{
  "slug": "capabilite",
  "nom": "Capabilité du processus",
  "numero": 55,
  "scenario_id": "CAS-MET",
  "question": "La distribution de largeur du fonctionnement de référence est-elle compatible avec la spécification fictive ?",
  "consigne": "Utiliser uniquement les 150 mesures de référence avec leur sous-groupage. Justifier les spécifications, étudier la mesure et la stabilité avant de commenter les indices.",
  "etapes": [
    "Séparer référence et surveillance; examiner les cartes et le système de mesure. Aucun indice n'est calculé sur les 50 mesures de surveillance contenant la dérive.",
    "Examiner distribution, sous-groupage, indépendance et représentativité. La génération du jeu utilise un bruit normal, mais la validité de ce modèle en entreprise demanderait des diagnostics.",
    "Estimer sigma_intra=Rbar/d2 pour Cp/Cpk; conserver s_global pour les indices descriptifs Pp/Ppk. Montrer le décentrage avec Cpk et les conventions de dispersion.",
    "Lire les intervalles bootstrap indicatifs et les limites d'interprétation; relier le diagnostic au risque client sans promettre absence de défaut futur."
  ],
  "entrees": [
    "met_mesures",
    "met_sous_groupes",
    "met_limites_controle",
    "met_rr_contexte",
    "met_specifications",
    "met_capabilite",
    "met_references"
  ],
  "resultat_pedagogique": "Sur150 mesures de référence simulées: Cp=1.7731, Cpk=1.5594, Pp=1.7336, Ppk=1.5247. La différence Cp/Cpk reflète ici le décentrage; celle Cp/Pp provient des conventions de dispersion. Les spécifications99,5/100,5 mm viennent de l'exercice. Les intervalles percentile par rééchantillonnage de 800 ensembles de 30 sous-groupes donnent un repère d'incertitude, pas une garantie. Définitions et hypothèses: https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm; sigma_intra: https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc321.htm.",
  "livrables": [
    "Spécification, caractéristique, unité et source",
    "Indices avec dispersion utilisée, sous-groupage et périmètre",
    "Diagnostic argumenté incluant stabilité, mesure, hypothèses et incertitude"
  ],
  "vigilance": [
    "Les indices ne remplacent ni l'analyse temporelle ni la vérification du système de mesure.",
    "Pp/Ppk décrivent ici la dispersion globale de la fenêtre de référence; elle ne suffit pas à représenter toutes les variations de long terme.",
    "Les limites de contrôle ne sont pas les limites de spécification. Un taux binaire88% de commandes complètes ne se transforme pas en Cpk.",
    "Bootstrap par sous-groupes: intervalle indicatif conditionnel à cet échantillon et à son mode de collecte; pas un intervalle de prédiction ni une preuve de normalité."
  ],
  "lecons": [
    "situation-initiale",
    "verifier-causes"
  ],
  "phases": [
    "mesurer",
    "analyser",
    "controler"
  ],
  "statut_donnees": "entierement_synthetiques",
  "scenario": {
    "id": "CAS-MET",
    "nom": "Mesurer et régler la largeur d’une étiquette",
    "perimetre": "Largeur nominale 100 mm, limites fictives 99,5–100,5 mm",
    "debut": "2026-03-02",
    "fin": "2026-05-29",
    "statut": "Séries, répétitions et plans expérimentaux synthétiques distincts des commandes"
  },
  "tables": {
    "met_mesures": [
      {
        "id": "MET-REFERENCE-01-1",
        "sous_groupe_id": "MET-REFERENCE-01",
        "ordre_piece": 1,
        "largeur_mm": 99.989,
        "horodatage": "2026-03-04T08:00:00"
      },
      {
        "id": "MET-REFERENCE-01-2",
        "sous_groupe_id": "MET-REFERENCE-01",
        "ordre_piece": 2,
        "largeur_mm": 100.038,
        "horodatage": "2026-03-04T08:00:10"
      },
      {
        "id": "MET-REFERENCE-01-3",
        "sous_groupe_id": "MET-REFERENCE-01",
        "ordre_piece": 3,
        "largeur_mm": 100.052,
        "horodatage": "2026-03-04T08:00:20"
      },
      {
        "id": "MET-REFERENCE-01-4",
        "sous_groupe_id": "MET-REFERENCE-01",
        "ordre_piece": 4,
        "largeur_mm": 100.126,
        "horodatage": "2026-03-04T08:00:30"
      },
      {
        "id": "MET-REFERENCE-01-5",
        "sous_groupe_id": "MET-REFERENCE-01",
        "ordre_piece": 5,
        "largeur_mm": 99.961,
        "horodatage": "2026-03-04T08:00:40"
      },
      {
        "id": "MET-REFERENCE-02-1",
        "sous_groupe_id": "MET-REFERENCE-02",
        "ordre_piece": 1,
        "largeur_mm": 100.108,
        "horodatage": "2026-03-04T08:15:00"
      },
      {
        "id": "MET-REFERENCE-02-2",
