Traditional imperfect fault coverage models only consider the coverage (including identification and isolation) of faulty components, and they do not consider the coverage of irrelevant (operational) components. One potential reason for the omission is that in these models the system is generally assumed to be coherent in which each component is initially relevant. In this paper, we first point out that an initially relevant component could become irrelevant afterwards due to the failures of some other components, and thus it is important to consider the handling of irrelevancy even the system is originally coherent. We propose an irrelevancy coverage model (IRCM) in which the coverage is extended to the irrelevant components in addition to the faulty components. The IRCM can not only significantly enhance system reliability by preventing the future system failures resulting from the not-covered failures of the irrelevant components, but may also play an important role in efficient energy use in practice by timely turning off the irrelevant components.