Por: Mennys-UTT-SPC

spcializados.blogspot.com

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.

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

=

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

Obtencion de limites para las medias y desviaciones estandar.

A3= 0.927

51.0 Limite Superior de Control (UCL)

44.0 Limite Central de Control (CL)

37.1 Limite Inferior de Control (LCL)

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

Media de las Medias Aritmeticas

Media Aritmetica de la Desviaciones Estandar

+

Limites de medias para graficar.

Graficar Limites de Control

2.33 Limite Central UCL LCL

46.38 X Y X Y X Y

48.71 1 44.00 1 51.00 1 37.10

41.72 30 44.00 30 51.00 30 37.10

39.39

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

Desviaciones Estandar Reales para Grafico de Medias

+

+2 2

+ 2 +2

Limites de desviciones para graficar.

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

10.95 30 7.5 30 12.70 30 2.40

5.83

4.12

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

Desviaciones Estandar Reales

+ +2

2 + +2 2

Grafica xrUCL 51.0 Limite Central 44.0 LCL 37.1

Limites de control para las medias aritméticas

40.9

48.5

46.0

44.4

45.645.0

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 44.845.5

46.6

43.4

48.7

44.3 44.344.00 44.00

51.00 51.00

46.38 46.38

48.71 48.71

41.72 41.72

39.39 39.39

37.10 37.10

36.0

38.0

40.0

42.0

44.0

46.0

48.0

50.0

52.0

0 5 10 15 20 25 30

Grafica xs.UCL 12.7 Limite Central 7.5 LCL 2.4

Limites de control para las desviaciones estandar

5.87

8.5

7.0

8.2

6.9

8.9

5.4

7.4

9.3

7.17.7

4.3

7.97.0

9.68.7

10.7

9.2

5.46.2 5.9

7.0

9.8 9.5 9.3

10.5

7.2

5.9

4.55.3

7.5 7.5

12.70 12.70

2.40 2.40

9.24 9.24

10.95 10.95

5.83 5.83

4.124.12

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0 5 10 15 20 25 30

Nelson rule numero 6: Four (or five) out of five points in a row are more than 1 standard deviation from the mean in the same direction.