On the ordinary distance between multivariate random systems in engineering
The study is concerned with the comparison of random systems exhibiting several significant response variables. For this purpose, the uncertainty in the observed difference of the sample mean vectors is quantified by defining a confidence region which contains the true difference of the population mean vectors with a prescribed probability. Since the confidence region is originally defined in the Mahalanobis space, transition to the natural or ordinary variables is discussed. In this connection the concept of the confidence radius is introduced for observations. The distance between population mean vectors is more accurately bounded by solving an extremum problem. The method is elucidated and the power of the procedure is investigated on selected test cases. Application is demonstrated for problems from aerospace and automotive engineering.
comparison of random systems confidence region multivariate statistics model validation structural engineering crashworthiness