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A sequenced process of Fault Detection followed by the erroneous node's Isolation and system Reconfiguration (node exclusion or recovery), that is, the FDIR process, characterizes the sustained operations of a fault-tolerant system. For distributed systems utilizing message passing, a number of diagnostic (and associated FDIR) approaches, including our prior algorithms, exist in literature and practice. Invariably, the focus is on proving the completeness and correctness (all and only the faulty nodes are isolated) for the chosen fault model, without explicitly segregating permanent from transient faulty nodes. To capture diagnostic issues related to the persistence of errors (transient, intermittent, and permanent), we advocate the integration of count-and-threshold mechanisms into the FDIR framework. Targeting pragmatic system issues, we develop an adaptive online FDIR framework that handles a continuum of fault models and diagnostic protocols and comprehensively characterizes the role of various probabilistic parameters that, due to the count-and-threshold approach, influence the correctness and completeness of diagnosis and system reliability such as the fault detection frequency. The FDIR framework has been implemented on two prototypes for automotive and aerospace applications. The tuning of the protocol parameters at design time allows a significant improvement with respect to prior design choices.