Control Estadistico
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Transcript of Control Estadistico
DATOS DE LA ANCHURA DE UN PRODUCTOSUBGRUPOS
1 2 3 4 5 6 7 8 9 10 11 12 131.88 1.93 1.92 1.89 1.95 2.00 1.95 1.87 1.96 1.99 1.93 1.95 1.881.93 1.97 1.95 1.89 1.93 1.95 1.93 1.98 1.92 1.93 1.95 1.98 1.931.98 1.89 1.90 1.90 1.90 1.94 1.97 1.96 1.98 2.01 1.90 1.89 1.881.88 1.94 1.98 1.94 1.93 1.89 1.85 2.04 1.88 2.02 1.93 1.90 1.90
MEDIAS 1.92 1.93 1.94 1.90 1.93 1.94 1.93 1.96 1.94 1.99 1.93 1.93 1.90RANGOS 0.10 0.08 0.08 0.05 0.05 0.11 0.12 0.17 0.10 0.09 0.05 0.09 0.05
GRAFICO DE CONTROL X
CONSTANTE DESVIACION ESTANDAR DE PROMEDIOS
n = 4.0 2.059 Ř = 0.085 σ = 0.0410
LIMITE SUPERIOR DE CONTROL
LSC = 1.99518
LINEA CENTRAL
X X = 1.9336
LIMITE INFERIOR DE CONTROL
LIC = 1.87207
OBSERVACIONES EN SUBGRUPO
PROMEDIO DE RANGOS
d2= σ = Ř / d2
LSC = X + 3 (σ/√n)
LIC = X - 3 (σ/√n)
LIC = 1.87207
GRAFICO DE CONTROL R
CONSTANTES DESVIACION ESTANDAR DE RANGOS
n = 4.0 2.059 0.88 Ř = 0.085
LIMITE SUPERIOR DE CONTROL
LSR = 0.1928
LINEA CENTRAL
Ř Ř = 0.0845
LIMITE INFERIOR DE CONTROL
LIR = -0.0238
LIC = X - 3 (σ/√n)
OBSERVACIONES EN SUBGRUPO
PROMEDIO DE RANGOS
d2= d3= σR = d3 Ř / d2
LSR = Ř + 3 σR
LIR = Ř - 3 σR
FACTORES PARA LIMITES DE CONTROL FACTORES PARA LIMITES DE CONTROL FACTORES PARA LIMITES DE CONTROL
n A2 2.121 1.880 2.659 0.7979 1.2533 0.000 3.267 0.000 2.606 1.128 0.8865 0.8533 1.732 1.023 1.954 0.8862 1.1284 0.000 2.568 0.000 2.276 1.693 0.5907 0.8884 1.500 0.729 1.628 0.9213 1.0854 0.000 2.266 0.000 2.088 2.059 0.4857 0.8805 1.342 0.577 1.427 0.9400 1.0638 0.000 2.089 0.000 1.964 2.326 0.4299 0.8646 1.225 0.483 1.287 0.9515 1.0510 0.030 1.970 0.029 1.874 2.534 0.3946 0.8487 1.134 0.419 1.182 0.9594 1.0423 0.118 1.882 0.113 1.806 2.704 0.3698 0.833
DATOS EN SUBGRUPO FACTORES PARA LINEA
CENTRAL
FACTORES PARA LINEA CENTRAL
A2 A3 C4 1/C4 B3 B4 B5 B6 d2 1/d2 d3
8 1.061 0.373 1.099 0.9650 1.0363 0.185 1.815 0.179 1.751 2.847 0.3512 0.8209 1.000 0.337 1.032 0.9693 1.0317 0.239 1.761 0.232 1.707 2.970 0.3367 0.80810 0.949 0.308 0.975 0.9727 1.0281 0.284 1.716 0.276 1.669 3.078 0.3249 0.79711 0.905 0.285 0.927 0.9754 1.0252 0.321 1.679 0.313 1.637 3.173 0.3152 0.78712 0.966 0.266 0.886 0.9776 1.0229 0.354 1.646 