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

1. Por: Mennys-UTT-SPC
spcializados.blogspot.com

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. 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. Calculo de la Desviacion Estandar
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 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. Obtencion de limites para las medias y
desviaciones 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. 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. 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. Grafica xr
Limites de control para las medias aritméticas
UCL 51.0 Limite Central 44.0 LCL 37.1
52.0 51.00 51.00
50.0 48.71 48.5 48.7 48.71
47.9
48.0 46.6
46.38 46.0 46.38
45.6 45.5 45.4 45.5 45.5
46.0 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 43.4
44.0
42.1
41.72 41.6 41.72
42.0 40.9 40.9 40.5
40.4
39.39 39.6 39.39
40.0 38.7
38.0 37.10 37.10
36.0
0 5 10 15 20 25 30

9. Grafica xs.
Limites de control para las desviaciones estandar
UCL 12.7 Limite Central 7.5 LCL 2.4
14.00 12.70 12.70
12.00 10.95 10.7 10.95
10.5
9.6 9.8 9.5
9.24 9.3 9.2 9.3 9.24
10.00 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