A test apparatus for characterizing a device under test includes a test case generator, a test unit, a data storage unit, and a data analysis unit. The test case generator is configured to randomly generate a plurality of test cases, which include values of one or more input variables of a set of input variables. The test unit is configured to perform the plurality of test cases on the device under test. The data storage unit may store sets of test data, which are associated to the test cases and include values of input variables of a respective test case and corresponding values of output variables of the device under test related to the respective test case. The data analysis unit may further analyze the test data and is further configured to determine dependencies within a subset of variables of the test data to characterize the device under test.