Health management systems that more accurately and quickly diagnose faults that may occur in different technical systems on-board a vehicle will play a key role in the success of future NASA missions. We discuss in this paper the diagnosis of abrupt continuous (or parametric) faults within the context of probabilistic graphical models, more specifically Bayesian networks that are compiled to arithmetic circuits. This paper extends our previous research, within the same probabilistic setting, on diagnosis of abrupt discrete faults. Our approach and diagnostic algorithm ProDiagnose are domain-independent; however we use an electrical power system testbed called ADAPT as a case study. In one set of ADAPT experiments, performed as part of the 2009 Diagnostic Challenge, our system turned out to have the best performance among all competitors. In a second set of experiments, we show how we have recently further significantly improved the performance of the probabilistic model of ADAPT. While these experiments are obtained for an electrical power system testbed, we believe they can easily be transitioned to real-world systems, thus promising to increase the success of future NASA missions.