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Multivariate analysis (MVA) is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time. In design and analysis, the technique is used to perform trade studies across multiple dimensions while taking into account the effects of all variables on the responses of interest.

Uses for multivariate analysis includes:

• Design for capability (also known as capability-based design)
• Inverse design, where any variable can be treated as an independent variable
• Analysis of alternatives, the selection of concepts to fulfill a customer need
• Analysis of concepts with respect to changing scenarios
• Identification of critical design drivers and correlations across hierarchical levels

Multivariate analysis can be complicated by the desire to include physics-based analysis to calculate the effects of variables for a hierarchical "system-of-systems." Often, studies that wish to use multivariate analysis are stalled by the dimensionality of the problem. These concerns are often eased through the use of surrogate models, highly accurate approximations of the physics-based code. Since surrogate models take the form of an equation, they can be evaluated very quickly. This becomes an enabler for large-scale MVA studies: while a Monte Carlo simulation across the design space is difficult with physics-based codes, it becomes trivial when evaluating surrogate models, which often take the form of response surface equations.

[edit] References

• Biltgen, Patrick T., Ender, Tommer R., Cole, Bjorn, and Dimitri N. Mavris, Development of a Collaborative Capability-Based Tradeoff Environment for Complex System Architectures, AIAA 2006-0728, Presented at the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 9-12, 2006.

• KV Mardia, JT Kent, and JM Bibby (1979). Multivariate Analysis. Academic Press,.

[edit] See also

• Analysis of covariance
• Analysis of variance
• Factor analysis
• Multiple regression
• Path analysis
• Statistical correlation
• Statistical regression

This page uses content from the English-language version of Wikipedia. The original article was at Multivariate analysis. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License.