  Process Monitoring involves tracking a system's behaviors, evaluating the
current state of the system, and discovering interesting events that require
immediate actions. In this paper, we consider monitoring temporal system state
sequences to help detect the changes of dynamic systems, check the divergence
of the system development, and evaluate the significance of the deviation. We
begin with discussions of data reduction, symbolic data representation, and the
anomaly detection in temporal discrete sequences. Time-series representation
methods are also discussed and used in this paper to discretize raw data into
sequences of system states. Markov Chains and stationary state distributions
are continuously generated from temporal sequences to represent snapshots of
the system dynamics in different time frames. We use generalized Jensen-Shannon
Divergence as the measure to monitor changes of the stationary symbol
probability distributions and evaluate the significance of system deviations.
We prove that the proposed approach is able to detect deviations of the systems
we monitor and assess the deviation significance in probabilistic manner.
