Computerized methods and software for communicating behavior of industrial systems to operators, for instance, in HMI environments. Various embodiments display values of different parameters of the system and an alert indicator for values that passed an operating limit established for the parameter during a particular preceding duration of time. In some embodiments, different indicators (e.g., shading, for example, adjacent to the value) are displayed for exceeding an upper operating limit or a lower operating limit (or both). In a number of embodiments, a plot is displayed for value that has passed an operating limit during the preceding duration of time, for instance, when the operator hovers a cursor over the value. In many embodiments, the operator can set the preceding duration of time, the operating limit(s), or both. In many embodiments, abnormal movements or process variability can be detected by the operator, for example, before the movements would otherwise be detectable.
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