Signal-Analytics Modeling of Fluorescence Maximum Time-to-Detection (TTD+) for E. coli in Treated Wastewater: A Joint Censoring and Sensor Model Approach Part II

Abstract Water security is a global priority and relies on reliable microbiological monitoring in treated effluents. In this work, we investigate a sensor-analytics component of Escherichia coli (E. coli) monitoring in treated wastewater through fluorescence time courses acquired with a miniaturized, Internet of Things-enabled incubation platform, named the Optical Bacterial Growth Sensor–Fluorescence Detector. The signal arises from hydrolysis of a β-d-glucuronide substrate mediated by E. coli-expressed β-glucuronidase activity, yielding characteristic kinetic profiles over time. Our primary target is the extraction and probabilistic modeling of the upper time-to-detection, TTD+, an operational timing feature of the recorded fluorescence response. In practical terms, TTD+ retrospectively identifies the onset of the upper stable signal region under the adopted criterion, providing a timing summary for assay duration planning. To model this time-domain boundary, we adopt the Joint Censoring and Sensor Model Approach (JCSMA) and further extend it by deriving analytical expressions for ordinary moments and entropy measures, including Rényi and Shannon entropies. The empirical comparison favors JCSMA within the evaluated model set, while simulation characterizes the sampling behavior of selected statistics under the fitted model. The resulting probabilities and quantiles provide summaries for assay duration planning under the adopted conditions. The study does not evaluate analytical figures of merit for E. coli quantification or the association between TTD+ and reference most probable number values.