Question: Suppose I want to reduce risk of a circuit breaker malfunctioning and failing to disconnect a shorted circuit.

What if I install two identical breakers sequentially (one after another) so that if one of them fails the other one steps in and disconnects the circuit? Is there any problem with such installation?

Answer: 
"Suppose I want to reduce risk of a circuit breaker malfunctioning and failing to disconnect a shorted circuit."

If you have a good quality panel... Square D, Eaton, Siemens, etc.. you really have no reason to worry about a circuit breaker malfunctioning in such a way that it doesn't trip if your load is greater than its ampacity. I have never seen this happen to any manufacturers circuit breakers not named Zinsco. In short, circuit breakers work and they work well you dont have to be afraid of them failing. If you are really nervous, install a arc fault circuit interrupter breaker in the existing ones place... any arcing and it will trip. Or an arc fault/ GFI combo breaker that will protect you from every angle.
Putting two breakers of same size and rating in series can be dangerous. manufacturers give the short circuit breaking current for ONE device.
Modern CB operated with the magnetic force generated during the short circuit. This magnetic repulsion of the contacts is linked to the energy generated during the short circuit. The breakers are designed to open according to this energy generated during the short circuit. the opening time and speed is defined according to this energy. If two breakers are in series it impossible to predicte the energy at the level of the two devices. The energy is distributed over the two devices. And the operation time and openning speed can be slower than with only one breaker. Putting two breaker of same size and same rating can be dangerous.