        "sous_groupe_id": "MET-REFERENCE-02",
        "ordre_piece": 2,
        "largeur_mm": 100.01,
        "horodatage": "2026-03-04T08:15:10"
      },
      {
        "id": "MET-REFERENCE-02-3",
        "sous_groupe_id": "MET-REFERENCE-02",
        "ordre_piece": 3,
        "largeur_mm": 100.076,
        "horodatage": "2026-03-04T08:15:20"
      },
      {
        "id": "MET-REFERENCE-02-4",
        "sous_groupe_id": "MET-REFERENCE-02",
        "ordre_piece": 4,
        "largeur_mm": 100.079,
        "horodatage": "2026-03-04T08:15:30"
      },
      {
        "id": "MET-REFERENCE-02-5",
        "sous_groupe_id": "MET-REFERENCE-02",
        "ordre_piece": 5,
        "largeur_mm": 99.979,
        "horodatage": "2026-03-04T08:15:40"
      },
      {
        "id": "MET-REFERENCE-03-1",
        "sous_groupe_id": "MET-REFERENCE-03",
        "ordre_piece": 1,
        "largeur_mm": 99.909,
        "horodatage": "2026-03-04T08:30:00"
      },
      {
        "id": "MET-REFERENCE-03-2",
        "sous_groupe_id": "MET-REFERENCE-03",
        "ordre_piece": 2,
        "largeur_mm": 100.124,
        "horodatage": "2026-03-04T08:30:10"
      },
      {
        "id": "MET-REFERENCE-03-3",
        "sous_groupe_id": "MET-REFERENCE-03",
        "ordre_piece": 3,
        "largeur_mm": 100.067,
        "horodatage": "2026-03-04T08:30:20"
      },
      {
        "id": "MET-REFERENCE-03-4",
        "sous_groupe_id": "MET-REFERENCE-03",
        "ordre_piece": 4,
        "largeur_mm": 100.039,
        "horodatage": "2026-03-04T08:30:30"
      },
      {
        "id": "MET-REFERENCE-03-5",
        "sous_groupe_id": "MET-REFERENCE-03",
        "ordre_piece": 5,
        "largeur_mm": 100.006,
        "horodatage": "2026-03-04T08:30:40"
      },
      {
        "id": "MET-REFERENCE-04-1",
        "sous_groupe_id": "MET-REFERENCE-04",
        "ordre_piece": 1,
        "largeur_mm": 99.993,
        "horodatage": "2026-03-04T08:45:00"
      },
      {
        "id": "MET-REFERENCE-04-2",
        "sous_groupe_id": "MET-REFERENCE-04",
        "ordre_piece": 2,
        "largeur_mm": 99.974,
        "horodatage": "2026-03-04T08:45:10"
      },
      {
        "id": "MET-REFERENCE-04-3",
        "sous_groupe_id": "MET-REFERENCE-04",
        "ordre_piece": 3,
        "largeur_mm": 99.997,
        "horodatage": "2026-03-04T08:45:20"
      },
      {
        "id": "MET-REFERENCE-04-4",
        "sous_groupe_id": "MET-REFERENCE-04",
        "ordre_piece": 4,
        "largeur_mm": 100.127,
        "horodatage": "2026-03-04T08:45:30"
      },
      {
        "id": "MET-REFERENCE-04-5",
        "sous_groupe_id": "MET-REFERENCE-04",
        "ordre_piece": 5,
        "largeur_mm": 100.104,
        "horodatage": "2026-03-04T08:45:40"
      },
      {
        "id": "MET-REFERENCE-05-1",
        "sous_groupe_id": "MET-REFERENCE-05",
        "ordre_piece": 1,
        "largeur_mm": 99.893,
        "horodatage": "2026-03-04T09:00:00"
      },
      {
        "id": "MET-REFERENCE-05-2",
        "sous_groupe_id": "MET-REFERENCE-05",
        "ordre_piece": 2,
        "largeur_mm": 100.182,
        "horodatage": "2026-03-04T09:00:10"
      },
      {
        "id": "MET-REFERENCE-05-3",
        "sous_groupe_id": "MET-REFERENCE-05",
        "ordre_piece": 3,
        "largeur_mm": 100.035,
        "horodatage": "2026-03-04T09:00:20"
      },
      {
        "id": "MET-REFERENCE-05-4",
        "sous_groupe_id": "MET-REFERENCE-05",
        "ordre_piece": 4,
        "largeur_mm": 100.062,
        "horodatage": "2026-03-04T09:00:30"
      },
      {
        "id": "MET-REFERENCE-05-5",
        "sous_groupe_id": "MET-REFERENCE-05",
        "ordre_piece": 5,
        "largeur_mm": 100.11,
        "horodatage": "2026-03-04T09:00:40"
      },
      {
        "id": "MET-REFERENCE-06-1",
        "sous_groupe_id": "MET-REFERENCE-06",
        "ordre_piece": 1,
        "largeur_mm": 100.139,
        "horodatage": "2026-03-04T09:15:00"
      },
      {
        "id": "MET-REFERENCE-06-2",
        "sous_groupe_id": "MET-REFERENCE-06",
        "ordre_piece": 2,
        "largeur_mm": 100.323,
        "horodatage": "2026-03-04T09:15:10"
      },
      {
        "id": "MET-REFERENCE-06-3",
        "sous_groupe_id": "MET-REFERENCE-06",
        "ordre_piece": 3,
        "largeur_mm": 99.99,
        "horodatage": "2026-03-04T09:15:20"
      },
      {
        "id": "MET-REFERENCE-06-4",
        "sous_groupe_id": "MET-REFERENCE-06",
        "ordre_piece": 4,
