A method of establishing statistically valid assay means and ranges for quality control materials, used to qualify medical testing machines, utilizes tests on a new lot of quality control material to establish an assay mean, and uses data from a database of historical test results to establish an assay range. The system may estimate the variability of test results from prior lot data, and then compute the limits of the assay range such that a new test on a new lot of the quality control material will be expected to fall within the range with a specified probability. Because historical data is used to estimate the test variability, the number of new tests required to specify a statistically valid mean and range may be dramatically reduced, as compared with establishing the mean and range based only on tests of the new lot of material.