{"paper":{"title":"Risk-Calibrated Process Capability Approval with Finite Samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Process capability approval decisions can be risk-calibrated to account for finite-sample estimation uncertainty and asymmetric operational losses.","cross_cats":["stat.ME"],"primary_cat":"stat.AP","authors_text":"Fei Jiang, Lei Yang","submitted_at":"2026-03-15T16:47:59Z","abstract_excerpt":"Process capability indices such as $C_{pk}$ are widely used in manufacturing to support supplier qualification, pilot-build release, and production approval. In practice, approval decisions are often based on deterministic threshold rules of the form $\\widehat{C}_{pk} \\ge C_0$. Because $\\widehat{C}_{pk}$ is estimated from finite samples, however, such decisions are inherently stochastic, especially when the true capability lies near the approval threshold. This paper develops a risk-calibrated decision framework for process capability approval that explicitly accounts for estimation uncertaint"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting formulation unifies several commonly used procedures, including deterministic thresholding, lower confidence bound rules, and probability-based approval rules, and naturally extends them to cost-sensitive decision rules derived from asymmetric operational loss.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The standard error of the C_pk estimator can be reliably computed from finite samples and that the underlying process distribution permits standard capability index estimation (typically normality).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Risk-calibrated process capability approval uses a threshold of C0 plus k times the standard error of the C_pk estimate, with k chosen from tolerable failure probability or false-accept/false-reject cost ratio.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Process capability approval decisions can be risk-calibrated to account for finite-sample estimation uncertainty and asymmetric operational losses.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a3792434c197dd0dbea6195b46f6211e0c0cbe842dce415ac5865b2e3c44d5c1"},"source":{"id":"2603.14479","kind":"arxiv","version":2},"verdict":{"id":"5f471c2d-2d6a-46af-b57e-33062338d9b8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T11:19:30.815210Z","strongest_claim":"The resulting formulation unifies several commonly used procedures, including deterministic thresholding, lower confidence bound rules, and probability-based approval rules, and naturally extends them to cost-sensitive decision rules derived from asymmetric operational loss.","one_line_summary":"Risk-calibrated process capability approval uses a threshold of C0 plus k times the standard error of the C_pk estimate, with k chosen from tolerable failure probability or false-accept/false-reject cost ratio.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The standard error of the C_pk estimator can be reliably computed from finite samples and that the underlying process distribution permits standard capability index estimation (typically normality).","pith_extraction_headline":"Process capability approval decisions can be risk-calibrated to account for finite-sample estimation uncertainty and asymmetric operational losses."},"references":{"count":42,"sample":[{"doi":"","year":1979,"title":"McGraw-hill New York, 1979","work_id":"ff226850-655a-463b-9b20-b4de5dfe62d9","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"John wiley & sons, 2020","work_id":"054e1346-fa1f-475f-9649-327da6fe7b1f","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Statisticalmethodsinprocessmanagement – capability and performance – part 1: General prin- ciples and concepts","work_id":"cb5a9d42-7805-4e84-ae6c-70d7dd28de7f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Statisticalmethodsinprocessmanagement – capability and performance – part 4: Process capa- bility estimates and performance measures","work_id":"bcb233f8-19e8-4b7c-8494-f81cd83fb82e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Victor E. Kane. Process Capability Indices.Jour- nal of Quality Technology, 18(1):41–52, January 14","work_id":"2ccf8be3-227c-4552-8c6f-222255716e6b","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":42,"snapshot_sha256":"075146babbaeeb20a7bc87a7573f192a904c78ce41914dfb4f95f1e8c0229cfc","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"}