0.346 1.610 3.258 0.3069 0.77813 0.832 0.249 0.850 0.9794 1.0210 0.382 1.618 0.374 1.585 3.336 0.2998 0.77014 0.802 0.235 0.817 0.9810 1.0194 0.406 1.594 0.399 1.563 3.407 0.2935 0.76315 0.775 0.223 0.789 0.9823 1.0180 0.428 1.572 0.421 1.544 3.472 0.2880 0.75616 0.750 0.212 0.763 0.9835 1.0168 0.448 1.552 0.440 1.526 3.532 0.2831 0.75017 0.728 0.203 0.739 0.9845 1.0157 0.466 1.534 0.458 1.511 3.588 0.2787 0.74418 0.707 0.194 0.718 0.9854 1.0148 0.482 1.518 0.475 1.496 3.640 0.2747 0.73919 0.688 0.187 0.698 0.9862 1.0140 0.497 1.503 0.490 1.483 3.689 0.2711 0.73420 0.671 0.180 0.680 0.9869 1.0133 0.510 1.490 0.504 1.470 3.735 0.2677 0.72921 0.655 0.173 0.663 0.9876 1.0126 0.523 1.477 0.516 1.459 3.778 0.2647 0.72422 0.640 0.167 0.647 0.9882 1.0119 0.534 1.466 0.528 1.448 3.819 0.2618 0.72023 0.626 0.162 0.633 0.9887 1.0114 0.545 1.455 0.539 1.438 3.858 0.2592 0.71624 0.612 0.157 0.619 0.9892 1.0109 0.550 1.445 0.549 1.429 3.895 0.2567 0.71225 0.600 0.153 0.606 0.9896 1.0105 0.565 1.435 0.559 1.420 3.931 0.2544 0.708
DATOS DE LA ANCHURA DE UN PRODUCTOSUBGRUPOS
14 15 16 17 18 19 201.97 1.91 1.98 1.93 1.82 2.00 1.981.88 1.91 1.90 1.94 1.92 1.97 1.941.92 1.96 1.92 1.95 1.95 1.99 1.961.96 1.93 1.91 1.90 1.94 1.95 1.88
1.93 1.93 1.93 1.93 1.91 1.98 1.940.09 0.05 0.08 0.05 0.13 0.05 0.10
GRAFICO DE CONTROL X
CONSTANTE
X = 1.9336 0.7290
LIMITE SUPERIOR DE CONTROL
LSC = 1.99523
LINEA CENTRAL
X X = 1.9336
LIMITE INFERIOR DE CONTROL
LIC = 1.87202
PROMEDIO DE PROMEDIOS
A2 =
LSC = X + A2 Ř
LIC = X - A2 Ř
LIC = 1.87202
GRAFICO DE CONTROL R
DESVIACION ESTANDAR DE RANGOS CONSTANTES
0.0361 0.000 2.282
LIMITE SUPERIOR DE CONTROL
LSR = 0.1928
LINEA CENTRAL
Ř Ř = 0.0845
LIMITE INFERIOR DE CONTROL
LIR = 0.0000
LIC = X - A2 Ř
σR = D3 = D4 =
LSR = D4 Ř
LIR = D3 Ř
FACTORES PARA LIMITES DE CONTROL
0.000 3.686 0.000 3.2670.000 4.358 0.000 2.5740.000 4.698 0.000 2.2820.000 4.918 0.000 2.1140.000 5.078 0.000 2.0040.204 5.204 0.076 1.924
D1 D2 D3 D4
0.388 5.306 0.136 1.8640.547 5.393 0.184 1.8160.687 5.469 0.223 1.7770.811 5.535 0.256 1.7440.922 5.594 0.283 1.7171.025 5.647 0.307 1.6931.118 5.696 0.328 1.6721.203 5.741 0.347 1.6531.282 5.782 0.363 1.6371.356 5.820 0.378 1.6221.424 5.856 0.391 1.6081.487 5.891 0.403 1.5971.549 5.921 0.415 1.5851.605 5.951 0.425 1.5751.659 5.979 0.434 1.5661.710 6.006 0.443 1.5571.759 6.031 0.451 1.5481.806 6.056 0.459 1.541
