Various methods and systems are provided for health assessments of a fuel system. In one example, a fuel system includes a low-pressure pump operable to pump fuel from a fuel source at a first pressure, a high-pressure pump operable to increase the first pressure to a second pressure, a valve positioned between the low-pressure pump and the high-pressure pump and operable to control fuel flow to the high-pressure pump, a common fuel rail fluidly coupling the high-pressure pump to a plurality of fuel injectors coupled to cylinders of an engine, and a controller. The controller is operable to adjust an amount of valve electrical current supplied to the valve to reach a commanded pressure of the common fuel rail during cylinder firing conditions, the supplied valve electrical current adjusted based on a valve pre-firing correction factor for the valve obtained based on valve electrical current prior to cylinder firing commencing.