        "largeur_mm": 100.095,
        "horodatage": "2026-03-04T09:15:30"
      },
      {
        "id": "MET-REFERENCE-06-5",
        "sous_groupe_id": "MET-REFERENCE-06",
        "ordre_piece": 5,
        "largeur_mm": 100.034,
        "horodatage": "2026-03-04T09:15:40"
      },
      {
        "id": "MET-REFERENCE-07-1",
        "sous_groupe_id": "MET-REFERENCE-07",
        "ordre_piece": 1,
        "largeur_mm": 99.97,
        "horodatage": "2026-03-04T09:30:00"
      },
      {
        "id": "MET-REFERENCE-07-2",
        "sous_groupe_id": "MET-REFERENCE-07",
        "ordre_piece": 2,
        "largeur_mm": 100.043,
        "horodatage": "2026-03-04T09:30:10"
      },
      {
        "id": "MET-REFERENCE-07-3",
        "sous_groupe_id": "MET-REFERENCE-07",
        "ordre_piece": 3,
        "largeur_mm": 100.14,
        "horodatage": "2026-03-04T09:30:20"
      },
      {
        "id": "MET-REFERENCE-07-4",
        "sous_groupe_id": "MET-REFERENCE-07",
        "ordre_piece": 4,
        "largeur_mm": 99.885,
        "horodatage": "2026-03-04T09:30:30"
      },
      {
        "id": "MET-REFERENCE-07-5",
        "sous_groupe_id": "MET-REFERENCE-07",
        "ordre_piece": 5,
        "largeur_mm": 100.158,
        "horodatage": "2026-03-04T09:30:40"
      },
      {
        "id": "MET-REFERENCE-08-1",
        "sous_groupe_id": "MET-REFERENCE-08",
        "ordre_piece": 1,
        "largeur_mm": 99.817,
        "horodatage": "2026-03-04T09:45:00"
      },
      {
        "id": "MET-REFERENCE-08-2",
        "sous_groupe_id": "MET-REFERENCE-08",
        "ordre_piece": 2,
        "largeur_mm": 99.98,
        "horodatage": "2026-03-04T09:45:10"
      },
      {
        "id": "MET-REFERENCE-08-3",
        "sous_groupe_id": "MET-REFERENCE-08",
        "ordre_piece": 3,
        "largeur_mm": 99.817,
        "horodatage": "2026-03-04T09:45:20"
      },
      {
        "id": "MET-REFERENCE-08-4",
        "sous_groupe_id": "MET-REFERENCE-08",
        "ordre_piece": 4,
        "largeur_mm": 100.156,
        "horodatage": "2026-03-04T09:45:30"
      },
      {
        "id": "MET-REFERENCE-08-5",
        "sous_groupe_id": "MET-REFERENCE-08",
        "ordre_piece": 5,
        "largeur_mm": 100.063,
        "horodatage": "2026-03-04T09:45:40"
      },
      {
        "id": "MET-REFERENCE-09-1",
        "sous_groupe_id": "MET-REFERENCE-09",
        "ordre_piece": 1,
        "largeur_mm": 100.134,
        "horodatage": "2026-03-04T10:00:00"
      },
      {
        "id": "MET-REFERENCE-09-2",
        "sous_groupe_id": "MET-REFERENCE-09",
        "ordre_piece": 2,
        "largeur_mm": 100.105,
        "horodatage": "2026-03-04T10:00:10"
      },
      {
        "id": "MET-REFERENCE-09-3",
        "sous_groupe_id": "MET-REFERENCE-09",
        "ordre_piece": 3,
        "largeur_mm": 100.032,
        "horodatage": "2026-03-04T10:00:20"
      },
      {
        "id": "MET-REFERENCE-09-4",
        "sous_groupe_id": "MET-REFERENCE-09",
        "ordre_piece": 4,
        "largeur_mm": 99.963,
        "horodatage": "2026-03-04T10:00:30"
      },
      {
        "id": "MET-REFERENCE-09-5",
        "sous_groupe_id": "MET-REFERENCE-09",
        "ordre_piece": 5,
        "largeur_mm": 100.083,
        "horodatage": "2026-03-04T10:00:40"
      },
      {
        "id": "MET-REFERENCE-10-1",
        "sous_groupe_id": "MET-REFERENCE-10",
        "ordre_piece": 1,
        "largeur_mm": 100.068,
        "horodatage": "2026-03-04T10:15:00"
      },
      {
        "id": "MET-REFERENCE-10-2",
        "sous_groupe_id": "MET-REFERENCE-10",
        "ordre_piece": 2,
        "largeur_mm": 99.996,
        "horodatage": "2026-03-04T10:15:10"
      },
      {
        "id": "MET-REFERENCE-10-3",
        "sous_groupe_id": "MET-REFERENCE-10",
        "ordre_piece": 3,
        "largeur_mm": 100.09,
        "horodatage": "2026-03-04T10:15:20"
      },
      {
        "id": "MET-REFERENCE-10-4",
        "sous_groupe_id": "MET-REFERENCE-10",
        "ordre_piece": 4,
        "largeur_mm": 99.997,
        "horodatage": "2026-03-04T10:15:30"
      },
      {
        "id": "MET-REFERENCE-10-5",
        "sous_groupe_id": "MET-REFERENCE-10",
        "ordre_piece": 5,
        "largeur_mm": 99.961,
        "horodatage": "2026-03-04T10:15:40"
      },
      {
        "id": "MET-REFERENCE-11-1",
        "sous_groupe_id": "MET-REFERENCE-11",
        "ordre_piece": 1,
        "largeur_mm": 100.267,
        "horodatage": "2026-03-04T10:30:00"
      },
