List of uncertainty propagation software

List of uncertainty propagation software used to perform propagation of uncertainty calculations:

Software

• ASUE Potent web interface powered by webMathematica to evaluate uncertainty symbolically using GUM. Webpage also allows symbolic uncertainty evaluation via ASUE framework (with reference), which is an extension to GUM framework
• Dempster Shafer with Intervals (DSI) Toolbox is a MATLAB toolbox for verified computing under Dempster–Shafer theory. It provides aggregation rules, fast (non) monotonic function propagation, plots of basic probability assignments, verified fault tree analysis (FTA), and much more.
• EasyGraph is a graphing package that supports error propagation directly into the error bars.
• Epc error propagating calculator (Epc) is an open source script based tool that calculates the propagation of errors in variables. To quote the text on the Epc web page "This is done by repeated calculation of the expression using variable-values which are generated using a random number generator whose mean and standard-deviation match the values specified for the variable".
• Error Calculator Free/libre cross-platform calculator with minimalist interface. Designed for use in practical courses at natural sciences. Exposes all formulae needed to calculate the results, interoperability with office, support for physical quantities with units.
• Error Propagation Calculator Free cross-platform calculator (macOS, Windows, Linux) written in Python. Essentially a GUI interface for the Python Uncertainties library. Easy to use and install.
• ErrorCalc is a scientific calculator app for iPhone or iPad that performs error propagation (Supports Algebraic and RPN modes of entry)
• FuncDesigner
• GUMsim is a Monte Carlo simulator and uncertainty estimator for Windows
• GUM Tree is a design pattern for propagating measurement uncertainty. An implementation exists in R and add-ons for Excel (real and complex numbers).
• GUM Tree Calculator is a programmable Windows command-line tool with full support for uncertainty calculations involving real and complex quantities.
• GUM Workbench implements a systematic way to analyze an uncertainty problem for single and multiple results. GUM + Monte Carlo. Free restricted educational version available.
• The Gustavus propagator is an open source calculator that supports error propagation developed by Thomas Huber.
• The laffers.net propagator is a web based tool for propagating errors in data. The tool uses the standard methods for propagation.
• Mathos Core Library Uncertainty package Open source (.NET targeting library).
• MC-Ed is a native Windows software to perform uncertainty calculations according to the Supplement 1 to the Guide to the expression of uncertainty in measurement using Monte-Carlo method.
• Measurements.jl is a free and open-source error propagation calculator and library. It supports real and complex numbers with uncertainty, arbitrary-precision arithmetic calculations, functional correlation between variables, and mathematical and linear algebra operations with matrices and arrays.
• Metas.UncLib is a C# software library. A MATLAB wrapper exists. It supports: multivariate uncertainties, complex values, correlations, vector, and matrix algebra.
• MUSE Measurement Uncertainty Simulation and Evaluation using the monte carlo method.
• OpenCOSSAN is a MATLAB toolbox for uncertainty propagation, reliability analysis, model updating, sensitivity and robust design optimization. Allows interacting with 3rd party solvers. Interfaces with HPC through GridEngine and OpenLava.
• OpenTURNS is a C++ and Python framework for probabilistic modelling and uncertainty management developed by the OpenTURNS consortium (Airbus, EDF R&D, IMACS, Phimeca). It contains state of the art algorithms for univariate, multivariate and infinite dimensional probabilistic modelling (arithmetic of independent random variables, copulas, Bayesian models, stochastic processes and random fields), Monte Carlo simulation, surrogate modelling (Kriging, functional chaos decomposition, low rank tensor approximation, Karhunen-Loeve decomposition, mixture of experts), rare event estimation (variance reduction, FORM/SORM reliability methods), robust optimization, global sensitivity analysis (ANCOVA, Sobol' indices). It can interact with third party software through a generic Python interface, which also allows to connect HPC facilities.
• QMSys GUM is a potent commercial tool for measurement uncertainty analysis including Monte Carlo simulation for Windows (free restricted educational version available).
• Risk Calc supports probability bounds analysis, standard fuzzy arithmetic, and classical interval analysis for conducting distribution-free or nonparametric risk analyses.
• SmartUQ is a commercial uncertainty quantification and analytics software package. Capabilities include DOE generation, emulator construction, uncertainty propagation, sensitivity analysis, statistical calibration, and inverse analysis.
• SOERP implements second-order error propagation as a free Python library. Calculations are carried out naturally in calculator format and correlations are maintained.
• SCaViS is a free data-analyais program written in Java and supports Python and Groovy.
• The Uncertainty Calculator is a JavaScript browser-based calculator that performs error propagation calculations.
• Uncertainties is a potent free calculator and Python software library for transparently performing calculations with uncertainties and correlations.
• Mathos Laboratory Uncertainty Calculator This is a web interface for uncertainty calculations.
• UQLab is a software framework for uncertainty quantification developed at ETH Zurich. It is a general-purpose software running in MATLAB which contains state-of-the-art methods for Monte Carlo simulation, dependence modelling (copula theory), surrogate modelling (polynomial chaos expansions, Kriging (a.k.a Gaussian process modelling), low-rank tensor approximations, global sensitivity analysis (ANOVA, Sobol’ indices, distribution-based indices), rare event simulation (a.k.a. reliability methods).

