{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3I5BVZZADWZMU5PB6OVSA5F7MV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"80ba69187acef7f2ed49529938bab3c73e2e39bb1c76642fb6aa9223412cf60b","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T13:25:38Z","title_canon_sha256":"558943bf9ec490742de3cc2e88c53a582e92c976e28721dad4b5e63dad942e82"},"schema_version":"1.0","source":{"id":"2606.06149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06149","created_at":"2026-06-05T01:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06149v1","created_at":"2026-06-05T01:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06149","created_at":"2026-06-05T01:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"3I5BVZZADWZM","created_at":"2026-06-05T01:15:35Z"},{"alias_kind":"pith_short_16","alias_value":"3I5BVZZADWZMU5PB","created_at":"2026-06-05T01:15:35Z"},{"alias_kind":"pith_short_8","alias_value":"3I5BVZZA","created_at":"2026-06-05T01:15:35Z"}],"graph_snapshots":[{"event_id":"sha256:d2fc526c325ca65e904ada781c65f4b0c37a1c2df372a70adc5f284eba3b309b","target":"graph","created_at":"2026-06-05T01:15:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.06149/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Kim Duc Tran, Kim Phuc Tran, Thi Hien Nguyen","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T13:25:38Z","title":"Effect of the measurement errors on one-sided Synthetic-RZ control charts for monitoring the ratio of two normal variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06149","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3a51d66050cb6ffa8aebf1dad477c3cf4686dcc7f507a3eeaabb0b245d442426","target":"record","created_at":"2026-06-05T01:15:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"80ba69187acef7f2ed49529938bab3c73e2e39bb1c76642fb6aa9223412cf60b","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T13:25:38Z","title_canon_sha256":"558943bf9ec490742de3cc2e88c53a582e92c976e28721dad4b5e63dad942e82"},"schema_version":"1.0","source":{"id":"2606.06149","kind":"arxiv","version":1}},"canonical_sha256":"da3a1ae7201db2ca75e1f3ab2074bf6566f5c4e28f7d14966fa68b02e6c4151d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da3a1ae7201db2ca75e1f3ab2074bf6566f5c4e28f7d14966fa68b02e6c4151d","first_computed_at":"2026-06-05T01:15:35.301475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:35.301475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0yjWnI9/l7QgxwnkzuQSOY+aAfhuAzOI8m3YD9260ptuKilxqJ+eGizSNxT8hvCgIp9g4ny+TppSqp23jfZMCg==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:35.302107Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a51d66050cb6ffa8aebf1dad477c3cf4686dcc7f507a3eeaabb0b245d442426","sha256:d2fc526c325ca65e904ada781c65f4b0c37a1c2df372a70adc5f284eba3b309b"],"state_sha256":"f953e95b000ad57b0871691495f901dd272bf56542c928d46c20fbe0d4f029f0"}