Limites de control para gráficos xr xs

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Ejercicio, elaboracion de graficas xr-xs tomando una muestra de 11 datos por 30 dias.

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Limites de control para gráficos xr xs

  1. 1. Por: Mennys-UTT-SPCspcializados.blogspot.com
  2. 2. Graficas de Control. Es una herramienta estadística que detecta la variabilidad, consistencia, control y mejora de un proceso. La gráfica de control se usa como una forma de observar, detectar y prevenir el comportamiento del proceso.
  3. 3. Datos.Datos 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 X1 43.7 68.0 41.3 41.4 45.1 31.6 36.7 46.7 41.8 46.7 29.3 51.2 43.8 41.4 44.9 36.1 31.7 49.5 38.0 50.4 42.4 36.6 33.8 46.9 44.5 46.8 40.1 59.2 38.9 39.9 X2 45.5 53.6 54.1 50.2 46.0 55.2 45.4 53.6 58.3 34.9 47.9 43.8 37.1 49.4 47.1 34.8 40.8 30.0 35.7 50.5 56.3 30.6 59.2 45.8 37.2 42.9 43.2 49.5 47.3 40.7 X3 47.9 51.1 53.9 33.1 51.7 39.6 43.3 52.5 53.5 39.7 34.6 43.7 33.1 49.0 49.5 23.5 33.2 44.7 42.3 42.3 45.1 41.7 49.1 41.5 47.3 18.4 59.2 53.1 41.5 42.6 X4 36.3 45.0 46.5 40.4 42.9 50.9 50.6 29.7 33.2 49.9 56.6 39.1 51.9 42.2 48.2 42.6 25.4 22.0 41.6 43.6 37.0 44.4 36.7 48.7 47.0 40.4 40.7 38.8 49.2 43.9 X5 43.4 51.2 30.7 50.3 54.6 43.4 47.8 44.8 35.3 54.7 33.5 43.4 47.2 45.9 37.5 30.4 47.3 46.9 38.3 40.1 57.0 49.8 33.2 46.4 47.7 50.8 42.3 41.6 44.8 57.0 X6 44.1 42.8 42.4 48.4 50.9 41.7 47.0 40.9 46.7 50.7 44.1 47.4 27.2 36.0 18.1 45.1 36.8 53.7 39.0 49.5 44.4 39.5 40.9 46.1 60.6 49.8 43.3 43.6 50.1 37.7 X7 30.8 42.6 49.8 27.6 41.2 29.7 51.4 33.1 53.0 46.8 34.9 49.9 54.2 40.2 52.0 42.3 38.7 29.8 45.6 42.5 53.2 45.3 48.3 20.6 30.6 54.6 28.8 51.3 50.0 47.2 X8 47.1 51.8 40.1 56.8 34.6 44.3 35.0 50.4 39.1 29.9 37.0 45.6 34.8 32.7 47.6 53.4 64.8 40.0 44.2 52.9 45.6 28.6 59.2 35.7 50.4 52.9 40.4 55.9 40.1 40.5 X9 30.4 39.1 44.5 50.6 33.2 57.5 43.1 45.2 52.4 48.5 48.7 41.2 39.2 58.7 46.3 43.6 56.3 37.2 44.2 34.3 50.4 37.1 58.1 48.5 32.8 60.4 40.5 49.8 36.2 41.3 X10 42.7 52.9 47.4 48.7 53.9 55.7 52.1 47.0 30.7 40.1 42.2 41.7 41.7 51.4 52.0 32.3 42.1 40.7 56.3 34.3 44.7 52.2 35.3 53.3 42.3 51.5 48.1 45.0 45.4 48.9 X11 37.9 35.1 55.1 40.5 47.9 45.3 48.6 37.1 54.9 42.1 40.8 53.7 34.4 47.3 34.5 51.7 40.0 31.6 38.0 48.8 51.3 39.2 40.7 59.0 60.6 43.7 50.3 47.4 43.6 48.0 ∑ 449.8 533.2 505.8 488.0 502.0 494.9 