  The characterization of errors in a quantum system is a fundamental step for
two important goals. First, learning about specific sources of error is
essential for optimizing experimental design and error correction methods.
Second, verifying that the error is below some threshold value is required to
meet the criteria of threshold theorems. We consider the case where errors are
dominated by the generalized damping channel (encompassing the common intrinsic
processes of amplitude damping and dephasing) but may also contain additional
unknown error sources. We demonstrate the robustness of standard $T_1$ and
$T_2$ estimation methods and provide expressions for the expected error in
these estimates under the additional error sources. We then derive expressions
that allow a comparison of the actual and expected results of fine-grained
randomized benchmarking experiments based on the damping parameters. Given the
results of this comparison, we provide bounds that allow robust estimation of
the thresholds for fault-tolerance.
