DocumentCode :
329731
Title :
Constrained mathematics analysis of uncertain variables
Author :
Cooper, J. Arlin
Author_Institution :
Sandia Nat. Labs., Albuquerque, NM, USA
Volume :
4
fYear :
1998
fDate :
11-14 Oct 1998
Firstpage :
3206
Abstract :
Analyses (e.g., safety analyses and reliability analyses) that are based on variable or uncertain inputs need to reflect the ranges of potential output variability or uncertainty. A challenging problem in mathematically processing the operands is that constraints inherent in the problem definition can require computations that are difficult to implement. Examples of possible constraints are that the sum of the probabilities of partitioned possible outcomes must be one, and repeated appearances of the same variable must all have the identical value. The latter, called the “repeated variable problem” will be addressed in this paper in order to show how range-based probabilistic evaluation of Boolean logic expressions, such as those describing the outcomes of fault trees and event trees, can be facilitated. The results are applicable to fuzzy mathematics, interval analysis, Monte Carlo analysis and other range-based techniques. The problem is important, because unconstrained computations result in wider ranges of outputs than those properly obtained with constrained mathematics. We illustrate techniques that can be used to transform complex constrained problems into trivial problems in most tree logic expressions, and into tractable problems in most other cases. The approach is based on the Boolean logic characteristics of “unateness” and “minimal compactness”, and differential calculus characteristics related to regions of monotonicity. Example problems are used to demonstrate the techniques and the advantages of constrained mathematics
Keywords :
Boolean algebra; Monte Carlo methods; constraint theory; fault trees; fuzzy set theory; probability; uncertain systems; Boolean logic expressions; Monte Carlo analysis; constrained mathematics analysis; differential calculus characteristics; event trees; fault trees; interval analysis; minimal compactness; monotonicity regions; partitioned possible outcomes; potential output variability; probabilities; range-based probabilistic evaluation; reliability analysis; repeated variable problem; safety analysis; tractable problems; tree logic expressions; unateness; uncertain variables; Boolean functions; Calculus; Fault trees; Laboratories; Mathematics; Monte Carlo methods; Probabilistic logic; Safety; Uncertainty; Upper bound;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Systems, Man, and Cybernetics, 1998. 1998 IEEE International Conference on
Conference_Location :
San Diego, CA
ISSN :
1062-922X
Print_ISBN :
0-7803-4778-1
Type :
conf
DOI :
10.1109/ICSMC.1998.726496
Filename :
726496
Link To Document :
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