501.0 481.0 498.9 484.0 449.6 500.7 444.6 494.2 477.7 435.8 457.1 426.1 463.2 489.2 527.4 445.0 494.5 492.5 501.0 512.2 476.9 535.2 487.1 487.7 = 40.9 48.5 46.0 44.4 45.6 45.0 45.5 43.7 45.4 44.0 40.9 45.5 40.4 44.9 43.4 39.6 41.6 38.7 42.1 44.5 47.9 40.5 45.0 44.8 45.5 46.6 43.4 48.7 44.3 44.3 s 5.87 8.5 7.0 8.2 6.9 8.9 5.4 7.4 9.3 7.1 7.7 4.3 7.9 7.0 9.6 8.7 10.7 9.2 5.4 6.2 5.9 7.0 9.8 9.5 9.3 10.5 7.2 5.9 4.5 5.3
  4. 4. Calculo de la Desviacion EstandarDatos 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 X1 7.9 381.3 21.9 8.8 0.3 179.3 78.2 8.8 12.6 7.3 133.9 32.3 11.4 12.4 2.2 12.4 97.1 115.9 16.9 35.1 30.8 14.9 124.4 4.5 1.1 0.1 10.6 111.2 29.0 19.7 X2 21.2 26.3 65.9 34.1 0.1 104.2 0.0 97.5 167.6 82.8 49.4 3.0 11.0 20.0 13.5 23.2 0.6 76.3 41.1 36.3 69.8 97.1 202.9 1.1 69.6 13.4 0.0 0.7 9.1 13.2 X3 49.1 6.9 62.7 126.9 36.8 29.1 5.0 77.0 66.3 18.5 39.3 3.3 53.6 16.6 36.9 259.8 69.8 35.6 0.0 4.7 8.1 1.6 17.2 10.7 3.1 793.2 251.1 19.8 7.7 3.0 X4 21.1 12.1 0.3 15.7 7.5 34.9 25.5 196.8 147.7 34.8 247.3 41.2 131.8 7.4 22.8 8.9 261.0 280.1 0.3 0.8 119.8 15.6 68.1 15.4 2.1 38.0 7.0 97.1 24.2 0.2 X5 6.3 7.4 233.5 35.2 80.3 2.5 5.1 1.2 101.1 114.5 54.4 4.5 46.0 0.9 35.1 85.0 33.0 66.6 14.5 19.1 82.0 87.3 138.2 2.6 4.6 17.9 1.1 49.8 0.3 160.4 X6 10.3 32.2 12.8 16.3 27.7 10.8 2.1 8.0 1.8 44.9 10.4 3.5 174.7 79.7 641.5 30.1 22.6 223.9 9.7 25.3 12.6 0.9 16.4 1.8 226.6 10.5 0.0 25.5 33.9 44.0 X7 101.8 34.5 14.6 281.0 19.7 233.8 34.3 112.9 58.5 7.8 35.7 19.2 189.9 22.3 73.5 7.2 8.1 79.9 12.2 3.9 27.6 23.5 11.2 584.3 223.4 64.6 211.8 7.0 32.7 8.2 X8 38.6 11.1 34.6 154.7 121.8 0.5 111.2 44.5 39.1 198.8 15.0 0.0 31.6 149.5 17.4 189.9 540.4 1.6 4.4 71.0 5.5 140.5 202.9 82.3 23.6 40.1 8.7 52.5 17.5 14.7 X9 110.1 87.8 2.2 38.9 154.7 156.5 6.0 2.2 49.6 20.3 61.3 18.6 1.5 189.7 8.3 15.9 217.4 2.4 4.4 103.5 6.0 11.3 172.8 13.9 162.4 191.4 8.1 1.3 65.3 9.2 X10 3.3 19.6 2.0 18.8 68.3 114.7 43.0 10.7 214.8 15.2 1.8 14.6 1.6 41.9 73.5 53.6 0.3 3.9 201.4 103.5 10.5 138.0 93.2 72.7 10.5 24.4 22.5 13.4 1.3 20.8 X11 8.9 178.8 83.1 14.9 5.1 0.1 9.3 43.9 91.1 3.6 0.0 66.9 36.2 5.6 79.7 146.0 2.4 50.9 16.9 18.7 11.3 1.6 18.1 202.4 226.6 8.2 48.2 1.6 0.5 13.4 ∑ 378.6 798.0 533.7 745.3 522.3 866.4 319.8 603.4 950.3 548.5 648.5 207.1 689.4 546.2 1004.3 831.8 1252.7 937.0 321.6 421.9 383.9 532.1 1065.5 991.8 953.8 1201.8 569.3 379.8 221.3 306.9 S2 34.4 