An apparatus for processing data 2 is provided with a time-to-digital converter 18 which serves to measure signal processing delay through one or more signal paths through a processing stage. This measured delay generates a delay value representing a plurality of instances of the signal processing delay which have been measured. Analysis is performed under software control to estimate a worst case signal processing delay through the processing stage based upon the delay values which have been generated. An adjustment of the operating parameters, such as supply voltage and clock frequency, of the apparatus is made to provide a timing margin through the processing stage sufficient to satisfy the worst case signal processing delay which has been estimated without an excessive margin.