Uncertainty operations with Statool

Uncertainty exists frequently in our knowledge of the real world. Probability is a common way to measure uncertainty. People sometimes define random variables whose values are derived from arithmetic operations on other random variables. Generally there are two classes of methods to handle this topic: analytical and numerical. Analytical methods are restricted to specific classes of input distributions. Numerical methods only give numerical results and are widely used in real applications if approximate results can be accepted. Monte Carlo simulation is one of the best-known numerical methods. However the approach of Monte Carlo has some limitations. Interval-based dependency analysis (DEnv) was developed by Berleant and Goodman-Strauss. Another approach is the copula-based approach. These two methods have been implemented in software. The copula-based approach is implemented in the commercial software RiskCalc. DEnv is implemented in Statool. The Current Statool supports a variety of dependence relationships: independence, unknown dependence, and specific correlation values. The algorithm extension to support correlation is a significant improvement. The current version of Statool uses the transportation simplex method to speed up computing. Cascaded operations, relational operations and monotonic binary functions are newly supported by the current Statool. These new functions, and using correlation as constraints, are the main advances in Statool. This software is based on a layer design including the user interface, the logical layer, and the computing layer. This is suitable for implementation and maintenance of distributed and other computing software. OO methods are adapted. Unified Modeling Language (UML) gives visualization and documentation support for the computing layer. The main algorithms are implemented in many objects. Currently it is developed for a Microsoft Windows platform. Visual C++ and Visual Basic were used for development. Dynamically linked libraries are used to contain the components of the computing layer