The problem of failure detection in dynamic systems is addressed. The approach is based on modelling and estimation methods and uses some known statistical tools as well as geometric arguments. A test decision. is derived which is based on the overlap between the confidence regions associated with two estimates, one obtained using online measurements and the other based on a priori information. The algorithm proposed here is suitable for on-line detection of "abrupt" changes and failures in the applications where "fast" on-line decisions are of importance. The implementation of a necessary and sufficient condition is shown to result in a scalar test which does not call for any optimization procedure and so offers the advantage of low computational expenditure.