Comparison

Name	Creator	License	Programming language	Handles correlations?	Cross-platform?	Calculator?	Library?	Remarks
ASUE	TC-32 - Fault Tolerant Measurement Systems	Free	Mathematica	No	Yes	Yes	No	Potent web interface powered by webMathematica to evaluate uncertainty symbolically using GUM. Webpage also allows symbolic uncertainty evaluation via ASUE framework (with reference), which is an extension to the GUM uncertainty propagation framework.
Error Propagation Calculator	R. Paul Nobrega	Free	Python	Yes	Yes	Yes	No	Desktop calculator (Windows, macOS, Linux), handles up to 26 variable and error pairs per computation. Evaluates native python expressions. No prior knowledge of python language is required for use. Windows installer includes python dependencies.
Abacus	Mischa Megens	Free	C, Win32	Yes	No	Yes	No	Desktop calculator (Windows), handles multiple expressions
App::ErrorCalculator	Steffen Müller	GNU GPL	Perl	No			Yes	Library and script to process tabular values
Colby College Uncertainty Calculator	T. W. Shattuck	Unknown	JavaScript	Yes	Yes	Yes	No	Web browser based. Formula input, then asks for values of variables.
Dempster Shafer with Intervals (DSI) Toolbox	Gabor Rebner	Free for private and academic use	MATLAB	No	Yes			Verified computation of basic probability assignments and fault tree analysis under Dempster–Shafer theory. Fast evaluation of (non) monotonic system functions and aggregation rules.
Error Calculator	Gregor Bollerhey	GNU GPL	Python	Yes	Yes	Yes		Standalone notebook calculator, optimized for lab classes (displays formula, export to spreadsheet or latex). Supports physical quantities with units.
Experimental Data Analyst (EDA)	David Harrison	Proprietary	Mathematica	Yes		No	Yes	Library
EPC: error-propagating calculator	Dan Kelley	GNU GPL	Perl	Yes	Yes	Yes		Perl Script. Monte Carlo evaluation of an expression.
ErrorCalc iPhone/iPad calculator app	Thomas Huber	Proprietary	Unknown	No	No	Yes	No	Scientific calculator app for iPhone or iPad that performs error propagation (Algebraic and RPN Entry modes)
FuncDesigner	Dmitrey	BSD	Python	No		Yes	Yes	Library and stand-alone (via the Python shell). Involves automatic differentiation, possibly large-scale sparse
GUM Workbench	Metrodata GmbH	Proprietary	Object Pascal (Delphi)	Yes		Yes	No	Standalone. Detailed consequences of a model equation. GUM + Monte Carlo. Free restricted educational version available.
GUM_MC	Jean-Marie Biansan	GNU GPL	Lazarus	Yes	Yes	Yes	No	Standalone. Gum framework and Monte Carlo method.
fussy	S. Bhatnagar	Free but copyrighted	C	Yes	No	Yes	Yes	Scripting language called 'fussy', similar to C.
Gustavus Adolphus error propagation calculator	Thomas Huber	GNU GPL	Unknown	No	No	Yes	No	Executable only. Desk calculator style (with no expression parentheses).
laffers.net error propagation calculator	Richard Laffers	Creative Commons	JavaScript	No	Yes	Yes	No	Web browser based, desk calculator style
Measurement Software Toolkit	Industrial Research Ltd	Proprietary, freeware noncommercial use	R, Excel plug-in	Yes		Yes	Yes	Library and plug-in
Measurements.jl	Mosè Giordano	MIT	Julia	Yes	Yes	Yes	Yes	Supports real and complex numbers with uncertainty, arbitrary-precision calculations, functional correlation between variables, and mathematical and linear algebra operations with matrices and arrays.
GUM Tree Calculator (GTC)	Industrial Research Ltd	Proprietary, freeware single-user, nontransferable	Python	Yes	No	Yes	No	A programmable command-line calculator for Windows. Suitable for calculations involving real and complex quantities. Programmable in Python. An IDE with syntax highlighting and on-line help is included.
MUSE	Measurement Uncertainty Research Group, ETH Zürich	Proprietary, freeware noncommercial use	C++	Yes		Yes	No	Standalone. Monte-Carlo sampling. Interprets an XML model description file.
Metas.UncLib	Michael Wollensack, METAS	Proprietary freeware, no redistribution	C#, MATLAB wrapper	Yes	No	Yes	Yes	Library, and command-line calculator, via MATLAB
Number::WithError	Steffen Müller	GNU GPL	Perl	No		No	Yes	Library
uncertainties	Eric O. Lebigot (EOL)	BSD	Python	Yes	Yes	Yes	Yes	Library and stand-alone command-line calculator (via the Python shell). Fully transparent calculations with correlations. Also handles matrices with uncertainties. Automatically calculates all the derivatives of an expression
soerp	Abraham Lee	BSD	Python	Yes	Yes	Yes	Yes	Free Python library and command-line calculator. Fully transparent second-order calculations with correlations. Automatically calculates all the first and second derivatives of an expression using the free Python package ad
Risk Calc	Scott Ferson	Proprietary	C++	Yes		Yes		Probabilistic and interval uncertainty. Also handles uncertainty about correlations.
S&T Missouri Uncertainty Calculator	Gary L. Bertrand	Unknown	JavaScript	No	Yes	Yes	No	Web browser based. Desk calculator style.
Uncertainty Calculator; Wilfrid Laurier University	Terry Sturtevant	Unknown	JavaScript	No	Yes	Yes	No	Web browser based. Desk calculator style.
propagate	Andrej-Nikolai Spiess	GNU GPL	R	Yes	Yes	No	Yes	An R package that conducts error propagation by first- and second-order Taylor approximation (GUM 2008) and Monte-Carlo simulation (GUM 2008 S1), using full covariance structure.
GUMsim	QuoData GmbH	Proprietary	Object Pascal (Delphi)	Yes	No	Yes	No	Standalone; detailed consequences of a model equation
SCaViS	JWork.ORG	GNU GPL	Java, Python	Yes	Yes	Yes	Yes	Standalone. Conducts error propagation by first- and second-order Taylor approximation and using a Monte Carlo approach for complex functions
QMSys GUM	Qualisyst Ltd.	Proprietary	Unknown	Yes	No			Standalone. Linear/nonlinear models, Monte Carlo method. (free restricted educational version available)
MC-Ed	Florian Platel (MetGen)	Free	Object Pascal (Delphi)	No	No	Yes	No	Desktop calculator (Win32 native application). Monte-Carlo simulations.
OpenCOSSAN	Institute of Risk and Uncertainty, University of Liverpool	GNU GPL	MATLAB	Yes	Yes	No	Yes	Provides an object-oriented programming interface to advanced algorithms and solution sequences.
OpenTURNS	Airbus, EDF R&D, IMACS, Phimeca	GNU LGPL	C++, Python	Yes	Yes	No	Yes	State of the art advanced probabilistic modelling (copulas, Bayesian models, stochastic processes, random fields), state of the art algorithms, Windows-Linux-macOS, C++ and Python APIs
SmartUQ	SmartUQ LLC	Proprietary	C++	Yes	Yes	No	No	Standalone application for Windows & Linux. MATLAB and Python APIs
UQLab	ETH Zürich, Chair of Risk, Safety and Uncertainty Quantification	Free for academic use	MATLAB	Yes	Yes	Yes	No	General purpose framework, fast learning curve, easy to link to third party codes.

