Monitoring of segmented processes using p-box aggregated data and fuzzy control charts

Abstract The monitoring of inhomogeneous and non-stationary processes composed of segments and subsegments is considered. The structure of this segmentation is typical for medical data, describing voice characteristics of Bipolar Disorder (BD) psychiatric patients, calculated from their recorded smartphone calls. Data from subsegments are described by different probability distributions and are represented by histograms. Then, data from subsegments belonging to the same segment are aggregated using probability boxes (p-boxes) methodology and a simple probabilistic method. Finally, the mean value of each of the aggregated segments is described by a fuzzy triangular number. Therefore, the stream of consecutive segments is represented by the stream of fuzzy numbers. Several control charts for such fuzzy data are proposed. Their statistical properties are evaluated using simulated synthetic data. The simulation model is related to the real-life data obtained from the monitoring of BD patients. The results of simulations demonstrate the applicability of the proposed procedure for monitoring of BD patients.