      {
        "id": "MET-REFERENCE-11-2",
        "sous_groupe_id": "MET-REFERENCE-11",
        "ordre_piece": 2,
        "largeur_mm": 100.081,
        "horodatage": "2026-03-04T10:30:10"
      },
      {
        "id": "MET-REFERENCE-11-3",
        "sous_groupe_id": "MET-REFERENCE-11",
        "ordre_piece": 3,
        "largeur_mm": 100.17,
        "horodatage": "2026-03-04T10:30:20"
      },
      {
        "id": "MET-REFERENCE-11-4",
        "sous_groupe_id": "MET-REFERENCE-11",
        "ordre_piece": 4,
        "largeur_mm": 100.163,
        "horodatage": "2026-03-04T10:30:30"
      },
      {
        "id": "MET-REFERENCE-11-5",
        "sous_groupe_id": "MET-REFERENCE-11",
        "ordre_piece": 5,
        "largeur_mm": 99.945,
        "horodatage": "2026-03-04T10:30:40"
      },
      {
        "id": "MET-REFERENCE-12-1",
        "sous_groupe_id": "MET-REFERENCE-12",
        "ordre_piece": 1,
        "largeur_mm": 99.962,
        "horodatage": "2026-03-04T10:45:00"
      },
      {
        "id": "MET-REFERENCE-12-2",
        "sous_groupe_id": "MET-REFERENCE-12",
        "ordre_piece": 2,
        "largeur_mm": 100.194,
        "horodatage": "2026-03-04T10:45:10"
      },
      {
        "id": "MET-REFERENCE-12-3",
        "sous_groupe_id": "MET-REFERENCE-12",
        "ordre_piece": 3,
        "largeur_mm": 100.177,
        "horodatage": "2026-03-04T10:45:20"
      },
      {
        "id": "MET-REFERENCE-12-4",
        "sous_groupe_id": "MET-REFERENCE-12",
        "ordre_piece": 4,
        "largeur_mm": 99.999,
        "horodatage": "2026-03-04T10:45:30"
      },
      {
        "id": "MET-REFERENCE-12-5",
        "sous_groupe_id": "MET-REFERENCE-12",
        "ordre_piece": 5,
        "largeur_mm": 100.037,
        "horodatage": "2026-03-04T10:45:40"
      },
      {
        "id": "MET-REFERENCE-13-1",
        "sous_groupe_id": "MET-REFERENCE-13",
        "ordre_piece": 1,
        "largeur_mm": 99.834,
        "horodatage": "2026-03-04T11:00:00"
      },
      {
        "id": "MET-REFERENCE-13-2",
        "sous_groupe_id": "MET-REFERENCE-13",
        "ordre_piece": 2,
        "largeur_mm": 99.995,
        "horodatage": "2026-03-04T11:00:10"
      },
      {
        "id": "MET-REFERENCE-13-3",
        "sous_groupe_id": "MET-REFERENCE-13",
        "ordre_piece": 3,
        "largeur_mm": 100.072,
        "horodatage": "2026-03-04T11:00:20"
      },
      {
        "id": "MET-REFERENCE-13-4",
        "sous_groupe_id": "MET-REFERENCE-13",
        "ordre_piece": 4,
        "largeur_mm": 100.042,
        "horodatage": "2026-03-04T11:00:30"
      },
      {
        "id": "MET-REFERENCE-13-5",
        "sous_groupe_id": "MET-REFERENCE-13",
        "ordre_piece": 5,
        "largeur_mm": 100.088,
        "horodatage": "2026-03-04T11:00:40"
      },
      {
        "id": "MET-REFERENCE-14-1",
        "sous_groupe_id": "MET-REFERENCE-14",
        "ordre_piece": 1,
        "largeur_mm": 100.18,
        "horodatage": "2026-03-04T11:15:00"
      },
      {
        "id": "MET-REFERENCE-14-2",
        "sous_groupe_id": "MET-REFERENCE-14",
        "ordre_piece": 2,
        "largeur_mm": 99.98,
        "horodatage": "2026-03-04T11:15:10"
      },
      {
        "id": "MET-REFERENCE-14-3",
        "sous_groupe_id": "MET-REFERENCE-14",
        "ordre_piece": 3,
        "largeur_mm": 100.041,
        "horodatage": "2026-03-04T11:15:20"
      },
      {
        "id": "MET-REFERENCE-14-4",
        "sous_groupe_id": "MET-REFERENCE-14",
        "ordre_piece": 4,
        "largeur_mm": 100.077,
        "horodatage": "2026-03-04T11:15:30"
      },
      {
        "id": "MET-REFERENCE-14-5",
        "sous_groupe_id": "MET-REFERENCE-14",
        "ordre_piece": 5,
        "largeur_mm": 100.071,
        "horodatage": "2026-03-04T11:15:40"
      },
      {
        "id": "MET-REFERENCE-15-1",
        "sous_groupe_id": "MET-REFERENCE-15",
        "ordre_piece": 1,
        "largeur_mm": 100.199,
        "horodatage": "2026-03-04T11:30:00"
      },
      {
        "id": "MET-REFERENCE-15-2",
        "sous_groupe_id": "MET-REFERENCE-15",
        "ordre_piece": 2,
        "largeur_mm": 100.157,
        "horodatage": "2026-03-04T11:30:10"
      },
      {
        "id": "MET-REFERENCE-15-3",
        "sous_groupe_id": "MET-REFERENCE-15",
        "ordre_piece": 3,
        "largeur_mm": 100.005,
        "horodatage": "2026-03-04T11:30:20"
      },
      {
        "id": "MET-REFERENCE-15-4",
        "sous_groupe_id": "MET-REFERENCE-15",
