The diagnostic device that detects a failure of a sensor. The sensor includes memory for repeatedly recording pairs of two absolute pressure values, the absolute pressure values being related to absolute pressures in the first and the second impulse lines, respectively. A processor repeatedly computes, from a prescribable number of pairs of the two absolute pressure values, a correlation value representative of the correlation between the two absolute pressure values. The processor can also compare correlation values to at least one correlation threshold value, and generate a diagnostic output depending on the result of the comparison. It is possible to derive the absolute pressure values from one differential pressure measurement and one absolute pressure measurement.