Most of the basic probabilistic calculations and most of the models used in the reliability field are relevant only for independent events. Two events, A and B, are independent if the occurrence of A is independent of that of B. Mathematically speaking, that means that the conditional probability of occurrence of B given the occurrence of A, P(B/A), is simply equal to P(B). Independent failures are, of course, a particular case of independent events.
Source: API STD 689, Collection and Exchange of Reliability and Maintenance Data for Equipment, First Edition, July 2007. Global Standards