Testing is done on earth in lab conditions, and some testing has been done in space. We've had good models of radiation energy and type in space for a while, so you can reproduce type and intensity of radiation on earth to test how the chip will behave. You can also fly chips for testing, where instrumentation and testing are controlled by known working hardware.
Diagnosing novel failures on hardware in space is hard, but the overall types of failures and their underlying physical phenomena are known. Obviously, in the case of a satellite that goes completely unresponsive you can't answer 100%, but you may have sensor data in the leadup to the failure, or from other "nearby" satellites that would allow you partially reproduce conditions before the failure in a test scenario.
Diagnosing novel failures on hardware in space is hard, but the overall types of failures and their underlying physical phenomena are known. Obviously, in the case of a satellite that goes completely unresponsive you can't answer 100%, but you may have sensor data in the leadup to the failure, or from other "nearby" satellites that would allow you partially reproduce conditions before the failure in a test scenario.