Quantification of Margins and Mixed Uncertainties Using Evidence Theory and Stochastic Expansions

Shah, Harsheel R.; Hosder, Serhat; Winter, Tyler

doi:10.2514/6.2014-0300

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…The DST defines three quantities that are the basic belief assignment (bba), also known as basic probability assignment or mass of belief, the belief (Bel) and the plausibility (Pl). The bba is the amount of knowledge associated with every subset ɛ i ∈ 2 Ω and it is denoted by bba(ɛ i ) [28,42]. It measures the belief exactly assigned to ɛ i and represents how strongly the evidence supports ɛ i .…”

Section: Theoretical Elementsmentioning

confidence: 99%

Assessment method of the multicomponent systems future ability to achieve productive tasks from local prognoses

González

Desforges

Archimède

2018

Reliability Engineering & System Safety

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Conditioned-based maintenance and prognostics and health management enable to optimize maintenance by scheduling the necessary repairs and replacements of technical system components according to their present and future health states. The assessment of future health states is the prognostics and health management keystone. Many technical production systems are made of numerous components implementing their functions. A method to assess the ability of multicomponent systems to carry out future production tasks is proposed to provide decision supports for production and maintenance planning for a better compromise between their objectives. It is based on components prognoses. To handle inherent uncertainties of these prognoses, the method is based on the Dempster Shafer theory and Bayesian networks inferences. Local prognoses are categorized and transformed to be compliant to Dempster Shafer theory. Patterns of systems are identified for which inferences are defined. The patterns are then used to model systems and to assess their abilities to achieve future tasks. An identification of components that should first undergo maintenance is proposed. An example implementing a fictitious complex systems is presented to show how the provided decision supports can be used for production and maintenance planning purposes.

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Section: Theoretical Elementsmentioning

confidence: 99%

Assessment method of the multicomponent systems future ability to achieve productive tasks from local prognoses

González

Desforges

Archimède

2018

Reliability Engineering & System Safety

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“…The Demspter-Shafer mathematical theory of evidence collates information from various sources and helps an individual reach a degree of belief that takes into consideration all of the available evidence (Maseleno et al 2015). Evidence theory has been applied to human reliability assessment (Su et al 2015), information fusion (Li et al 2017), reliability analysis (Zhang et al 2015, Tang et al 2015a), complex engineering systems (Shah et al 2015), and in aeronautics (Tang et al 2015b).…”

Section: Literature Reviewmentioning

confidence: 99%

The Hurwicz Decision Rule’s Relationship to Decision Making with the Triangle and Beta Distributions and Exponential Utility

Sivaprasad

MacKenzie

2018

Decision Analysis

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Non-probabilistic approaches to decision making have been proposed for situations in which an individual does not have enough information to assess probabilities over an uncertainty. One non-probabilistic method is to use intervals in which an uncertainty has a minimum and maximum but nothing is assumed about the relative likelihood of any value within the interval. The Hurwicz decision rule in which a parameter trades off between pessimism and optimism generalizes the current rules for making decisions with intervals. This article analyzes the relationship between intervals based on the Hurwicz rule and traditional decision analysis using a few probability distributions and an exponential utility functions. This article shows that the Hurwicz decision rule for an interval is logically equivalent to: (i) an expected value decision with a triangle distribution over the interval; (ii) an expected value decision with a beta distribution; and (iii) an expected utility decision with constant absolute risk aversion with a uniform distribution. These probability distributions are not exhaustive. There are likely other distributions and utility functions for which equivalence with the Hurwicz decision rule can also be established. Since a frequent reason for the use intervals is that intervals assume less information than a probability distribution, the results in this article call into question whether decision making based on intervals really assumes less information than subjective expected utility decision making.Abstract Non-probabilistic approaches to decision making have been proposed for situations in which an individual does not have enough information to assess probabilities over an uncertainty. One nonprobabilistic method is to use intervals in which an uncertainty has a minimum and maximum but nothing is assumed about the relative likelihood of any value within the interval. The Hurwicz decision rule in which a parameter trades off between pessimism and optimism generalizes the current rules for making decisions with intervals. This article analyzes the relationship between intervals based on the Hurwicz rule and traditional decision analysis using a few probability distributions and an exponential utility functions.This article shows that the Hurwicz decision rule for an interval is logically equivalent to: (i) an expected value decision with a triangle distribution over the interval; (ii) an expected value decision with a beta distribution; and (iii) an expected utility decision with constant absolute risk aversion with a uniform distribution. These probability distributions are not exhaustive. There are likely other distributions and utility functions for which equivalence with the Hurwicz decision rule can also be established. Since a frequent reason for the use intervals is that intervals assume less information than a probability distribution, the results in this article call into question whether decision making based on intervals really assumes less information than subjective expected utility decisio...

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“…The belief and the plausibility are very interesting because they are respectively the lowest and the highest value of the probability of the item Sxj [23,24].…”

Section: ) Plausibility and Beliefmentioning

confidence: 99%

Towards a generic prognostic function of technical multi-component systems taking into account the uncertainties of the predictions of their components

Gonzalez¹,

Desforges²,

Archimède³

2017

2017 4th International Conference on Control, Decision and Information Technologies (CoDIT)

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This article presents the first elements of a generic function that assesses the capacity of technical multi-component systems to accomplish the assigned productive tasks from production planning. This assessment is based on the prognostics of their components. It must so be able to process inaccuracies and uncertainties of these prognostics. For its implementation the aimed function combines the Dempster-Shafer theory combined and Bayesian inferences. The paper presents the multicomponent system modeling and the inferences for the different identified structures as well as a general algorithm. The final aim of the proposed generic function is to compute decision supports for cooperative maintenance and production management.

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Quantification of Margins and Mixed Uncertainties Using Evidence Theory and Stochastic Expansions

Cited by 5 publications

References 25 publications

Assessment method of the multicomponent systems future ability to achieve productive tasks from local prognoses

Assessment method of the multicomponent systems future ability to achieve productive tasks from local prognoses

The Hurwicz Decision Rule’s Relationship to Decision Making with the Triangle and Beta Distributions and Exponential Utility

Towards a generic prognostic function of technical multi-component systems taking into account the uncertainties of the predictions of their components

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