A method and apparatus for controlling a fuel pump assembly comprising a plurality of pump elements, each pump element comprising a cam-driven plunger to perform at least one pumping event per engine revolution and a control valve. Each pumping event corresponds to an associated cam lobe of the associated cam. The method comprises, for each pumping event of each pump element, controlling the control valve of said pump element in response to an output control signal derived from at least one previous pumping event. Fuel pressure is measured within a rail volume and compared with a demanded rail pressure value to derive a rail pressure error. A proportional term and an integral term for the rail pressure error are derived and combined to derive the output control signal. Monitoring of the integral term for each pumping event provides a means for identifying and diagnosing a fault condition.