graficos X,R

1. GRAFICAS “X” “R”

2. 8 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
1 12.5 10.9 14.5 13.5 3.1 9.5 12.6 7.9 14.6 12 8.3 13 10.3 16.5 13 7 11.9 11.6 7.4 8.2 9.6 8 17.3 11.7 13.2 14.3 12.2 9.4 17.1 8.7
2 15.1 10.5 14 16.4 15.2 14.8 11.9 11.4 4.5 9.8 14.5 13.7 10.4 5.4 14 12.5 15.1 10 6.7 8.9 13.9 11.1 9.2 11.4 10.8 8.7 5.7 15.6 10 9.5
3 12.2 16.3 11.4 13.6 14 10.4 16.3 14.5 14.8 13.3 13.1 18.7 11.2 13.4 14.1 11.3 8.9 12.6 14.4 9.7 8.8 15.3 11.4 14.2 17.8 12.1 17 8.6 12.3 10.8
4 13.2 15.9 11 15.3 11.6 11.4 13.1 13.1 14.3 12.2 9.3 13.7 14.4 12.1 11.6 12.8 9.2 10.9 11.3 15.9 11.3 12 13.7 17.3 10.2 16 14.4 17.4 9.6 12.3
5 15.1 19.7 10.1 13.7 6.5 11.4 11.8 12.4 2.9 7.4 6.8 5 16.5 9.6 6.3 12.7 14.2 10.2 15 12.3 11.9 16 6.4 11.7 16.5 13.2 10.7 11.3 12.5 16
6 13.7 9.2 10.6 11.7 9.6 10.5 7.8 13.2 18.9 10.3 15.8 12.6 11.3 13.5 12.4 15.1 9.3 13 10.1 7.5 13.1 5 14.9 16 11 12.2 7.2 12 10.2 9.3
7 11.3 15.3 11.6 10.5 10.9 13.5 12.2 11.4 10.1 8.2 12.4 10.6 14.6 9.9 12.5 8.1 15.1 15.1 16.7 10.4 10.5 13.4 10.2 9.5 12.3 6.8 16.8 9.2 9.2 11.2
8 12.6 12.3 10.2 15.1 13.3 10.7 10.2 17.4 11.5 8.2 13.6 11.3 9.6 12 16.2 16 8.9 16.3 11 13.1 7.3 11.9 13.2 13.5 11.3 14.7 14.5 13.4 12.1 14.6
9 9.2 8.2 8.2 11.6 10.2 5.6 11.5 6.3 10.8 14.9 4.4 15.7 17.2 14.1 9.5 15.9 11.7 11.2 16.2 11.7 16.3 10 14.1 12.4 10 13 12.9 15.4 9.7 11.2
10 11 10.7 13.3 16.6 10.6 15 15.3 13.7 12.7 9.1 12.1 10.3 17.9 15.5 10.3 12.1 19.5 12.6 15.4 12.1 3.4 14.9 12.7 8.4 14 8.5 17.5 12.8 17.1 12
11 10.9 9.8 11 12.8 12.7 9.5 13.3 11.0 10.0 13.9 14.8 11.3 19.3 16.3 10.7 15.3 9.5 12.6 9.9 10.7 13.7 15.6 9.9 12.9 9.4 10 6.3 13.5 8.9 9.2
∑ 136.8 138.8 125.9 150.8 117.7 122.3 136 132.3 125.1 119.3 125.1 135.9 152.7 138.3 130.6 138.8 133.3 136.1 134.1 120.5 119.8 133.2 133 139 136.5 129.5 135.2 138.6 128.7 124.8
M 12.4 12.6 11.4 13.7 10.7 11.1 12.4 12.0 11.4 10.8 11.4 12.4 13.9 12.6 11.9 12.6 12.1 12.4 12.2 11.0 10.9 12.1 12.1 12.6 12.4 11.8 12.3 12.6 11.7 11.3
s 1.7 3.5 1.8 1.9 3.3 2.5 2.2 2.9 4.4 2.4 3.5 3.3 3.3 3.2 2.5 2.9 3.3 1.9 3.4 2.3 3.4 3.3 2.9 2.5 2.6 2.8 4.1 2.7 2.8 2.2

3. UCL CL LCL
1 14.67 1 12.03 1 9.39
Media aritmética de las medias
limite superior de control 30 14.67 30 12.03 30 9.39
14.665 (UCL)
limite central de control DESVIACIÓN ESTÁNDAR REAL
12.026 (CL) xm + 1s xm + 2s
limite inferior de control 1 12.91 1 13.79
9.387 (LCL) 30 12.91 30 13.79
xm -1s xm-2s
1 11.15 1 10.27
30 11.15 30 10.27

4. 15.0
14.0 EL grafico se encuentra
aleatorio controlado o
13.0
bajo un control.
12.0
11.0
10.0
9.0
8.0

5. Media aritmética de las desviaciones estándar
4.780 limite superior de control (UCL)
2.847 limite central de control (CL)
0.914 limite inferior de control (LCL)
DESVIACIÓN ESTÁNDAR REAL
s + 1s s+2s
1 3.491 1 4.136
30 3.491 30 4.136
s-1s s-2s
1 2.203 1 1.558
30 2.203 30 1.558
UCL CL LCL
1 4.780 1 2.847 1 0.914
30 4.780 30 2.847 30 0.914

6. 6.0
EL grafico se encuentra aleatorio
controlado o bajo un control.
5.0
4.0
3.0
2.0
1.0
0.0