{"paper":{"title":"Effect of the measurement errors on one-sided Synthetic-RZ control charts for monitoring the ratio of two normal variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Kim Duc Tran, Kim Phuc Tran, Thi Hien Nguyen","submitted_at":"2026-06-04T13:25:38Z","abstract_excerpt":"In numerous industrial production settings, keeping track of the ratio formed by two normally distributed random variables is a task of considerable practical interest. The present work examines how measurement errors influence the behaviour of a pair of one-sided Synthetic control charts designed to monitor such a ratio (referred to here as Synthetic-RZ charts), with the analysis covering both the zero-state and the steady-state average run length ($ARL$). To incorporate measurement error into the operation of these charts, we adopt a linear covariate error model. We describe, step by step, h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06149","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06149/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}