{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3I5BVZZADWZMU5PB6OVSA5F7MV","short_pith_number":"pith:3I5BVZZA","schema_version":"1.0","canonical_sha256":"da3a1ae7201db2ca75e1f3ab2074bf6566f5c4e28f7d14966fa68b02e6c4151d","source":{"kind":"arxiv","id":"2606.06149","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.06149","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T13:25:38Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"558943bf9ec490742de3cc2e88c53a582e92c976e28721dad4b5e63dad942e82","abstract_canon_sha256":"80ba69187acef7f2ed49529938bab3c73e2e39bb1c76642fb6aa9223412cf60b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:35.302107Z","signature_b64":"0yjWnI9/l7QgxwnkzuQSOY+aAfhuAzOI8m3YD9260ptuKilxqJ+eGizSNxT8hvCgIp9g4ny+TppSqp23jfZMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da3a1ae7201db2ca75e1f3ab2074bf6566f5c4e28f7d14966fa68b02e6c4151d","last_reissued_at":"2026-06-05T01:15:35.301475Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:35.301475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.06149","created_at":"2026-06-05T01:15:35.301542+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06149v1","created_at":"2026-06-05T01:15:35.301542+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06149","created_at":"2026-06-05T01:15:35.301542+00:00"},{"alias_kind":"pith_short_12","alias_value":"3I5BVZZADWZM","created_at":"2026-06-05T01:15:35.301542+00:00"},{"alias_kind":"pith_short_16","alias_value":"3I5BVZZADWZMU5PB","created_at":"2026-06-05T01:15:35.301542+00:00"},{"alias_kind":"pith_short_8","alias_value":"3I5BVZZA","created_at":"2026-06-05T01:15:35.301542+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV","json":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV.json","graph_json":"https://pith.science/api/pith-number/3I5BVZZADWZMU5PB6OVSA5F7MV/graph.json","events_json":"https://pith.science/api/pith-number/3I5BVZZADWZMU5PB6OVSA5F7MV/events.json","paper":"https://pith.science/paper/3I5BVZZA"},"agent_actions":{"view_html":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV","download_json":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV.json","view_paper":"https://pith.science/paper/3I5BVZZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06149&json=true","fetch_graph":"https://pith.science/api/pith-number/3I5BVZZADWZMU5PB6OVSA5F7MV/graph.json","fetch_events":"https://pith.science/api/pith-number/3I5BVZZADWZMU5PB6OVSA5F7MV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV/action/storage_attestation","attest_author":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV/action/author_attestation","sign_citation":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV/action/citation_signature","submit_replication":"https://pith.science/pith/3I5BVZZADWZMU5PB6OVSA5F7MV/action/replication_record"}},"created_at":"2026-06-05T01:15:35.301542+00:00","updated_at":"2026-06-05T01:15:35.301542+00:00"}