See also

• Automatic differentiation#Software, also can be used to obtain uncertainties

References

• Y. C. Kuang, A. Rajan, M. P.-L. Ooi, and T. C. Ong (2014), "Standard uncertainty evaluation of multivariate polynomial," Measurement, vol. 58, pp. 483–494, Dec. 2014
• A. Rajan, M. P. Ooi, Y. C. Kuang, and S. N. Demidenko, "Analytical Standard Uncertainty Evaluation Using Mellin Transform," Access, IEEE, vol. 3, pp. 209–222, 2015.
• Auer, E., Luther, W., Rebner, G., Limbourg, P. (2010) A Verified MATLAB Toolbox for the Dempster-Shafer Theory. Proceedings of the Workshop on the Theory of Belief Functions
• Bevington, P.R. and Robinson, D.K. (2002) Data Reduction and Error Analysis for the Physical Sciences, 3rd Ed., McGraw-Hill ISBN 0-07-119926-8
• Ferson, S., Kreinovich, V., Hajagos, J., Oberkampf, W. and Ginzburg, L. (2007) "Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty". Sandia National Laboratories Report: SAND2007-0939.
• Patelli, E., An Open Computational Framework for Reliability Based Optimization, In proceeding of: The Eleventh International Conference on Computational Structures Technology, Dubrovnik, Croatia 4–7 September 2012