On the ordinary distance between multivariate random systems in engineering

The study is concerned with the comparison of random systems exhibiting sev eral significant response variables. For this purpose, the uncertainty in t he observed difference of the sample mean vectors is quantified by defining a confidence region which contains the true difference of the population m ean vectors with a prescribed probability. Since the confidence region is o riginally defined in the Mahalanobis space, transition to the natural or or dinary variables is discussed. In this connection the concept of the confid ence radius is introduced for observations. The distance between population mean vectors is more accurately bounded by solving an extremum problem. Th e method is elucidated and the power of the procedure is investigated on se lected test cases. Application is demonstrated for problems from aerospace and automotive engineering. (C) 2001 Elsevier Science B.V. All rights reser ved.