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201.84
1.86
1.88
1.90
1.92
1.94
1.96
1.98
2.00
GRAFICO DE CONTROL X (DE PROMEDIOS)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
GRAFICO DE CONTROL R (DE RANGOS)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O
VALORES CODIFICADOS DE RESISTENCIA A LA COMPRESION DE BLOQUES DE CONCRETOSUBGRUPOS
1 2 3 4 5 6 7 8 9 10 11 12 1311.10 9.60 9.70 10.10 12.40 10.10 11.00 11.20 10.60 8.30 10.60 10.80 10.709.40 10.80 10.00 8.40 10.00 10.20 11.50 10.00 10.40 10.20 9.90 10.20 10.7011.20 10.10 10.00 10.70 10.70 10.20 11.80 10.90 10.50 9.80 10.70 10.50 10.8010.40 10.80 9.80 9.40 10.10 11.20 11.00 11.20 10.50 9.50 10.20 8.40 8.6010.10 11.00 10.40 11.00 11.30 10.10 11.30 11.00 10.90 9.80 11.40 9.90 11.40
MEDIAS 10.44 10.46 9.98 9.92 10.90 10.36 11.32 10.86 10.58 9.52 10.56 9.96 10.44RANGOS 1.80 1.40 0.70 2.60 2.40 1.10 0.80 1.20 0.50 1.90 1.50 2.40 2.80
GRAFICO DE CONTROL X
CONSTANTE DESVIACION ESTANDAR DE PROMEDIOS
n = 5.0 2.326 Ř = 1.58 σ = 0.68
LIMITE SUPERIOR DE CONTROL
LSC = 11.59
LINEA CENTRAL
X X = 10.68
LIMITE INFERIOR DE CONTROL
LIC = 9.76
OBSERVACIONES EN SUBGRUPO
PROMEDIO DE RANGOS
d2= σ = Ř / d2
LSC = X + 3 (σ/√n)
LIC = X - 3 (σ/√n)
LIC = 9.76
GRAFICO DE CONTROL R
CONSTANTES DESVIACION ESTANDAR DE RANGOS
n = 5.0 2.326 0.864 Ř = 1.580
LIMITE SUPERIOR DE CONTROL
LSR = 3.34
LINEA CENTRAL
Ř Ř = 1.58
LIMITE INFERIOR DE CONTROL
LIR = -0.18
LIC = X - 3 (σ/√n)
OBSERVACIONES EN SUBGRUPO
PROMEDIO DE RANGOS
d2= d3= σR = d3 Ř / d2
LSR = Ř + 3 σR
LIR = Ř - 3 σR
VALORES CODIFICADOS DE RESISTENCIA A LA COMPRESION DE BLOQUES DE CONCRETOSUBGRUPOS
14 15 16 17 18 19 2011.30 11.40 10.10 10.70 11.90 10.80 12.4011.40 11.20 10.10 12.80 11.90 12.10 11.1010.40 11.40 9.70 11.20 11.60 11.80 10.8010.60 10.10 9.80 11.20 12.40 9.40 11.0011.10 11.60 10.50 11.30 12.40 11.60 11.90
10.96 11.14 10.04 11.44 12.04 11.14 11.441.00 1.50 0.80 2.10 0.80 2.70 1.60
GRAFICO DE CONTROL X
CONSTANTE
X = 10.68 0.577
LIMITE SUPERIOR DE CONTROL
LSC = 11.59
LINEA CENTRAL
X X = 10.68
LIMITE INFERIOR DE CONTROL
LIC = 9.76
PROMEDIO DE PROMEDIOS
A2 =
LSC = X + A2 Ř
