RAMAS Risk Calc 4.0 Software: Risk Assessment with Uncertain Numbers

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Sign in. Get my own profile Cited by View all All Since Citations h-index 48 27 iindex Co-authors View all Lev R. Confidence bands for cumulative distribution functions of continuous random variables - Cheng, Iles - Response surface methodology—current status and future directions - Myers - Correlations, dependency bounds and extinction risks. Biological Conservation - Ferson, Burgman - A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Analysis 7 1 - Iman - An examination of response surface methodologies for uncertainty analysis in assessment models - Downing, Gardner, et al.

Distribution-free and other prediction intervals - Konijn - Response Surface Methodology - Morton - Varying correlation coefficients can underes-timate uncertainty in probabilistic models. Reliability Engineering - Ferson, Hajagos - An approach to the construction of parametric confidence bands on cumulative distribution functions - Kanofsky, Srinivasan.

Probability Theory, edited by L. Bretthorst - Jaynes. The uniformity principle: a new tool for probabilistic robustness control - Barmish, Lagoa - Condence band estimations for distributions used in probabilistic design - Cheng, Evans, et al.

Environmental Protection Agency]. Pages in Sensitivity Analysis, edited by - Helton, Davis. Conceptual basis of a systems prioritization methodology for the Waste Isolation Pilot Plant. Competing failure risk analysis using evidence theory.

Risk Analysis 25 - b. Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links. Reliability Engineering and System Safety - a.

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A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. The use of logistic regression in sensitivity analysis of population viability models. Confidence bands for quantile functions: a parametric and graphic alternative for testing goodness of fit.

The American Statistician 54 - Rosenkrantz. Global sensitivity analysis: novel settings and methods. Pages 71ff - Saltelli. Tonon a. Tonon b. They include ordinary scalar numbers and intervals as special cases. Fuzzy set theory is also used in other areas of science and engineering, including, for instance, fuzzy cluster analysis and fuzzy control theory. In particular, fuzzy arithmetic is a proper subset of possibility theory which handles general fuzzy sets of the real numbers which could be multimodal or might not reach unity called possibility distributions.

When is fuzzy arithmetic better than analogous Monte Carlo methods? There are several reasons why one might be interested in using fuzzy methods. Consider the following list. Reasons to use fuzzy arithmetic. Fuzzy arithmetic requires less data. The following table indicates the requirements for various methods of uncertainty propagation. Fuzzy arithmetic is applicable to all kinds of uncertainty, no matter what its source or nature. Although probability theory makes a similar claim, one is required to adopt a subjectivist interpretation of probability to get this generality. I believe that a subjectivist interpretation is inappropriate for public health risk assessments.

If you disallow subjectivism, then Monte Carlo methods cannot be used on all forms of uncertainty and using them anyway can lead to non-protective conclusions. Fuzzy arithmetic is more general because it is a weaker theory. Like Monte Carlo methods, fuzzy arithmetic provides a comprehensive distribution that characterizes results of all possible magnitudes, rather than just specifying upper or lower bounds. For this reason it should be preferred over worst case or interval analysis.

Fuzzy methods are fast and easy to compute. Fuzzy arithmetic is more conservative than Monte Carlo simulations that assume independence. Although many analysts seem to believe it is okay to assume all the input variables are independent of one another, it is easy to show this is false and can have a substantial effect on the results of a risk assessment. Although there are Monte Carlo methods that can be used when correlations are known, such empirical information is often unavailable. Although conservative, fuzzy arithmetic is not hyperconservative like worst case or interval analysis.

In this sense, fuzzy arithmetic is in between worst case and probability theory.

RAMAS Risk Calc 4.0 Software: Risk Assessment with Uncertain Numbers

In fuzzy arithmetic, deconvolutions which are required for back-calculations and remediation planning are easy to solve. Deconvolutions are generally pretty difficult or even impossible with Monte Carlo methods. Fuzzy arithmetic is easy to explain to lay people.


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Well, easier than probability theory anyway. It is just interval analysis done at many levels of confidence about uncertainty. Reasons not to use fuzzy arithmetic. The following are serious concerns about using the method.

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Fuzzy methods are controversial. Many probabilists insist that they are errant or incorrect.

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The alpha levels which index fuzziness may not be comparable for different variables. It makes sense that my best estimate of A at, say, the top of a triangular fuzzy number ought be arithmetically combined with my best estimate of B. It also seems to make some sense that my most conservative estimates of A and B, at the bottoms of the fuzzy numbers, should be combined together. What if the two fuzzy numbers were measured by different people who had different opinions about uncertainty? Fuzzy arithmetic does not yield conservative results when the dependencies among variables are unknown.

Projecting uncertainty through black boxes (2008)