The present invention has been made in order to retrieve data including gross errors and to use accurate measurement data. The present invention provides a method for detecting gross errors and a method for correcting data to ensure accuracy in process operation. It is intended to provide a way to do this. It is also an object of the present invention to provide a method and system capable of detecting gross errors under constraints of mass conservation equations using Lagrange multiplier. The gross error detection method using the Lagrange multiplier method according to the present invention comprises the steps of measuring the process variable to generate measurement data; Generating estimated data of the process variable by applying a Lagrange multiplier method to the measured data; And detecting a gross error of the measured data based on the measured data, the estimated data, and a standard deviation of the measured data.
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