Dependability Modelling under Uncertainty: An Imprecise by Philipp Limbourg

By Philipp Limbourg

Mechatronic layout strategies became shorter and extra parallelized, prompted by way of growing to be time-to-market strain. tools that permit quantitative research in early layout levels are required, may still dependability analyses goal to steer the layout. end result of the constrained quantity of information during this part, the extent of uncertainty is excessive and particular modeling of those uncertainties turns into necessary.

This paintings introduces new uncertainty-preserving dependability tools for early layout levels. those contain the propagation of uncertainty via dependability versions, the activation of knowledge from related elements for analyses and the combination of doubtful dependability predictions into an optimization framework. it really is proven that Dempster-Shafer conception should be a substitute for chance thought in early layout degree dependability predictions. professional estimates may be represented, enter uncertainty is propagated in the course of the procedure and prediction uncertainty might be measured and interpreted. The ensuing coherent method could be utilized to symbolize the uncertainty in dependability models.

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Examples for the family of Archimedean copulas are the Frank [61] and the Mardia copula [116]. Archimedean copulas are popular in case of two variables, but can’t be readily extended to the multivariate case [113]. The most commonly used copula for more than two dimensions is the Gaussian copula. Its big advantage is the easy communicability. The set of parameters for estimating the dependencies is a n × n correlation matrix ρ . 20) −1 is an inverse standard normal distribution (mean zero, standard deviation 1) and FGauss n,ρ FGauss a multivariate standard normal distribution with correlation matrix ρ .

Of course, the coin follows a distribution and if multiple throws were carried out, evidence would grow. 4. However, before doing so, there is no evidence for assuming any possible distribution without neglecting that reality may be anywhere else. Hence, epistemic uncertainty is the inability to model reality. Epistemic uncertainties occur in small or large amounts in almost all system dependability models, especially in EDS. ) are excessive and pose constraints to the project. 2). While the application of probability theory is the reasonable choice for modeling aleatory uncertainties, this is not necessarily the case for epistemic quantities.

3) P(X ∈ x) = ∑ m(x) x∈x As a special case of eq. 3, the cumulative distribution function (CDF) F(x) := P(X ≤ x) is completely determined by m. In the discrete probability representation, a mass is defined for each possible value of x ∈ X (eq. 2). Dempster-Shafer mass functions on the real line are similar to discrete distributions with one important difference. The probability mass function is not a mapping m : X → [0, 1] but instead a mapping m : P(X) → [0, 1], where masses are assigned to subsets of X instead of elements in X.

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