  We introduce and explore an empirical index of increase that works in both
deterministic and random environments, thus allowing to assess monotonicity of
functions that are prone to random measurement-errors. We prove consistency of
the index and show how its rate of convergence is influenced by deterministic
and random parts of the data. In particular, the obtained results suggest a
frequency at which observations should be taken in order to reach any
pre-specified level of estimation precision. We illustrate the index using data
arising from purely deterministic and error-contaminated functions, which may
or may not be monotonic.
