Quality of Service issues, at the heart of ATM, represented by bounded performance guarantees, are very closely related to reliability constraints in safety-critical systems. Reliability measures the effects of rare events on the operation of a network or system. Rare events, in this context, also impact on other QoS parameters, so developing reasoning tools for these will hopefully allow us to capture similar detail at a network performance level. This paper is concerned with reliability within safety-critical systems. It takes us from a fairly common notion of system equivalence to a method of minimal reasoning which allows us to justify a system's overall reliability. By introducing a method of successive approximation to equivalences, we show how it might be possible to obtain a theoretical minimum for the amount of computation required to prove a system's reliability. In doing so, it allows us to reason about operations on safety-critical systems--composition, restriction, specialisation--and still demonstrate operational reliability.