  When dealing with control systems, it is useful and even necessary to assess
the performance of underlying transfer functions. The functions may or may not
be linear, may or may not be even monotonic. In addition, they may have
structural breaks and other abberations that require monitoring and
quantification to aid decision making. The present paper develops such a
methodology, which is based on an index of increase that naturally arises as
the solution to an optimization problem. We show theoretically and illustrate
numerically that the empirical counterpart of the index needs to be used with
great care and in-depth knowledge of the problem at hand in order to achieve
desired large-sample properties, such as consistency.
