Summary: We consider the optimal structure of safety monitoring systems composed of unnecessarily stochastically independent \(n\) sensors, which output signals in response to the state of the monitored system. In this paper the conditional entropy of safety monitoring systems with respect to the monitored system is used as the optimality criterion. This conditional entropy means the ambiguity level of signals which the safety monitoring systems output. We formulate safety monitoring systems as monotone systems which are well known concept in reliability theory, and then show that a \(k\)-out-of-\(n\) system is one of the systems which minimize the conditional entropy among monotone systems composed of at most \(n\) sensors, when the transition probability is exchangeable. Furthermore, assuming that the monitored system has only two states, i.e., normal and abnormal, and the transition probability is dual, we show that one of the optimal structures of safety monitoring systems is series or parallel.