Reliable testing of a mechanical system requires the procedures used for the evaluation to be repeatable and reproducible. However, it is never possible to exactly repeat or reproduce the tests that are used for evaluation. To overcome this limitation, a statistical evaluation procedure can generally be used. However, most of the statistical procedures use scalar values as input without the ability to handle vectors or time-histories. To overcome these limitations, two numerical/statistical methods for determining if the impact time-history response of a mechanical system is repeatable or reproducible are evaluated and elaborated upon. Such a system could be a vehicle, a biological human surrogate, an Anthropometric Test Device (ATD or dummy), etc. The responses could be sets of time-histories of accelerations, forces, moments, etc., of a component or of the system. The example system evaluated is the BioRID II rear impact dummy. The evaluation begins by transforming the sets of time-histories into sets of relative-shapes and magnitudes of those response time histories. The two statistical procedures use the t and T2-tests. One uses a statistical comparison between the average time history of a set (Representative Curve (RC)) and the individual time histories of that set or other sets. The other procedure uses a statistical comparison of sets of time histories.