        "ordre_piece": 4,
        "largeur_mm": 100.039,
        "horodatage": "2026-03-04T11:30:30"
      },
      {
        "id": "MET-REFERENCE-15-5",
        "sous_groupe_id": "MET-REFERENCE-15",
        "ordre_piece": 5,
        "largeur_mm": 99.914,
        "horodatage": "2026-03-04T11:30:40"
      },
      {
        "id": "MET-REFERENCE-16-1",
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        "moyenne_mm": 100.0488,
        "etendue_mm": 0.07099999999999795,
        "debut": "2026-03-04T15:15:00",
        "evenement_connu_du_generateur": "Réglage de référence simulé",
        "signal_xbar": 0,
        "signal_r": 0
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      {
        "id": "MET-SURVEILLANCE-01",
        "serie": "surveillance",
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        "etendue_mm": 0.35700000000001353,
        "debut": "2026-03-05T08:00:00",
        "evenement_connu_du_generateur": "Réglage de référence simulé",
        "signal_xbar": 0,
        "signal_r": 0
      },
      {
        "id": "MET-SURVEILLANCE-02",
        "serie": "surveillance",
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        "effectif": 5,
        "moyenne_mm": 100.0372,
        "etendue_mm": 0.19599999999999795,
        "debut": "2026-03-05T08:15:00",
        "evenement_connu_du_generateur": "Réglage de référence simulé",
        "signal_xbar": 0,
        "signal_r": 0
      },
      {
        "id": "MET-SURVEILLANCE-03",
        "serie": "surveillance",
        "numero": 3,
        "effectif": 5,
        "moyenne_mm": 100.0386,
        "etendue_mm": 0.1290000000000049,
        "debut": "2026-03-05T08:30:00",
        "evenement_connu_du_generateur": "Réglage de référence simulé",
        "signal_xbar": 0,
        "signal_r": 0
      },
      {
        "id": "MET-SURVEILLANCE-04",
        "serie": "surveillance",
        "numero": 4,
        "effectif": 5,
        "moyenne_mm": 100.1382,
        "etendue_mm": 0.27300000000001035,
        "debut": "2026-03-05T08:45:00",
        "evenement_connu_du_generateur": "Réglage de référence simulé",
        "signal_xbar": 0,
        "signal_r": 0
      },
      {
        "id": "MET-SURVEILLANCE-05",
        "serie": "surveillance",
        "numero": 5,
        "effectif": 5,
        "moyenne_mm": 100.0992,
        "etendue_mm": 0.1880000000000024,
        "debut": "2026-03-05T09:00:00",
        "evenement_connu_du_generateur": "Réglage de référence simulé",
        "signal_xbar": 0,
        "signal_r": 0
      },
      {
        "id": "MET-SURVEILLANCE-06",
        "serie": "surveillance",
        "numero": 6,
        "effectif": 5,
        "moyenne_mm": 100.4156,
        "etendue_mm": 0.16900000000001114,
        "debut": "2026-03-05T09:15:00",
        "evenement_connu_du_generateur": "Déplacement de centrage simulé; investigation à mener",
        "signal_xbar": 1,
        "signal_r": 0
      },
      {
        "id": "MET-SURVEILLANCE-07",
        "serie": "surveillance",
        "numero": 7,
        "effectif": 5,
        "moyenne_mm": 100.3584,
        "etendue_mm": 0.1700000000000017,
        "debut": "2026-03-05T09:30:00",
        "evenement_connu_du_generateur": "Déplacement de centrage simulé; investigation à mener",
        "signal_xbar": 1,
        "signal_r": 0
      },
      {
        "id": "MET-SURVEILLANCE-08",
        "serie": "surveillance",
        "numero": 8,
        "effectif": 5,
        "moyenne_mm": 100.4042,
        "etendue_mm": 0.29599999999999227,
        "debut": "2026-03-05T09:45:00",
        "evenement_connu_du_generateur": "Déplacement de centrage simulé; investigation à mener",
        "signal_xbar": 1,
        "signal_r": 0
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      {
        "id": "MET-SURVEILLANCE-09",
        "serie": "surveillance",
        "numero": 9,
        "effectif": 5,
        "moyenne_mm": 100.3952,
        "etendue_mm": 0.2469999999999999,
        "debut": "2026-03-05T10:00:00",
        "evenement_connu_du_generateur": "Déplacement de centrage simulé; investigation à mener",
        "signal_xbar": 1,
        "signal_r": 0
      },
      {
        "id": "MET-SURVEILLANCE-10",
        "serie": "surveillance",
        "numero": 10,
        "effectif": 5,
        "moyenne_mm": 100.4122,
        "etendue_mm": 0.284000000000006,
        "debut": "2026-03-05T10:15:00",
        "evenement_connu_du_generateur": "Déplacement de centrage simulé; investigation à mener",
