  By achieving their purposes through interactions with the physical world,
Cyber-Physical Systems (CPS) pose new challenges in terms of dependability.
Indeed, the evolution of the physical systems they control with transducers can
be affected by surrounding physical processes over which they have no control
and which may potentially hamper the achievement of their purposes. While it is
illusory to hope for a comprehensive model of the physical environment at
design time to anticipate and remove faults that may occur once these systems
are deployed, it becomes necessary to evaluate their degree of effectiveness in
vivo. In this paper, the degree of effectiveness is formally defined and
generalized in the context of the measure theory. The measure is developed in
the context of the Transferable Belief Model (TBM), an elaboration on the
Dempster-Shafer Theory (DST) of evidence so as to handle epistemic and aleatory
uncertainties respectively pertaining the users' expectations and the natural
variability of the physical environment. The TBM is used in conjunction with
the Input/Output Hidden Markov Modeling framework (we denote by Ev-IOHMM) to
specify the expected evolution of the physical system controlled by the CPS and
the tolerances towards uncertainties. The measure of effectiveness is then
obtained from the forward algorithm, leveraging the conflict entailed by the
successive combinations of the beliefs obtained from observations of the
physical system and the beliefs corresponding to its expected evolution. The
proposed approach is applied to autonomous vehicles and show how the degree of
effectiveness can be used for bench-marking their controller relative to the
highway code speed limitations and passengers' well-being constraints, both
modeled through an Ev-IOHMM.
