Control Estadistico

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DATOS DE LA ANCHURA DE SUBGRUPOS 1 2 3 4 5 6 7 8 9 10 11 1.88 1.93 1.92 1.89 1.95 2.00 1.95 1.87 1.96 1.99 1.93 1.93 1.97 1.95 1.89 1.93 1.95 1.93 1.98 1.92 1.93 1.95 1.98 1.89 1.90 1.90 1.90 1.94 1.97 1.96 1.98 2.01 1.90 1.88 1.94 1.98 1.94 1.93 1.89 1.85 2.04 1.88 2.02 1.93 MEDIAS 1.92 1.93 1.94 1.91 1.93 1.95 1.93 1.96 1.94 1.99 1.93 RANGOS 0.10 0.08 0.08 0.05 0.05 0.11 0.12 0.17 0.10 0.09 0.05 GRAFICO DE CONTR CONSTANTE DESVIACION ESTAND n = 4.0 2.059 Ř = 0.085 LIMITE SUPERIOR DE CONTROL LSC = 1.9952 LINEA CENTRAL X X = 1.9336 LIMITE INFERIOR DE CONTROL LIC = 1.8721 OBSERVACIONES EN SUBGRUPO PROMEDIO DE RANGOS d2= σ = Ř / d2 LSC = X + 3 (σ/√n) LIC = X - 3 (σ/√n)

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)

C17
INTRODUCE EL NUMERO DE ELEMENTOS DE SUBGRUPO.

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

C38
INTRODUCE EL NUMERO DE ELEMENTOS DE SUBGRUPO.

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

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SUBGRUPO

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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)

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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)

C17
INTRODUCE EL NUMERO DE ELEMENTOS DE SUBGRUPO.

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

C38
INTRODUCE EL NUMERO DE ELEMENTOS DE SUBGRUPO.

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

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SUBGRUPO

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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)

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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)

C17
INTRODUCE EL NUMERO DE ELEMENTOS DE SUBGRUPO.

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

C38
INTRODUCE EL NUMERO DE ELEMENTOS DE SUBGRUPO.

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)

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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

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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)

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LIC = X - A2 Ř LIC = 28.8401 LIR = D3 Ř LIR = 0

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

C17
INTRODUCE EL NUMERO DE ELEMENTOS DE SUBGRUPO.

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)

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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

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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)

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LIMITE INFERIOR DE CONTROL LIMITE INFERIOR DE CONTROLLIC = X - A3 S LIC = 1.59 LIS = B4 S LIR = 5.46