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In monitoring-based diagnosis of active systems, the observation is fragmented over time: at the occurrence of each fragment, the internal representation of the observation received so far is updated, new monitoring states are estimated, and a new set of candidate diagnoses is output. When the observation is temporally uncertain, a problem arises about the dependability of the monitoring output: Two consecutive sets of diagnoses, relevant to two consecutive observation fragments, may be unrelated to one another, and, even worse, they may be unrelated to the actual diagnosis. To cope with this problem, the notion of monotonic monitoring is introduced, which is supported by specific constraints on the fragmentation of the uncertain temporal observation, leading to the notion of stratification. Stratified observations support monotonic monitoring of active systems.