For example suppose it is critical that the output of an ADC be monotonic for the circuit to work properly, how would one setup a test jig to verify that a particular part did in fact produce monotonic output?
For an ADC, you apply positive sloping ramp on the input, and test to make sure all readings are equal or greater then the preceding reading.
For a DAC, you step through each incrementing voltage starting at 0 - say one step per millisecond. Put a differentiator on the output such as a 1nF capacitor from the output to the - input of an opamp with a 2.2 M feedback resistor. If the DAC is not monotonic at any point, there will be a positive spike on the opamp output.