1. En la fabricación de pernos, el diámetro es una
característica importante para su uso. Con el objeto de
determinar si un lote cumple con las especificaciones del
cliente, se extrae una muestra de 300 piezas y se
inspecciona.
7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1.474 1.478 1.524 1.485 1.524 1.488 1.506 1.476 1.443 1.522 1.491 1.493 1.541 1.531 1.513 1.585 1.486 1.505 1.582 1.495 valor max= 1.594
2 1.482 1.474 1.497 1.495 1.425 1.589 1.475 1.520 1.453 1.510 1.505 1.501 1.529 1.475 1.505 1.514 1.504 1.452 1.509 1.517 valor min= 1.420
3 1.504 1.492 1.552 1.542 1.540 1.501 1.505 1.536 1.494 1.471 1.521 1.505 1.553 1.584 1.528 1.490 1.503 1.574 1.515 1.473 rango= 0.174
4 1.486 1.506 1.504 1.502 1.486 1.479 1.519 1.481 1.555 1.481 1.518 1.512 1.480 1.543 1.507 1.502 1.545 1.561 1.543 1.477 # intervalo= 9
5 1.493 1.506 1.503 1.507 1.555 1.443 1.474 1.466 1.444 1.531 1.503 1.450 1.530 1.524 1.515 1.489 1.543 1.537 1.520 1.568 0.01933333 0.020
6 1.533 1.546 1.492 1.531 1.515 1.420 1.507 1.536 1.508 1.576 1.524 1.513 1.520 1.580 1.486 1.544 1.507 1.483 1.527 1.461
7 1.518 1.482 1.478 1.456 1.489 1.491 1.544 1.461 1.536 1.501 1.506 1.550 1.516 1.550 1.518 1.501 1.544 1.464 1.526 1.538
8 1.501 1.486 1.501 1.484 1.477 1.542 1.488 1.503 1.441 1.510 1.465 1.478 1.515 1.535 1.459 1.509 1.534 1.518 1.458 1.557
9 1.452 1.528 1.529 1.499 1.556 1.557 1.543 1.546 1.529 1.450 1.504 1.493 1.527 1.540 1.523 1.438 1.588 1.453 1.524 1.432
10 1.449 1.559 1.459 1.468 1.484 1.553 1.495 1.477 1.466 1.567 1.489 1.495 1.513 1.486 1.551 1.483 1.535 1.537 1.470 1.501
11 1.473 1.549 1.516 1.490 1.559 1.480 1.457 1.533 1.518 1.484 1.516 1.545 1.585 1.468 1.466 1.455 1.482 1.542 1.513 1.532
12 1.594 1.540 1.484 1.479 1.484 1.546 1.526 1.446 1.466 1.492 1.515 1.570 1.533 1.543 1.501 1.531 1.575 1.517 1.520 1.507
13 1.470 1.521 1.499 1.525 1.513 1.515 1.529 1.434 1.517 1.480 1.484 1.457 1.537 1.536 1.507 1.516 1.475 1.499 1.479 1.486
14 1.482 1.472 1.540 1.513 1.477 1.514 1.509 1.506 1.514 1.525 1.535 1.548 1.463 1.500 1.467 1.425 1.460 1.531 1.493 1.528
15 1.496 1.536 1.501 1.435 1.548 1.453 1.464 1.512 1.464 1.560 1.505 1.461 1.503 1.484 1.480 1.453 1.499 1.497 1.426 1.468

2. INTERVALOS APARENTES INTERVALOS REALES MARCAS FRECUENCIAS MEDIDAS DE TENDENCIA CENTRAL Y DISPERCION
LIM INF LIM SUP LIM INF LIM SUP DE CLASE Fi Fai Fri Frai Fi*Xi (Xi-Xtes)*Fi (Xi-Xtes)^2*Fi
1 1.418 1.437 1.4175 1.4375 1.4275 7 7 0.02333333 0.02333333 9.9925 0.54693333 0.042733724
2 1.438 1.457 1.4375 1.4575 1.4475 19 26 0.06333333 0.08666667 27.5025 1.10453333 0.064210204
3 1.458 1.477 1.4575 1.4775 1.4675 37 63 0.12333333 0.21 54.2975 1.41093333 0.053803591
4 1.478 1.497 1.4775 1.4975 1.4875 57 120 0.19 0.4 84.7875 1.0336 0.018742613
5 1.498 1.517 1.4975 1.5175 1.5075 72 192 0.24 0.64 108.54 0.1344 0.00025088
6 1.518 1.537 1.5175 1.5375 1.5275 54 246 0.18 0.82 82.485 1.1808 0.02582016
7 1.538 1.557 1.5375 1.5575 1.5475 36 282 0.12 0.94 55.71 1.5072 0.06310144
8 1.558 1.577 1.5575 1.5775 1.5675 10 292 0.03333333 0.97333333 15.675 0.61866667 0.038274844
9 1.578 1.597 1.5775 1.5975 1.5875 8 300 0.02666667 1 12.7 0.65493333 0.053617209
0.0005
TOTALES= 451.69 8.192 0.360554667
MEDIA a= 1.50563333
DESVIACION MEDIA= 0.02730667
VARIANZA= 0.001201849
DESVIACION ESTANDAR= 0.034667692

