Aggregation of Inhomogeneous Non-stationary Time Series Using P-Boxes

Monitoring of inhomogeneousHryniewicz, O.  Kaczmarek-Majer, K. non-stationary processes has been considered. The application of well-known statistical methods for the analysis of such processes may be questionable, and in the case of long streams of data even infeasible. In the paper, we consider processes consisting of segments and subsegments. The data from subsegments belonging to respective segments are represented by histograms. For consecutive segments, they are aggregated using probability boxes (p-boxes) and a simple probabilistic method. As a result of this aggregation, consecutive segments of the monitored process are represented by triangular fuzzy numbers. These fuzzy numbers may be used for process monitoring using statistical process control (SPC) methods, such as, e.g., control charts, for fuzzy data.