72.5 48.5 67.8 47.5 78.8 29.1 54.9 86.4 49.9 59.0 18.8 62.7 49.7 91.3 75.6 113.9 85.2 29.2 38.4 34.9 48.4 96.9 90.2 86.7 109.3 51.8 34.5 20.1 27.9 s 5.867 8.517 6.965345 8.231124 6.890609 8.875037 5.391974 7.406642 9.294609 7.061419 7.678079 4.339421 7.91659 7.046481 9.554922 8.69596 10.67157 9.22943 5.40731 6.19341 5.90783 6.95523 9.842059 9.49537 9.31161 10.4526 7.19424 5.876357 4.4857 5.282092
  5. 5. Obtencion de limites para las medias ydesviaciones estandar. Media de las Medias Aritmeticas A3= 0.927 + 51.0 Limite Superior de Control (UCL) 44.0 Limite Central de Control (CL) 37.1 Limite Inferior de Control (LCL) Media Aritmetica de la Desviaciones Estandar B4= 1.679 12.7 Limite Superior de Control (UCL) 7.5 Limite Central de Control (CL) 2.4 Limite Inferior de Control (LCL) B3= 0.321
  6. 6. Limites de medias para graficar. Desviaciones Estandar Reales para Grafico de Medias Graficar Limites de Control 2.33 Limite Central UCL LCL + 46.38 X Y X Y X Y +2 48.71 1 44.00 1 51.00 1 37.10 41.72 30 44.00 30 51.00 30 37.10 2 39.39 + +2 2 X Y X Y X Y X Y 1 46.38 1 48.71 1 41.72 1 39.39 30 46.38 30 48.71 30 41.72 30 39.39
  7. 7. Limites de desviciones para graficar. Desviaciones Estandar Reales Desviacion Estandar Limite Central UCL LCL 1.71 X Y X Y X Y + 9.24 1 7.5 1 12.70 1 2.40 +2 10.95 30 7.5 30 12.70 30 2.40 5.83 2 4.12 + +2 2 X Y X Y X Y X Y 1 9.24 1 10.95 1 5.83 1 4.12 30 9.24 30 10.95 30 5.83 30 4.12
  8. 8. Grafica xr Limites de control para las medias aritméticasUCL 51.0 Limite Central 44.0 LCL 37.152.0 51.00 51.0050.0 48.71 48.5 48.7 48.71 47.948.0 46.6 46.38 46.0 46.38 45.6 45.5 45.4 45.5 45.546.0 45.0 44.9 45.0 44.8 44.4 44.5 44.3 44.3 44.00 43.7 44.0 44.00 43.4 43.444.0 42.1 41.72 41.6 41.7242.0 40.9 40.9 40.5 40.4 39.39 39.6 39.3940.0 38.738.0 37.10 37.1036.0 0 5 10 15 20 25 30
  9. 9. Grafica xs. Limites de control para las desviaciones estandarUCL 12.7 Limite Central 7.5 LCL 2.414.00 12.70 12.7012.00 10.95 10.7 10.95 10.5 9.6 9.8 9.5 9.24 9.3 9.2 9.3 9.2410.00 8.5 8.9 8.7 8.2 7.9 7.5 7.4 7.7 7.5 8.00 7.0 6.9 7.1 7.0 7.0 7.2 5.873 6.2 5.9 5.9 5.83 5.4 5.4 5.3 6.00 4.3 Nelson rule numero 6:Four (or 4.5 4.12 4.12 4.00 five) out of five points in a row 2.40 2.40 are more than 1 standard 2.00 deviation from the mean in the 0.00 0 5 10 15 20 same direction. 25 30

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