The present invention may include measuring tool induced shift (TIS) on at least one wafer of a lot of wafers via an omniscient sampling process, randomly generating a plurality of sub-sampling schemes, each of the set of randomly generated sub-sampling schemes having the same number of sampled fields, measuring TIS at each location of each of the randomly generated sub-sampling schemes, approximating a set of TIS values for each of the randomly generated sub-sampling schemes utilizing the TIS measurements from each of the randomly generated sub-sampling schemes, wherein each set of TIS values for each of the randomly generated sub-sampling schemes is calculated utilizing an interpolation process configured to approximate a TIS value for each location not included in a randomly generated sub-sampling scheme, and determining a selected sub-sampling scheme by comparing each of the calculated sets of TIS values to the measured TIS of the omniscient sampling process.