Fundamentals of the Dempster-Shafer theory and its applications to system safety and reliability modelling
Journal of Polish Safety and Reliability AssociationPublished 1 January 2007
Rakowsky Uwe Kay
Citations45
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
This contribution shows how to apply the calculus to safety and reliability modelling, especially to expert judgement; Failure Modes, Effects, and Criticality Analysis; Event Tree Analysis, Fault Tree analysis, and Reliability Centred Maintenance.
Abstract
The Dempster-Shafter Theory is well-known for its usefulness to express uncertain judgments of experts. This contribution shows how to apply the calculus to safety and reliability modelling, especially to expert judgement; Failure Modes, Effects, and Criticality Analysis; Event Tree Analysis, Fault Tree Analysis, and Reliability Centred Maintenance. Including a tutorial introduction to the Dempster-Shafer Theory, the differences between the Probability and the Dempster-Shafer Theory are discussed widely.
Keywords
Computer ScienceDecision SciencesEngineering
Studies in fuzziness and soft computingUpper and Lower Probabilities Induced by a Multivalued Mapping
5,299 Citations2008Arthur P. Dempster
A distinctive feature of the present approach is a rule for conditioning, or more generally, arule for combining sources of information, as discussed in Sects.
European Journal of Operational ResearchFuzzy sets, uncertainty, and information
3,193 Citations1989
The fuzzy sets uncertainty and information is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Artificial IntelligenceThe transferable belief model
2,165 Citations1994Philippe Smets, Robert Kennes
Studies in fuzziness and soft computingA Generalization of Bayesian Inference
1,722 Citations2008Arthur P. Dempster
Procedures of statistical inference are described which generalize Bayesian inference in specific ways and some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures.
Elsevier eBooksCognitive Reliability and Error Analysis Method (CREAM)
1,099 Citations1998
This book discusses the role of HRA in PSA, the need for HRA, and the need to Predict, as well as some of the principles of Predictive Use of the Classification Scheme.
Constructing Probability Boxes and Dempster-Shafer Structures
732 Citations2003Scott Ferson, VLADIK KREINOVICK +2 more
A variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge are summarized.
The Annals of Mathematical StatisticsNew Methods for Reasoning Towards Posterior Distributions Based on Sample Data
196 Citations1966A. P. Dempster
IEEE ExpertUncertainty management in expert systems
167 Citations1990K.-C. Ng, Bruce Abramson
The focus is on subjective probability theory, Dempster-Shafer theory, and possibility theory, although a number of other methods are mentioned.
International Journal of Approximate ReasoningReasoning with imprecise belief structures
167 Citations1999Thierry Denœux
This paper extends the theory of belief functions by introducing new concepts and techniques, allowing to model the situation in which the beliefs held by a rational agent may only be expressed (or are only known) with some imprecision.
Information SciencesGeneralized probabilities of fuzzy events from fuzzy belief structures
161 Citations1982Ronald R. Yager
Under the condition of Bayesian belief structure a whole family of possible definitions for the probability of fuzzy sets is obtained and a procedure for including belief qualification in pruf is suggested.
Studies in fuzziness and soft computingNew Methods for Reasoning Towards Posterior Distributions Based on Sample Data
149 Citations2008Arthur P. Dempster
This paper redefines the concept of sampling from a population with a given parametric form and thus leads up to some proposed alternatives to the existing Bayesian and fiducial arguments for deriving posterior distributions.
Some qualitative approaches to applying the Dempster-Shafer theory
51 Citations1994Simon Parsons
Reliability Engineering & System SafetyModeling of uncertainties in reliability centered maintenance — a probabilistic approach
49 Citations2001Siegfried Eisinger, Uwe K. Rakowsky
An alternative approach, opening for specified uncertainties is shown to correct this defect, and a simple fire detection system is discussed.
IEEE Transactions on ReliabilityA probabilistic foundation for vagueness and imprecision in fault-tree analysis
47 Citations1991Michael A. S. Guth
A theoretical framework, based on Dempster-Shafer theory (DST), that accommodates vagueness and shows how imprecision can give rise to false-negative and false-positive inferences is proposed.
Journal of Applied Science and EngineeringUncertainties in Fault Tree Analysis
25 Citations2000Yue-Lung Cheng