Statistical process monitoring (SPM) is a quality control method that employs statistical methods to monitor and control a process, e.g., industrial production processes. We focus on profile monitoring of spatiotemporal functional data. Profile monitoring can generally be applied to any process where a functional relationship between one or more quality characteristics of interest (as the response variable/s) and one or more explanatory process variables is present. Then, the stability of this functional relationship is continuously monitored, and changes from the target relationship should quickly be detected. Profile monitoring is conducted in two phases, the first of which is a retrospective phase. The main goal of this phase, or the so-called Phase I, is to analyze historical data to elucidate and find a suitable model for the target process. Thus, the Phase I data should not contain anomalous or outlying observations, which must be identified and removed in this first phase. This study focuses on environmental applications, where the physical variables are observed in a functional domain over a two-dimensional space (e.g., georeferenced locations) and time. More precisely, we consider a functional hidden dynamic geostatistical model (f-HDGM). We show the Phase I analysis for a case study on the active monitoring of a bike-sharing scheme in Helsinki. Active monitoring of such a process is relevant for rebalancing the available bikes at each station in case of abnormal usage, e.g., because of events.

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Phase I of Spatiotemporal Profile Monitoring for Functional Data

  • Mohammadreza Nasiriboroujeni,
  • Philipp Otto

摘要

Statistical process monitoring (SPM) is a quality control method that employs statistical methods to monitor and control a process, e.g., industrial production processes. We focus on profile monitoring of spatiotemporal functional data. Profile monitoring can generally be applied to any process where a functional relationship between one or more quality characteristics of interest (as the response variable/s) and one or more explanatory process variables is present. Then, the stability of this functional relationship is continuously monitored, and changes from the target relationship should quickly be detected. Profile monitoring is conducted in two phases, the first of which is a retrospective phase. The main goal of this phase, or the so-called Phase I, is to analyze historical data to elucidate and find a suitable model for the target process. Thus, the Phase I data should not contain anomalous or outlying observations, which must be identified and removed in this first phase. This study focuses on environmental applications, where the physical variables are observed in a functional domain over a two-dimensional space (e.g., georeferenced locations) and time. More precisely, we consider a functional hidden dynamic geostatistical model (f-HDGM). We show the Phase I analysis for a case study on the active monitoring of a bike-sharing scheme in Helsinki. Active monitoring of such a process is relevant for rebalancing the available bikes at each station in case of abnormal usage, e.g., because of events.