Ejercicios Graficas de Control
Escuela de Ingeniería Industrial Control Estadístico de Calidad Ejercicios En una empresa del ramo metal-mecánico se fab
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- Marcos Javier Camacho López
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Escuela de Ingeniería Industrial Control Estadístico de Calidad Ejercicios En una empresa del ramo metal-mecánico se fabrican válvulas, en particular el cuerpo de cierta válvula debe tener un diámetro exterior de 0.02 m (2.0 cm), con tolerancia de ± 25 μm (1 μm = 0.000001 m). En una de las últimas etapas del proceso de fabricación de las válvulas, cada hora se mide el diámetro de 5 válvulas, como se muestra a continuación: Subgrupo 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
-20 3 -12 14 -1 0 -3 2 6 16 14 4 0 -12 1 3 5 -21 -8 -1 6 9 -13 -18 9
Mediciones del diámetro -4 20 2 2 6 21 6 -10 -6 6 25 6 12 5 -19 3 2 8 -1 -4 10 -12 2 -12 -1 4 10 2 1 -22 -4 1 11 0 1 -15 -1 -3 -15 0 -5 10 -3 13 -5 1 18 0 7 1 8 0 -1 1 9 -7 -9 -2 -12 13 4 0 0 6 -7 -13 27 9 -1 1 6 11 4 13 -3
-11 -17 6 -3 5 -9 1 8 3 -3 4 9 9 3 -1 5 -3 -6 -1 -2 0 -32 -1 -8 3
promedio -2.6 3 -3.2 9.6 0.4 0.8 0.6 -2.4 4.4 -1.2 5.2 -0.2 -2 -0.8 1 5.4 3.6 -5.4 -3.2 -0.8 2 -7.4 4.2 -1.6 5.2 60.0
20.00
0.584
15.00
50.0
10.00
40.0
5.00
LCS promedio
30.0
60.0
20.00 15.00
50.0
10.00
40.0
5.00 0.00 1
-5.00
3
5
7
9
11
13
15
17
19
21
23
25
LCS promedio LX-C LCI
30.0 20.0 10.0
-10.00 0.0 -15.00
1
3
5
7
9
11
13
LX-C
LCS 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584
LCI 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13 14.13
RANGO
LR-C
-12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96 -12.96
40 38 18 28 31 17 14 20 11 38 18 24 24 22 18 18 11 22 18 25 6 41 40 29 16
PROMEDIO R
23.48
0.0
0.0
0.0
0.0
LCS LR-C
LCS 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48 23.48
LCI 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7 49.7
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.0
0.0
0.0 LCS LR-C RANGO LCI Column M
0.0
0.0
0.0
0.0 1
3
5
7
9
11
13
15
17
19
21
23
25
TABLA DE CONSTANTES
Subgrupo 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
Mediciones del diámetro -4 20 2 2 6 21 6 -10 -6 6 25 6 12 5 -19 3 2 8 -1 -4 10 -12 2 -12 -1 4 10 2 1 -22 -4 1 11 0 1 -15 -1 -3 -15 0 -5 10 -3 13 -5 1 18 0 7 1 8 0 -1 1 9 -7 -9 -2 -12 13 4 0 0 6 -7 -13 27 9 -1 1 6 11 4 13 -3
-20 3 -12 14 -1 0 -3 2 6 16 14 4 0 -12 1 3 5 -21 -8 -1 6 9 -13 -18 9
-11 -17 6 -3 5 -9 1 8 3 -3 4 9 9 3 -1 5 -3 -6 -1 -2 0 -32 -1 -8 3
20.00
15.00
10.00
5.00
0.00 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
10.00
5.00
0.00 1 -5.00
-10.00
-15.00
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
MEDIA
X DOBLE BARRA S BARRA
DESVIACIÓN ESTANDAR -2.6 15.06 3 13.55 -3.2 8.67 9.6 10.50 0.4 11.78 0.8 6.22 0.6 5.59 -2.4 9.10 4.4 4.04 -1.2 13.66 5.2 7.33 -0.2 8.98 -2 8.60 -0.8 8.29 1 7.07 5.4 7.30 3.6 4.56 -5.4 9.13 -3.2 7.50 -0.8 8.93 2 2.83 -7.4 16.47 4.2 14.94 -1.6 11.55 5.2 6.10 0.584
9.11
LSC LC LIC 15
16
17
18
19
20
21
22
23
24
FORMULAS A UTILIZAR LSCx= X (barra) +A3S (barra LICX=X(barra) -A3S (barra) LCx=(barra)
LSC LC LIC 15
16
17
18
19
20
21
22
23
24
A3 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427 1.427
LIC -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42 -12.42
LC 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584
LSC 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58 13.58
20.00 18.00 16.00 14.00 12.00 10.00 8.00 6.00
FORMULAS LSC=B4S(BARRA) LIC=B3S(BARRA) LC=S (BARRA)
12.00 10.00 8.00 6.00 4.00 2.00 0.00 1
2
3
4
5
6
7
8
9
10
11
B3
B4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
LIC 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089 2.089
LC 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
LSC 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11 9.11
19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03 19.03
LSC LC LIC
LSC LC LIC
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24