        "signal_xbar": 1,
        "signal_r": 0
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    ],
    "met_limites_controle": [
      {
        "id": "LIM-XBAR",
        "carte": "Xbar",
        "centre_mm": 100.06026,
        "limite_basse_mm": 99.93410856666667,
        "limite_haute_mm": 100.18641143333333,
        "reference": "30 sous-groupes de5; règle annoncée: un point hors limites3sigma"
      },
      {
        "id": "LIM-R",
        "carte": "R",
        "centre_mm": 0.21863333333333515,
        "limite_basse_mm": 0.0,
        "limite_haute_mm": 0.4624095000000039,
        "reference": "Même référence; aucune réestimation automatique sur surveillance"
      }
    ],
    "met_rr_contexte": [
      {
        "id": "RR-USAGE",
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        "nombre_operateurs": 3,
        "repetitions_par_cellule": 2,
        "sigma_process_reference_mm": 0.09613974937244242,
        "sigma_rr_mm": 0.009171968163917545,
        "ratio_sigma_rr_sigma_process_pct": 9.540245552737634,
        "categories_distinctes_estimees": 16,
        "modele": "ANOVA croisée aléatoire avec interaction, conservée sans test de regroupement; composantes négatives bornées à0; percentages non additifs en ecart-type"
      }
    ],
    "met_specifications": [
      {
        "id": "SPEC-LARG-001",
        "scenario_id": "CAS-MET",
        "caracteristique": "Largeur d'étiquette",
        "unite": "mm",
        "nominal": 100.0,
        "lsl": 99.5,
        "usl": 100.5,
        "resolution": 0.001,
        "statut": "Spécification fictive pour exercice; aucune portée réglementaire"
      }
    ],
    "met_capabilite": [
      {
        "id": "CAP-01",
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        "indicateur": "effectif",
        "valeur": 150.0,
        "unite": "mesures",
        "formule": "30sous-groupes×5mesures",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-02",
        "ordre": 2,
        "indicateur": "moyenne",
        "valeur": 100.06026,
        "unite": "mm",
        "formule": "Somme des150mesures/150",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-03",
        "ordre": 3,
        "indicateur": "rbar",
        "valeur": 0.21863333333333515,
        "unite": "mm",
        "formule": "Moyenne des30étendues",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-04",
        "ordre": 4,
        "indicateur": "sigma_intra",
        "valeur": 0.09399541415878553,
        "unite": "mm",
        "formule": "Rbar/2,326",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-05",
        "ordre": 5,
        "indicateur": "s_global",
        "valeur": 0.09613974937244242,
        "unite": "mm",
        "formule": "Écart-type échantillon des150mesures, dénominateur149",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-06",
        "ordre": 6,
        "indicateur": "cp",
        "valeur": 1.7731361488031567,
        "unite": "indice",
        "formule": "(USL−LSL)/(6sigma_intra)",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-07",
        "ordre": 7,
        "indicateur": "cpk",
        "valeur": 1.559437780149402,
        "unite": "indice",
        "formule": "min(USL−moyenne,moyenne−LSL)/(3sigma_intra)",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-08",
        "ordre": 8,
        "indicateur": "pp",
        "valeur": 1.7335874885735882,
        "unite": "indice",
        "formule": "(USL−LSL)/(6s_global)",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-09",
        "ordre": 9,
        "indicateur": "ppk",
        "valeur": 1.524655524450701,
        "unite": "indice",
        "formule": "min(USL−moyenne,moyenne−LSL)/(3s_global)",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-10",
        "ordre": 10,
        "indicateur": "cp_boot_p025",
        "valeur": 1.574121140819585,
        "unite": "indice",
        "formule": "Percentile2,5% de800rééchantillonnages des sous-groupes",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-11",
        "ordre": 11,
        "indicateur": "cp_boot_p975",
        "valeur": 2.041452200731216,
        "unite": "indice",
        "formule": "Percentile97,5% de800rééchantillonnages des sous-groupes",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-12",
        "ordre": 12,
        "indicateur": "cpk_boot_p025",
        "valeur": 1.362727114609997,
        "unite": "indice",
        "formule": "Percentile2,5% de800rééchantillonnages des sous-groupes",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-13",
