Monitoring of histogram-valued data

Histogram-valued data frequently arise in modern process monitoring applications, where each observation is represented by an entire distribution rather than a single measurement. Existing SVDD-based control charts, however, do not provide explicit finite-sample control of Type I error rates. To address this limitation, this study proposes a conformal prediction-based support vector data description (CP-OCSVM) chart for monitoring histogram-valued data. The proposed method combines conformal prediction with the SVDD algorithm and uses a Wasserstein-distance-based kernel to capture the geometric structure of histogram-valued distributions. Under the exchangeability assumption, the CP-OCSVM provides finite-sample Type I error control while retaining the flexibility of kernel-based one-class classification. Simulation studies and a real-data application to weekly traffic speed data from the Seoul TOPIS system demonstrate that the proposed chart maintains empirical Type I error rates close to the nominal level and achieves higher or comparable detection power relative to existing methods. The proposed chart also exhibits stable performance under moderate Phase I contamination and varying histogram resolutions. These results indicate that the proposed CP-OCSVM chart provides a statistically principled and practically effective approach for monitoring histogram-valued data.