Various methods and systems are provided for diagnosing an engine component based on a measured engine speed during an engine shutdown event. As one embodiment, a method for an engine includes measuring an engine speed drop rate, via an engine speed sensor, during an engine shutdown event; and indicating a change in performance of one of the engine speed sensor or an additional engine component in response to the measured engine speed drop rate deviating from a reference engine speed drop rate by a pre-set or pre-defined threshold rate.