Free Essay

General Management in Pr

In: Other Topics

Submitted By JPostigo
Words 796
Pages 4
Problema # 1:

Un ingeniero diseña una herramienta para trabajar en máquinas las cuales se encuentran a distintas temperaturas. El único parámetro de diseño que él puede seleccionar en este punto es el material con que se recubrirá la herramienta y cuenta con cuatro alternativas. El ingeniero no tiene control sobre los extremos de temperatura que tendrán las máquinas donde operarán las herramientas y sabe por experiencia que es probable que la temperatura influya en la duración de de la herramienta.

El ingeniero probará la herramienta a tres temperaturas: 100 ºF, 200 ºF y 300 ºF. Se prueban dos herramientas a cada combinación de material de recubrimiento y temperatura y las 24 pruebas se ejecutan al azar.

Tipo de material Temperatura (ºF) 100 200 300 Ti
1 4
2 10
12 15
15 58
2 5
3 5
7 5
7 32
3 4
4 10
11 4
6 39
4 3
3 12
12 10
12 52
Tj 28 79 74 181

Solución.-

i)

Ho: σj² = σ² Vj
Ho: σj² ≠ σ² al menos uno Vj

Aplicando la dócima Cochran:

Cc = 2 / 14.5 = 0.14 < > Ct,n-1,r-,95% = 0.60

Entonces:

Cc < Ct  Ho

ii)

Ho: Bj = 0 Vj
Ho: Bj ≠ 0 al menos uno Vj

SCT = (N-1) x S²

SCT = (24 – 1) x 16.78

SCT = 385.96

SCTr = 36 / 2 + 64 / 2 + 64 / 2 + 36 / 2 +484 / 2 + 144 / 2 + 441 / 2 + 576 / 2 + 900 / 2 + 144 / 2 +100 / 2 + 484 / 2 - 181² / 24

SCTr = 1686.5 – 1365.04

SCTr = 321.4

SCE = SCT - SCTr

SCE = 64.56

ANVA:

F.V. G.L. S.C. S.C.M. Fc
Tratamiento 12 – 1 = 11 321.4 29.22 5.43
Error 12 64.56 5.38
Total 24 – 1 = 23 385.96

Fc = 5.43 < > Ft,11,12,95% = 2.73

Entonces:

Fc > Ft  HA

iii)

Ho: (AB)jj = 0 Vj
Ho: (AB)ij ≠ 0 al menos uno Vj

SCA = 58² / 6 + 32² / 6 + 39² / 6 + 52² / 6 - 181² / 24 SCA = 70.46

SCB = 28² / 8 + 79² / 8 + 74² / 8 - 181² / 24 SCB = 197.58

SCAB = 321.4 – 70.46 – 197.58 SCAB = 53.36

ANVA:

F.V. G.L. S.C. S.C.M. Fc
Tratamiento 11 321.4 29.22 5.43
A 3 70.46 23.49 4.37
B 2 197.58 98.79 18.36
AB 6 53.36 8.89 1.65
Error 12 64.56 5.38
Total 23 385.96

iv) Gráfica:

Problema # 2:

Un ingeniero cuenta con cuatro tipos de empaquetaduras las cuales tienen distinto peso para reemplazarlas en un dispositivo, además cada una de ellas viene en 3 distintas alturas. Es probable que el tamaño de empaquetadura usado influya en el desempeño del dispositivo.

El ingeniero probará los 3 tamaños de empaquetadura: 15 cm, 25 cm, 35 cm. Se probarán 3 empaquetaduras en cada combinación de peso y altura y las 24 pruebas se ejecutarán al azar.

Peso (g) Altura (cm) 15 25 35 Ti
10 3
4
2 5
10
12 7
15
15 73
20 3
5
3 3
5
7 5
7
1 39
30 2
4
4 2
10
11 4
6
1 44
40 2
3
3 12
2
12 10
12
1 57
Tj 38 91 84 213

Solución.-

i)

Ho: σj² = σ² Vj
Ho: σj² ≠ σ² al menos uno Vj

Aplicando la dócima Cochran:

Cc = 2 / 14.5 = 0.14 < > Ct,n-1,r-,95% = 0.60

Entonces:

Cc < Ct  Ho

ii)

Ho: Bj = 0 Vj
Ho: Bj ≠ 0 al menos uno Vj

SCT = (N-1) x S²

SCT = (36 – 1) x 17.45

SCT = 610.75

SCTr = 81 / 3 + 121 / 3 + 100 / 3 + 64 / 3 + 27² / 3 + 225 / 3 + 23² / 3 + 26² / 3 + 37² / 3 + 169 / 3 +121 / 3 + 23² / 3 - 213² / 36

SCTr = 1298 – 1260.25

SCTr = 37.75

SCE = SCT - SCTr

SCE = 573

ANVA:

F.V. G.L. S.C. S.C.M. Fc
Tratamiento 12 – 1 = 11 573 23.88 6.96
Error 24 37.75 3.43
Total 36 – 1 = 35 610.75

Fc = 6.96 < > Ft,11,12,95% = 2.20

Entonces:

Fc > Ft  HA

iii)

Ho: (AB)jj = 0 Vj
Ho: (AB)ij ≠ 0 al menos uno Vj

SCA = 73² / 9 + 39² / 9 + 44² / 9 + 57² / 9 - 213² / 36 SCA = 76.97

SCB = 38² / 12 + 91² / 12 + 84² / 12 - 213² / 36 SCB = 138.17

SCAB = 573 – 76.97– 138.17 SCAB = 357.86

ANVA:

F.V. G.L. S.C. S.C.M. Fc
Tratamiento 11 573 23.88 6.96
A 3 76.97 25.66 7.48
B 2 138.17 69.085 20.14
AB 6 357.86 59.64 17.39
Error 24 37.75 3.43
Total 35 610.75

iv) Gráfica:

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