LIC = X - A2 Ř
LIC = 9.76
GRAFICO DE CONTROL R
DESVIACION ESTANDAR DE RANGOS CONSTANTES
0.5869 0.000 2.114
LIMITE SUPERIOR DE CONTROL
LSR = 3.34
LINEA CENTRAL
Ř Ř = 1.58
LIMITE INFERIOR DE CONTROL
LIR = 0.00
LIC = X - A2 Ř
σR = D3 = D4 =
LSR = D4 Ř
LIR = D3 Ř
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 209.00
9.50
10.00
10.50
11.00
11.50
12.00
12.50
GRAFICO DE CONTROL X (DE PROMEDIOS)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
GRAFICO DE CONTROL R (DE RANGOS)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O
TERCER EXAMEN PARCIALSUBGRUPOS
1 2 3 4 5 6 7 8 9 10 11 12 1325 27 29 29 32 31 32 28 30 3230 30 31 32 33 32 32 29 35 3333 31 32 36 35 37 33 30 37 3636 34 35 38 38 38 33 31 39 3738 40 38 40 39 40 37 31 40 39
MEDIAS 32.40 32.40 33.00 35.00 35.40 35.60 33.40 29.80 36.20 35.40RANGOS 13.00 13.00 9.00 11.00 7.00 9.00 5.00 3.00 10.00 7.00
GRAFICO DE CONTROL X
CONSTANTE DESVIACION ESTANDAR DE PROMEDIOS
n = 5.0 2.326 Ř = 8.70 σ = 3.74
LIMITE SUPERIOR DE CONTROL
LSC = 38.88
LINEA CENTRAL
X X = 33.86
LIMITE INFERIOR DE CONTROL
LIC = 28.84
OBSERVACIONES EN SUBGRUPO
PROMEDIO DE RANGOS
d2= σ = Ř / d2
LSC = X + 3 (σ/√n)
LIC = X - 3 (σ/√n)
LIC = 28.84
GRAFICO DE CONTROL R
CONSTANTES DESVIACION ESTANDAR DE RANGOS
n = 5.0 2.326 0.864 Ř = 8.700
LIMITE SUPERIOR DE CONTROL
LSR = 18.39
LINEA CENTRAL
Ř Ř = 8.70
LIMITE INFERIOR DE CONTROL
LIR = -0.99
LIC = X - 3 (σ/√n)
OBSERVACIONES EN SUBGRUPO
PROMEDIO DE RANGOS
d2= d3= σR = d3 Ř / d2
LSR = Ř + 3 σR
LIR = Ř - 3 σR
TERCER EXAMEN PARCIALSUBGRUPOS
14 15 16 17 18 19 20
GRAFICO DE CONTROL X
CONSTANTE
X = 33.86 0.577
LIMITE SUPERIOR DE CONTROL
LSC = 38.88
LINEA CENTRAL
X X = 33.86
LIMITE INFERIOR DE CONTROL
LIC = 28.84
PROMEDIO DE PROMEDIOS
A2 =
LSC = X + A2 Ř
LIC = X - A2 Ř
LIC = 28.84
GRAFICO DE CONTROL R
DESVIACION ESTANDAR DE RANGOS CONSTANTES
3.2316 0.000 2.114
LIMITE SUPERIOR DE CONTROL
LSR = 18.39
LINEA CENTRAL
Ř Ř = 8.70
LIMITE INFERIOR DE CONTROL
LIR = 0.00
LIC = X - A2 Ř
σR = D3 = D4 =
LSR = D4 Ř
LIR = D3 Ř
1 2 3 4 5 6 7 8 9 1025 27 29 29 32 31 32 28 30 3230 30 31 32 33 32 32 29 35 3333 31 32 36 35 37 33 30 37 3636 34 35 38 38 38 33 31 39 3738 40 38 40 39 40 37 31 40 39
MEDIAS 32.4 32.4 33 35 35.4 35.6 33.4 29.8 36.2 35.4RANGOS 13 13 9 11 7 9 5 3 10 7
