Analysis of Relevance and Importance of Components in System Reliability

A component is relevant if its status (failed or not) do affect the system state, which is traditionally a qualitative concept. In contrast, the importance is a quantitative measure to represent the contribution of component reliability to system reliability. Few researches have focused on the relation between relevance and importance, probably because components are usually assumed to be relevant to rule out trivial cases in reliability engineering. In this paper, we elaborate on the observations that an initially relevant component could become irrelevant later due to the failures of other components, and an irrelevant component may play an important role in system reliability when the fault coverage is imperfect. We then propose a dynamic relevance measure to represent the conditions and probability that a component can keep its relevance in all system states, and we compare it with the standard Birnbaum Importance measure with both qualitative and quantitative results. The analysis may serve as a corner stone for future study on appropriate relevance and importance measures in various coverage models.