摘要:AbstractOptimally designed alarm systems In this work, we derive expressions for probabilities of detecting alarms with various delays when on-delay timer is used. In the on-delay timer strategy, an alarm is generated if thresholds are violated fornconsecutive instants with n being user specified. We rigorously derive the probability expressions using geometric random variable modeling. The derived expressions are shown to be identical to those available in literature using Markov chain modeling. Use of geometric random variable enables us to obtain a recursive form for these expressions which offers insights about the variation in probabilities as a function of the delay.