” Interval Computations 2 48 70
- Berleant, D. Goodman-Strauss, C. 1998 “Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals,” Reliable Computing 4 2 147 165
- Yager, R. R. 1986 “Arithmetic and Other Operations on Dempster-Shafer Structures,” International Journal of Man-Machine Studies 25 357 366
- Ling, J. M. Aughenbaugh, J. M. Paredis, C. J. J. 2006 “Managing the Collection of Information under Uncertainty Using Information Economics,” Journal of Mechanical Design 128 4 980 990
- Ferson, S. 2002 “RAMAS Risk Calc 4.0 Software: Risk Assessment with Uncertain Numbers,” Lewis Publishers Boca Raton, Florida
- Williamson, R. C. Downs, T. 1990 “Probabilistic Arithmetic I: Numerical Methods for Calculating Convolutions and Dependency Bounds” “International Journal of Approximate Reasoning 4 89 158
- Moore, R. E. 1979 Methods and Applications of Interval Analysis Society for Industrial and Applied Mathematics Philadelphia
- Bruns, M. Paredis, C. J. J. 2006 “Numerical Methods for Propagating Imprecise Uncertainty,” ASME 2006 International Design Engineering Technical Conferences and Computers in Information Engineering Conference Philadelphia, PA
- Leamer, E. E. 1990 “Sensitivity Analysis Would Help.,” Modelling Economic Series Granger, C. W. J. Clarendon Press Oxford
- Frey, H. C. Patil, S. R. 2002 “Identification and Review of Sensitivity Analysis Methods,” Risk Analysis 22 3 553 578
- Liu, H. Chen, W. 2006 “Relative Entropy Based Method for Probabilistic Sensitivity Analysis in Engineering Design,” Journal of Mechanical Design 128 326 336
- Felli, J. C. Hazen, G. B. 2004 “Javelin Diagrams: A Graphical Tool for Probabilistic Sensitivity Analysis,” Decision Analysis 1 2 93 107
- Homma, T. Saltelli, A. 1996 “Importance Measures in Global Sensitivity Analysis of Nonlinear Models,” Reliability Engineering & System Safety 52 1 17
- Sobol, I. M. 2001 “Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates,” Mathematics and Computers in Simulation 55 271 280
- Chen, W. Jin, R. Sudjianto, A. 2004 “Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design under Uncertainty,” ASME 2005 International Design Engineering Technical Conferences Salt Lake City, UT, USA
- von Holstein, C.-A. S. S. 1983 “A Tutorial in Decision Analysis,” Readings on the Principles and Applications of Decision Analysis Howard, R. A. Matheson, J. E. Strategic Decisions Group I 131 157
- Howard, R. A. 1983 “The Science of Decision-Making,” Readings on the Principles and Applications of Decision Analysis Howard, R. A. Matheson, J. E. Strategic Decisions Group I 161 176
- Eschenbach, T. G. 1992 “Spiderplots Versus Tornado Diagrams for Sensitivity Analysis,” Interfaces 22 6 40
- Moore, R. E. 1966 Interval Analysis Prentice-Hall Englewood Cliffs, NJ
- Hall, J. W. 2006 “Uncertainty-Based Sensitivity Indices for Imprecise Probability Distributions,” Reliability Engineering & System Safety 91 10-11 1443 1451
- Klir, G. 2006 Uncertainty and Information: Foundations of Generalized Information Theory Wiley-Interscience Hoboken, NJ
- Ferson, S. Kreinovich, V. Ginzburg, L. Myers, D. S. Sentz, K. 2002 “Constructing Probability Boxes and Dempster-Shafer Structures,” Sandia National Laboratories Albuquerque, New Mexico