1 2 3 4 5 6 7 8 9 1028.84
30.84
32.84
34.84
36.84
38.84
GRAFICO DE CONTROL X (DE PROMEDIOS)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O
LIMITE SUPERIOR DE CONTROL LIMITE SUPERIOR DE CONTROLLSC = X + A2 Ř LSC = 38.8799 LSR = D4 Ř LSR = 18.3918
LINEA CENTRAL LINEA CENTRALX X = 33.86 Ř Ř = 8.7
LIMITE INFERIOR DE CONTROL LIMITE INFERIOR DE CONTROL
1 2 3 4 5 6 7 8 9 1028.84
30.84
32.84
34.84
36.84
38.84
GRAFICO DE CONTROL X (DE PROMEDIOS)
SUBGRUPOA
NCH
UR
A D
E U
N P
RO
DU
CTO
1 2 3 4 5 6 7 8 9 100.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
GRAFICO DE CONTROL R (DE RANGOS)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O
TERCER EXAMEN PARCIALSUBGRUPOS
1 2 3 4 5 6 7 8 9 10 11 12 139 8 6 4 3 5 4 4 3 25 5 3 8 8 7 9 7 6 57 9 8 2 5 2 6 2 5 74 3 9 1 2 9 2 9 9 32 2 6 9 9 2 1 8 3 9
MEDIAS 5.40 5.40 6.40 4.80 5.40 5.00 4.40 6.00 5.20 5.20DESV. STD 2.42 2.73 2.06 3.19 2.73 2.76 2.87 2.61 2.23 2.56
GRAFICO DE CONTROL X
CONSTANTES
n = 5.0 0.000 2.089 S = 2.61
LIMITE SUPERIOR DE CONTROL
LSC = 9.05
LINEA CENTRAL
X X = 5.32
LIMITE INFERIOR DE CONTROL
LIC = 1.59
OBSERVACIONES EN SUBGRUPO
PROMEDIO DE DESVIACION ESTANDAR
B3= B4=
LSC = X + A3 S
LIC = X - A3 S
TERCER EXAMEN PARCIALSUBGRUPOS
14 15 16 17 18 19 20
GRAFICO DE CONTROL X
CONSTANTE
X = 5.32 1.427
LIMITE SUPERIOR DE CONTROL
LSR = 0.00
LINEA CENTRAL
S Ř = 2.61
LIMITE INFERIOR DE CONTROL
LIR = 5.46
PROMEDIO DE PROMEDIOS
A3 =
LSS = B3 S
LIS = B4 S
1 2 3 4 5 6 7 8 9 109 8 6 4 3 5 4 4 3 25 5 3 8 8 7 9 7 6 57 9 8 2 5 2 6 2 5 74 3 9 1 2 9 2 9 9 32 2 6 9 9 2 1 8 3 9
MEDIAS 5.40 5.40 6.40 4.80 5.40 5.00 4.40 6.00 5.20 5.20DESV. STD 2.42 2.73 2.06 3.19 2.73 2.76 2.87 2.61 2.23 2.56
1 2 3 4 5 6 7 8 9 101.50
2.50
3.50
4.50
5.50
6.50
7.50
8.50
GRAFICO DE CONTROL X (DE PROMEDIOS)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O
LIMITE SUPERIOR DE CONTROL LIMITE SUPERIOR DE CONTROLLSC = X + A3 S LSC = 9.05 LSS = B3 S LSR = 0.00
LINEA CENTRAL LINEA CENTRALX X = 5.32 S Ř = 2.61
1 2 3 4 5 6 7 8 9 101.50
2.50
3.50
4.50
5.50
6.50
7.50
8.50
GRAFICO DE CONTROL X (DE PROMEDIOS)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O
1 2 3 4 5 6 7 8 9 100.00
1.00
2.00
3.00
4.00
5.00
GRAFICO DE CONTROL S (DE DESVIACIONES)
SUBGRUPO
AN
CHU
RA
DE
UN
PR
OD
UCT
O