        "ordre": 13,
        "indicateur": "cpk_boot_p975",
        "valeur": 1.812446901981139,
        "unite": "indice",
        "formule": "Percentile97,5% de800rééchantillonnages des sous-groupes",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      },
      {
        "id": "CAP-14",
        "ordre": 14,
        "indicateur": "hors_specification_observes",
        "valeur": 0.0,
        "unite": "mesures",
        "formule": "Comptage sur référence seulement, sans prédiction de zéro défaut futur",
        "perimetre": "Référence complète de150mesures; jamais la surveillance avec dérive"
      }
    ],
    "met_references": [
      {
        "id": "REF-SPC",
        "organisme": "NIST/SEMATECH",
        "titre": "Shewhart X-bar and R and S Control Charts",
        "url": "https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc321.htm",
        "consulte_le": "2026-10-21",
        "usage": "Formules et constantes A2/D3/D4 de la carte Xbar-R; convention D4=2,115"
      },
      {
        "id": "REF-ANOVA",
        "organisme": "NIST/SEMATECH",
        "titre": "Two-Way Crossed ANOVA",
        "url": "https://www.itl.nist.gov/div898/handbook/ppc/section2/ppc232.htm",
        "consulte_le": "2026-10-21",
        "usage": "Plan croisé, moyennes, sommes de carrés et degrés de liberté; composantes par moments développées dans l'étude"
      },
      {
        "id": "REF-CAPA",
        "organisme": "NIST/SEMATECH",
        "titre": "What is Process Capability?",
        "url": "https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm",
        "consulte_le": "2026-10-21",
        "usage": "Définitions des indices et hypothèses; conventions intra/globale précisées dans l'étude"
      },
      {
        "id": "REF-DOE",
        "organisme": "NIST/SEMATECH",
        "titre": "Two-level full factorial designs",
        "url": "https://www.itl.nist.gov/div898/handbook/pri/section3/pri3331.htm",
        "consulte_le": "2026-10-21",
        "usage": "Plan2^3, codage−1/+1, répétition et orthogonalité"
      },
      {
        "id": "REF-D2",
        "organisme": "Minitab, documentation éditeur",
        "titre": "Methods and formulas for estimating sigma for Xbar Chart",
        "url": "https://support.minitab.com/en-us/minitab/help-and-how-to/quality-and-process-improvement/control-charts/how-to/variables-charts-for-subgroups/xbar-chart/methods-and-formulas/estimating-sigma/",
        "consulte_le": "2026-10-21",
        "usage": "Constante d2(5)=2,326; ne pas confondre d4 d'une autre table et D4 de la carte R"
      }
    ]
  },
  "resultats": [
    {
      "indicateur": "effectif",
      "valeur": 150.0,
      "unite": "mesures",
      "formule": "30sous-groupes×5mesures"
    },
    {
      "indicateur": "moyenne",
      "valeur": 100.06026,
      "unite": "mm",
      "formule": "Somme des150mesures/150"
    },
    {
      "indicateur": "rbar",
      "valeur": 0.21863333333333515,
      "unite": "mm",
      "formule": "Moyenne des30étendues"
    },
    {
      "indicateur": "sigma_intra",
      "valeur": 0.09399541415878553,
      "unite": "mm",
      "formule": "Rbar/2,326"
    },
    {
      "indicateur": "s_global",
      "valeur": 0.09613974937244242,
      "unite": "mm",
      "formule": "Écart-type échantillon des150mesures, dénominateur149"
    },
    {
      "indicateur": "cp",
      "valeur": 1.7731361488031567,
      "unite": "indice",
      "formule": "(USL−LSL)/(6sigma_intra)"
    },
    {
      "indicateur": "cpk",
      "valeur": 1.559437780149402,
      "unite": "indice",
      "formule": "min(USL−moyenne,moyenne−LSL)/(3sigma_intra)"
    },
    {
      "indicateur": "pp",
      "valeur": 1.7335874885735882,
      "unite": "indice",
      "formule": "(USL−LSL)/(6s_global)"
    },
    {
      "indicateur": "ppk",
      "valeur": 1.524655524450701,
      "unite": "indice",
      "formule": "min(USL−moyenne,moyenne−LSL)/(3s_global)"
    },
    {
      "indicateur": "cp_boot_p025",
      "valeur": 1.574121140819585,
      "unite": "indice",
      "formule": "Percentile2,5% de800rééchantillonnages des sous-groupes"
    },
    {
      "indicateur": "cp_boot_p975",
      "valeur": 2.041452200731216,
      "unite": "indice",
      "formule": "Percentile97,5% de800rééchantillonnages des sous-groupes"
    },
    {
      "indicateur": "cpk_boot_p025",
      "valeur": 1.362727114609997,
      "unite": "indice",
