Uncertainty Analysis Methods

Both test-based and simulation-based reliability methodologies draw extensively on computational methods involving probability and statistics, stochastic processes and fields, response surfaces and design of experiments, sampling techniques, and optimization. Many of the classical methods in these topics are well known and Vanderbilt University already has a sound educational program that provides comprehensive graduate level coursework in these topics. In addition, complex multidisciplinary systems are requiring the development of newer methods in these areas. Faculty in several schools have research programs that address this need. Examples include stochastic time series modeling, simulation, and extreme value analyses, neural networks, decision trees, and inductive learning and classification, fuzzy sets-based methods for risk assessment with qualitative information, Bayesian methods for system life-cycle engineering, design optimization under uncertainty, and stochastic processes, signal processing and detection methods.
Uncertainty in systems analysis and design arises from several sources. Some of the "known" sources are:

1. Physical uncertainty or inherent variability: The demands on an engineering system as well as its properties always have some variability associated with them, due to environmental factors and variations in operating conditions, manufacturing processes, quality control etc. This type of uncertainty may be handled through probabilistic analysis, if adequate data is available.
2. Informational Uncertainty: This includes statistical uncertainty due to small number of samples, qualitative uncertainty due to vagueness and imprecision, etc. The former type of uncertainty is handled through Bayesian analysis, while latter type of uncertainty requires the non-probabilistic approaches such as fuzzy sets theory, evidence theory, interval analysis etc.
3. Modeling Error: This results from approximate mathematical models of the system behavior, and from numerical approximations during the computational process. For new and complex engineering systems, this type of uncertainty is not quantifiable a priori. This type of uncertainty has been addressed through Bayesian as well as non-probabilistic approaches.

Vanderbilt University researchers are developing methods that address all three types of uncertainty in systems reliability and risk assessment.

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