With correct discrimination, a single fault on one rack power supply will trip the local MCB in the power distribution unit, but not the distribution circuit breaker or worse still, the main circuit breaker.
In the same way, a fault on the power distribution unit will trip the distribution breaker feeding it, not the main circuit breaker. The intention is to limit the service interruption to the minimum amount for any fault, whether this fault is overload or short-circuit.
This all sounds very obvious and straightforward but as always the devil is in the detail. To correctly design a system the designer has to know the likely fault current at every point in the system and the time-current characteristics of each circuit breaker (or fuse). The graphs of these time-current (and time-energy) characteristics are then correlated to the calculated fault currents so that trip timings of the breakers can be assessed. The IEE Regulations stipulate that the final sub-circuit breakers open on earth fault in 0.4 secs, whereas the distribution circuit breakers must open in a maximum of 5 secs. The fault currents will be much less for faults at the final sub-circuits than faults at the power source or distribution switchboard due to the circuit impedances. These days all of these fault currents are worked out in software models rather than by hand, many factors such as cable type and size affect the fault current and hence the breaker trip opening times.