In nuclear power plants, instrument failures must be detected and compensated for before a significant decrease in plant performance occurs. The improved generalized likelihood ratio method to detect and identify a failure and a control algorithm in the event of an instrument failure is developed. The failure detection algorithm and the control algorithm are combined and applied to a pressurized water reactor pressurizer. Computer simulation tests show that on-line prompt failure detection and compensation through control action can be performed very successfully even when there is an instrument failure.