3. HISTOGRAMA
X Y
1.4175 0
120 HISTOGRA
1.4175 7 MA
OSL
LSL
TV
1.4375 7 X
1.4375 0 100 x+s
x+2s
x+3s
x+4s
x-4s
x-2s
x-3s
x+s
x-s
1.4375 19
X
1.4575 19 x+2s
1.4575 0 80
x+3s
1.4575 37
x-s
1.4775 37
60
1.4775 0 x-2s
1.4775 57
x-3s
1.4975 57 40
1.4975 0 TV
1.4975 72 LSL
1.5175 72 20
1.5175 0 OSL
1.5175 54 0 eje x
1.5375 54
1.4175
1.4375
1.5175
1.5975
1.4575
1.4775
1.4975
1.5375
1.5575
1.5775
x+4s
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.15 x y
1.5775 10 1.50563333 0 1.5 0
1.5775 0 1.50563333 87 1.5 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.65 0
1.54030103 87 1.47096564 87 1.65 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.35 0
1.4375 0 1.57496872 87 1.43629795 87 1.35 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0
1.5975 0 1.6443041 87 1.36696256 87

4. CONCLUSION
 Como se puede observar en este histograma, se tomó una
muestra de 300 pernos para poder medir y saber si están dentro
del rango dado por nuestro cliente, y al hacerlo se dio en cuenta
que tenemos 4.17 sigmas, lo que significa que tenemos una
buena calidad porque estamos cumpliendo con las
especificaciones y rangos dados por el cliente. Pero aun así no
alcanzamos la excelencia en la calidad de nuestro trabajo, a lo
cual solo se puede decir que somos buenos ya que la mayor parte
de nuestra muestra está muy cerca de las especificaciones dadas.

5. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
1.4375 7 X
1.4375 0 100 x+s
x+2s
x+4s
x+3s
x-4s
x-3s
x-2s
x+s
x-s
1.4375 19
X
x+2s
1.4575 19 x+3s
1.4575 0 80
x-s
1.4575 37
1.4775 37 x-2s
60
1.4775 0 x-3s
1.4775 57 TV
1.4975 57 40 LSL
1.4975 0
OSL
1.4975 72
1.5175 72 20 x+4s
1.5175 0 x-4s
1.5175 54 eje x
0
1.5375 54
1.5575
1.5775
1.5975
1.4175
1.4375
1.4575
1.4775
1.4975
1.5175
1.5375
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.15 x y
1.5775 10 1.50563333 0 1.4 0
1.5775 0 86.4 1.50563333 87 1.4 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.55 0
1.54030103 87 1.47096564 87 1.55 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.25 0
1.4375 0 1.57496872 87 1.43629795 87 1.25 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0

6. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
1.4375 7
1.4375 0 100
x+2s
x+3s
x+4s
x-4s
x-3s
x-2s
X
x+s
x-s
1.4375 19
X
1.4575 19
1.4575 0 80
1.4575 37 x+s
1.4775 37
60
1.4775 0
1.4775 57 x+2s
1.4975 57 40
1.4975 0
1.4975 72 x+3s
1.5175 72 20
1.5175 0
1.5175 54
0
1.5375 54
1.4575
1.4775
1.4975
1.5175
1.4175
1.4375
1.5375
1.5575
1.5775
1.5975
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.15 x y
1.5775 10 1.50563333 0 1.45 0
1.5775 0 86.4 1.50563333 87 1.45 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.6 0
1.54030103 87 1.47096564 87 1.6 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.3 0
1.4375 0 1.57496872 87 1.43629795 87 1.3 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0
1.5975 0 1.6443041 87 1.36696256 87

7. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
1.4375 7 X
1.4375 0 100 x+s
x+3s
x+4s
x+2s
x-4s
x-3s
x-2s
x+s
x-s
1.4375 19
X
x+2s
1.4575 19 x+3s
1.4575 0 80
x-s
1.4575 37
1.4775 37 x-2s
60
1.4775 0 x-3s
1.4775 57 TV
1.4975 57 40 LSL
1.4975 0
OSL
1.4975 72
1.5175 72 20 x+4s
1.5175 0 x-4s
1.5175 54 eje x
0
1.5375 54
1.4575
1.5175
1.5575
1.4175
1.4375
1.4775
1.4975
1.5375
1.5775
1.5975
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.15 x y
1.5775 10 1.50563333 0 1.55 0
1.5775 0 86.4 1.50563333 87 1.55 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.7 0
1.54030103 87 1.47096564 87 1.7 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.4 0
1.4375 0 1.57496872 87 1.43629795 87 1.4 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0
1.5975 0 1.6443041 87 1.36696256 87

8. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
1.4375 7 X
1.4375 0 100 x+s
x+4s
x+2s
x+3s
x-4s
x-3s
x-2s
x+s
x-s
1.4375 19
X
x+2s
1.4575 19 x+3s
1.4575 0 80
x-s
1.4575 37
1.4775 37 x-2s
60
1.4775 0 x-3s
1.4775 57 TV
1.4975 57 40 LSL
1.4975 0
OSL
1.4975 72
1.5175 72 20 x+4s
1.5175 0 x-4s
1.5175 54 eje x
0
1.5375 54
1.5375
1.5575
1.5775
1.5975
1.4175
1.4375
1.4575
1.4775
1.4975
1.5175
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.15 x y
1.5775 10 1.50563333 0 1.6 0
1.5775 0 86.4 1.50563333 87 1.6 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.75 0
1.54030103 87 1.47096564 87 1.75 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.45 0
1.4375 0 1.57496872 87 1.43629795 87 1.45 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0
1.5975 0 1.6443041 87 1.36696256 87

9. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
1.4375 7 X
1.4375 0 100 x+s
x+2s
x+3s
x+4s
x-4s
x-3s
x-2s
x+s
x-s
1.4375 19
X
x+2s
1.4575 19 x+3s
1.4575 0 80
x-s
1.4575 37
1.4775 37 x-2s
60
1.4775 0 x-3s
1.4775 57 TV
1.4975 57 40 LSL
1.4975 0
OSL
1.4975 72
1.5175 72 20 x+4s
1.5175 0 x-4s
1.5175 54 eje x
0
1.5375 54
1.4375
1.4575
1.5375
1.5575
1.4175
1.4775
1.4975
1.5175
1.5775
1.5975
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.2 x y
1.5775 10 1.50563333 0 1.4 0
1.5775 0 86.4 1.50563333 87 1.4 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.6 0
1.54030103 87 1.47096564 87 1.6 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.2 0
1.4375 0 1.57496872 87 1.43629795 87 1.2 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0
1.5975 0 1.6443041 87 1.36696256 87

10. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
1.4375 7 X
1.4375 0 100 x+s
x+2s
x+3s
x+4s
x-4s
x-3s
x-2s
x+s
x-s
1.4375 19
X
x+2s
1.4575 19 x+3s
1.4575 0 80
x-s
1.4575 37
1.4775 37 x-2s
60
1.4775 0 x-3s
1.4775 57 TV
1.4975 57 40 LSL
1.4975 0
OSL
1.4975 72
1.5175 72 20 x+4s
1.5175 0 x-4s
1.5175 54 eje x
0
1.5375 54
1.4175
1.4575
1.5575
1.5975
1.4375
1.4775
1.4975
1.5175
1.5375
1.5775
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.2 x y
1.5775 10 1.50563333 0 1.45 0
1.5775 0 86.4 1.50563333 87 1.45 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.65 0
1.54030103 87 1.47096564 87 1.65 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.25 0
1.4375 0 1.57496872 87 1.43629795 87 1.25 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0
1.5975 0 1.6443041 87 1.36696256 87

11. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
X
1.4375 7
x+s
1.4375 0 100
x+2s
x+3s
x+4s
x+5s
x-5s
x-4s
x-3s
x-2s
x+2s
x+s
x-s
1.4375 19
X
x+3s
1.4575 19
1.4575 0 80 x-s
1.4575 37 x-2s
1.4775 37 x-3s
60
1.4775 0 TV
1.4775 57 LSL
1.4975 57 40 OSL
1.4975 0 x+4s
1.4975 72 x-4s
1.5175 72 20
eje x
1.5175 0 x+5s
1.5175 54 x-5s
0
1.5375 54
1.4175
1.5175
1.5575
1.5975
1.4375
1.4575
1.4775
1.4975
1.5375
1.5775
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.2 x y
1.5775 10 1.50563333 0 1.5 0
1.5775 0 86.4 1.50563333 87 1.5 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.7 0
1.54030103 87 1.47096564 87 1.7 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.3 0
1.4375 0 1.57496872 87 1.43629795 87 1.3 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0
1.5975 0 1.6443041 87 1.36696256 87
x+5s x-5s
1.67897179 0 1.33229487 0
1.67897179 87 1.33229487 87

12. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
1.4375 7 X
1.4375 0 100 x+s
x+4s
x+2s
x+3s
x-4s
x-3s
x-2s
x+s
x-s
1.4375 19
X
x+2s
1.4575 19 x+3s
1.4575 0 80
x-s
1.4575 37
1.4775 37 x-2s
60
1.4775 0 x-3s
1.4775 57 TV
1.4975 57 40 LSL
1.4975 0
OSL
1.4975 72
1.5175 72 20 x+4s
1.5175 0 x-4s
1.5175 54 eje x
0
1.5375 54
1.5375
1.5575
1.5775
1.4175
1.4375
1.4575
1.4775
1.4975
1.5175
1.5975
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.2 x y
1.5775 10 1.50563333 0 1.55 0
1.5775 0 86.4 1.50563333 87 1.55 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.75 0
1.54030103 87 1.47096564 87 1.75 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.35 0
1.4375 0 1.57496872 87 1.43629795 87 1.35 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0
1.5975 0 1.6443041 87 1.36696256 87

13. HISTOGRAMA
X Y
1.4175 0 120 Series1
1.4175 7
OSL
LSL
TV
1.4375 7 X
1.4375 0 100 x+s
x+2s
x+3s
x+4s
x-4s
x-3s
x-2s
x+s
x-s
1.4375 19
X
x+2s
1.4575 19 x+3s
1.4575 0 80
x-s
1.4575 37
1.4775 37 x-2s
60
1.4775 0 x-3s
1.4775 57 TV
1.4975 57 40 LSL
1.4975 0
OSL
1.4975 72
1.5175 72 20 x+4s
1.5175 0 x-4s
1.5175 54 eje x
0
1.5375 54
1.4575
1.4775
1.5775
1.5975
1.4175
1.4375
1.4975
1.5175
1.5375
1.5575
1.5375 0
1.5375 36
1.5575 36
1.5575 0 MEDIA (x) T.V.
1.5575 10 X Y 0.2 x y
1.5775 10 1.50563333 0 1.6 0
1.5775 0 86.4 1.50563333 87 1.6 104
1.5775 8
1.5975 8 x+s x-s LSL
1.5975 0 1.54030103 0 1.47096564 0 1.8 0
1.54030103 87 1.47096564 87 1.8 104
eje x x+2s x-2s OSL
1.4175 0 1.57496872 0 1.43629795 0 1.4 0
1.4375 0 1.57496872 87 1.43629795 87 1.4 104
1.4575 0
1.4775 0 x+3s x-3s
1.4975 0 1.60963641 0 1.40163026 0
1.5175 0 1.60963641 87 1.40163026 87
1.5375 0
1.5575 0 x+4s x-4s
1.5775 0 1.6443041 0 1.36696256 0

14. CIRCULAR
X Y
360
0.02333333 8.4
CIRCULAR
0.06333333 22.8
0.12333333 44.4 12 9.6 8.4 0.023333333
0.19 68.4
22.8 0.063333333
0.24 86.4 43.2 44.4
0.18 64.8 0.123333333
0.12 43.2 64.8 0.19
0.03333333 12 68.4
0.24
0.02666667 9.6 0.18
86.4
0.12
0.033333333
0.026666667

15. POLIGONOS
X Y
0.973333333
0.02333333 1
0.08666667 2
POLIGONOS
0.21 3 1.2
0.94
1
0.4 4
0.82
1
0.64 5
0.82 6
0.64
0.8
0.94 7
0.97333333 8 0.6
0.086666667
POLIGONOS
0.4
0.023333333
1 9
0.4
0.21
0.2
0
1 2 3 4 5 6 7 8 9

16. LIMITE INF
X Y
1.4275 3
1.4275 7
CUARTIL 1
X Y
1.4475 3 8
1.4475 7 LIM INF
7
CUAR T 1
LINEA 1 6
LINEA 1
X Y 5 CUAR T 2
1.4275 5
4 CUAR T 3
1.4475 5
LINEA 2
3
CUARIL 2 LINEA 3
X Y 2
LIM S UP
1.4275
1.5675
1.5875
1.4475
1.4875
1.4875 3 1 LINEA 4
1.4875 7
0 cajas y bigotes
1.4000 1.4500 1.5000 1.5500 1.6000
CUARTIL 3
X Y
1.5675 3 caj as y bi gotes
1.5675 7 x y
1.4275 2
LINEA 2 1.4475 2
X Y 1.4875 2
1.4475 7 1.5675 2
1.5675 7 1.5875 2
LINEA 3
X Y
1.4475 3
1.5675 3
LIMITE SUPERIOR
X Y
1.5875 3
1.5875 7
LINEA 4
X Y
1.5675 5
1.5875 5