{"abstract":"Fay replicate shrinkage understates variance.","category":"Survey sampling estimators","checks":6,"contract":"replicates are nonempty estimates; rho lies in [0,1). Return Fay BRR variance using the supplied full estimate as center, rounded to eight decimals.","evaluation_group":"model-ce45b07ff7216f97","failed_approach":"Centering on the replicate mean erases a common replicate displacement.","family":"z-survey_sampling-fay-replicates","id":"FA-12631","implementations":{"attempt":{"sha256":"9332ca8de8f98643d9261ace85eca8e9dcc7013c0e96c1d033efc4d9ccaa3f0a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(full, replicates, rho):\n    center=sum(replicates)/len(replicates)\n    return round(sum((r-center)**2 for r in replicates)/(len(replicates)*(1-rho)**2),8)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('half shrinkage',solve(N,[N-1,N+1],0.5),4)\ncheck('common displacement',solve(N,[N+1,N+1],0.5),4)\ncheck('ordinary BRR boundary',solve(N,[N-2,N+2],0),4)\ncheck('identical full replicates',solve(N,[N,N],0.5),0)\ncheck('asymmetric deviations',solve(N,[N,N+2],0.5),8)\ncheck('quarter residual scale',solve(N,[N-1,N+1],0.75),16)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"f4cea12721da88ba9b689fb8c488175950ead340cf82b6a4f620acfdfc44905a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(full, replicates, rho):\n    return round(sum((r-full)**2 for r in replicates)/len(replicates),8)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('half shrinkage',solve(N,[N-1,N+1],0.5),4)\ncheck('common displacement',solve(N,[N+1,N+1],0.5),4)\ncheck('ordinary BRR boundary',solve(N,[N-2,N+2],0),4)\ncheck('identical full replicates',solve(N,[N,N],0.5),0)\ncheck('asymmetric deviations',solve(N,[N,N+2],0.5),8)\ncheck('quarter residual scale',solve(N,[N-1,N+1],0.75),16)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"4e0d2d57091ee5b2503eb6e300606a66d836fe9041334c3ed1888007b25b66e5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(full, replicates, rho):\n    return round(sum((r-full)**2 for r in replicates)/(len(replicates)*(1-rho)**2),8)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('half shrinkage',solve(N,[N-1,N+1],0.5),4)\ncheck('common displacement',solve(N,[N+1,N+1],0.5),4)\ncheck('ordinary BRR boundary',solve(N,[N-2,N+2],0),4)\ncheck('identical full replicates',solve(N,[N,N],0.5),0)\ncheck('asymmetric deviations',solve(N,[N,N+2],0.5),8)\ncheck('quarter residual scale',solve(N,[N-1,N+1],0.75),16)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Controlled finite fixtures; not a general survey-analysis package. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"z-survey_sampling-fay-replicates","generated_at":"2026-09-29T14:38:58.748365+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"A deterministic survey-design model isolates this sampling contract before it is embedded in a larger estimation pipeline.","repair":"Divide the average squared deviation from full estimate by (1-rho)^2.","root_cause":"BRR replicate deviations are averaged without undoing Fay shrinkage.","sha256":"57021b261efc019db998bb25e250d7e84af6b13e9f90c97ec9ec49e060fa1541","title":"Fay replicate shrinkage understates variance · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.559,"exit_code":1,"observations":[{"actual":4.0,"check":"half shrinkage","expected":4,"passed":true},{"actual":0.0,"check":"common displacement","expected":4,"passed":false},{"actual":4.0,"check":"ordinary BRR boundary","expected":4,"passed":true},{"actual":0.0,"check":"identical full replicates","expected":0,"passed":true},{"actual":4.0,"check":"asymmetric deviations","expected":8,"passed":false},{"actual":16.0,"check":"quarter residual scale","expected":16,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"half shrinkage\", \"actual\": 4.0, \"expected\": 4, \"passed\": true}, {\"check\": \"common displacement\", \"actual\": 0.0, \"expected\": 4, \"passed\": false}, {\"check\": \"ordinary BRR boundary\", \"actual\": 4.0, \"expected\": 4, \"passed\": true}, {\"check\": \"identical full replicates\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}, {\"check\": \"asymmetric deviations\", \"actual\": 4.0, \"expected\": 8, \"passed\": false}, {\"check\": \"quarter residual scale\", \"actual\": 16.0, \"expected\": 16, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.842,"exit_code":1,"observations":[{"actual":1.0,"check":"half shrinkage","expected":4,"passed":false},{"actual":1.0,"check":"common displacement","expected":4,"passed":false},{"actual":4.0,"check":"ordinary BRR boundary","expected":4,"passed":true},{"actual":0.0,"check":"identical full replicates","expected":0,"passed":true},{"actual":2.0,"check":"asymmetric deviations","expected":8,"passed":false},{"actual":1.0,"check":"quarter residual scale","expected":16,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"half shrinkage\", \"actual\": 1.0, \"expected\": 4, \"passed\": false}, {\"check\": \"common displacement\", \"actual\": 1.0, \"expected\": 4, \"passed\": false}, {\"check\": \"ordinary BRR boundary\", \"actual\": 4.0, \"expected\": 4, \"passed\": true}, {\"check\": \"identical full replicates\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}, {\"check\": \"asymmetric deviations\", \"actual\": 2.0, \"expected\": 8, \"passed\": false}, {\"check\": \"quarter residual scale\", \"actual\": 1.0, \"expected\": 16, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":38.762,"exit_code":0,"observations":[{"actual":4.0,"check":"half shrinkage","expected":4,"passed":true},{"actual":4.0,"check":"common displacement","expected":4,"passed":true},{"actual":4.0,"check":"ordinary BRR boundary","expected":4,"passed":true},{"actual":0.0,"check":"identical full replicates","expected":0,"passed":true},{"actual":8.0,"check":"asymmetric deviations","expected":8,"passed":true},{"actual":16.0,"check":"quarter residual scale","expected":16,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"half shrinkage\", \"actual\": 4.0, \"expected\": 4, \"passed\": true}, {\"check\": \"common displacement\", \"actual\": 4.0, \"expected\": 4, \"passed\": true}, {\"check\": \"ordinary BRR boundary\", \"actual\": 4.0, \"expected\": 4, \"passed\": true}, {\"check\": \"identical full replicates\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}, {\"check\": \"asymmetric deviations\", \"actual\": 8.0, \"expected\": 8, \"passed\": true}, {\"check\": \"quarter residual scale\", \"actual\": 16.0, \"expected\": 16, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}