      "formule": "Percentile2,5% de800rééchantillonnages des sous-groupes"
    },
    {
      "indicateur": "cpk_boot_p975",
      "valeur": 1.812446901981139,
      "unite": "indice",
      "formule": "Percentile97,5% de800rééchantillonnages des sous-groupes"
    },
    {
      "indicateur": "hors_specification_observes",
      "valeur": 0.0,
      "unite": "mesures",
      "formule": "Comptage sur référence seulement, sans prédiction de zéro défaut futur"
    }
  ],
  "preuves": [
    {
      "id": "MET-SPC",
      "scenario_id": "CAS-MET",
      "type": "releve_synthetique",
      "titre": "Largeur d'étiquette : référence et surveillance séparées",
      "description": "Une référence construite par génération gaussienne (seed1021), 30 sous-groupes de 5 étiquettes consécutives; puis10 sous-groupes de surveillance avec déplacement simulé du centrage au groupe 6. Les nombres ne proviennent d'aucune machine réelle.",
      "statut": "simule",
      "date": "2026-03-04"
    },
    {
      "id": "MET-RR",
      "scenario_id": "CAS-MET",
      "type": "protocole_et_releve_synthetiques",
      "titre": "R&R croisée équilibrée de la largeur",
      "description": "Dix pièces identifiées, trois opérateurs fictifs et deux répétitions, ordre randomisé et pièces masquées. Le modèle à effets aléatoires avec interaction est conservé; les composantes négatives sont déclarées puis bornées à zéro pour les écarts-types, sans regroupement automatique de l'interaction.",
      "statut": "simule",
      "date": "2026-03-03"
    },
    {
      "id": "MET-SPEC",
      "scenario_id": "CAS-MET",
      "type": "exigence_pedagogique",
      "titre": "Spécification fictive de largeur",
      "description": "Nominal100 mm, limites99,5 et100,5 mm, résolution instrument0,001 mm. Exigence conçue pour l'exercice, distincte des limites statistiques et sans statut réglementaire.",
      "statut": "hypothese",
      "date": "2026-03-02"
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        "name": "largeur_mm",
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        "name": "horodatage",
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        "name": "evenement_connu_du_generateur",
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    "met_rr_contexte": [
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        "name": "nombre_pieces",
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        "name": "nombre_operateurs",
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        "name": "repetitions_par_cellule",
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        "name": "sigma_process_reference_mm",
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        "name": "ratio_sigma_rr_sigma_process_pct",
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        "name": "categories_distinctes_estimees",
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    "met_specifications": [
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        "name": "lsl",
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      {
        "name": "usl",
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        "not_null": true
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      {
        "name": "resolution",
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        "name": "statut",
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    "met_capabilite": [
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        "name": "ordre",
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        "name": "indicateur",
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        "name": "valeur",
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      {
        "name": "formule",
        "type": "TEXT",
        "not_null": true
      },
      {
        "name": "perimetre",
        "type": "TEXT",
        "not_null": true
      }
    ],
    "met_references": [
      {
        "name": "id",
        "type": "TEXT",
        "not_null": true
      },
      {
        "name": "organisme",
        "type": "TEXT",
        "not_null": true
      },
      {
        "name": "titre",
        "type": "TEXT",
        "not_null": true
      },
      {
        "name": "url",
        "type": "TEXT",
        "not_null": true
      },
      {
        "name": "consulte_le",
        "type": "TEXT",
        "not_null": true
      },
      {
        "name": "usage",
        "type": "TEXT",
        "not_null": true
      }
    ]
  }
}