trabajo practico 2
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N° de muestra Observaciones1 2 3 4 5 Xi
1 2184.1 2183.1 2184.2 2181 2183.2 2183.122 2184.3 2182.5 2183.6 2184 7 2182.1 2183.1253 2184.6 2183.9 2184.7 2183.2 2184.7 2184.224 2183.2 2183.4 2184.3 2183.1 2183.9 2183.585 2184.3 2182.5 2183.6 2184 7 2182.9 2183.3256 2184.2 2181 2183.2 2184.6 2185.3 2183.667 2184.6 2183.9 2184.7 2183.1 2184.6 2184.188 2184.1 2181 2185 2185.1 2182.1 2183.469 2183.2 2182.5 2183.6 2184.7 2182.9 2183.38
10 2183.9 2183.2 2182.1 2181.7 2183.1 2182.811 2183.2 2184.6 2183.9 2184.7 2183.1 2183.912 2184.3 2182.5 2183.6 2184.7 2182.1 2183.4413 2184.1 2183.1 2184.2 2184.3 2185.2 2184.1814 2184.6 2183.9 2184.7 2183.1 2184.6 2184.1815 2183.4 2183.9 2183.2 2184.3 2185.1 2183.9816 2182.5 2183.6 2184.7 2181.7 2183.1 2183.1217 2182.5 2183.6 2184.7 2183.1 2184.6 2183.718 2184.3 2182.5 2183.1 2183.9 2182.5 2183.2619 2183.9 2184.7 2183.1 2181 2183.2 2183.1820 2183.2 2182.5 2183.2 2183.1 2184.2 2183.2421 2183.4 2181.9 2183.1 2183.2 2181.9 2182.722 2182.5 2183 2181.6 2182.1 2182.6 2182.3623 2182.1 2181.9 2183.6 2183.1 2183.4 2182.8224 2183.5 2183.1 2183.4 2182.4 2182.9 2183.0625 2182.9 2183.2 2183.1 2183.1 2184.1 2183.28
2183.41
B4 (n=5) 2.089
A3 (n=5) 1.427 B3 (n=5) 0
CARTA X CARTA SLSC LC LIC LSC LC LIC2184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 0
2184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 02184.66989025 2183.41 2182.15011 0 0.8828943596 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 252180.5
2181
2181.5
2182
2182.5
2183
2183.5
2184
2184.5
2185
CARTA X
LSCLCLICXi
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
CARTA S
LSCLCLICSi
D4 (n=5) 2.004
A2 (n=5) 0.577 D3 (n=5) 0
CARTA X CARTA RLSC LC LIC LSC LC LIC
2184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 02184.642472 2183.41 2182.17753 4.280544 2.136 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
CARTA S
LSCLCLICSi
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 252180.5
2181
2181.5
2182
2182.5
2183
2183.5
2184
2184.5
2185
CARTA X
LSCLCLICXi
σ= 0.9392493188 c4 (n=5) 0.94
σ= 0.91831470 d2 (n=5) 2.326
VALOR DE σ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 252180.5
2181
2181.5
2182
2182.5
2183
2183.5
2184
2184.5
2185
CARTA X
LSCLCLICXi
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
CARTA R
LSCLCLICRi
LSE 2199LIE 2167
Cp= 5.678RCP es mayor a 1,33 de modo que tiene alta capacidad
Cp= 5.808
Probabilidad de hallar una falsa alarma
α=P(X>LSC) + P(X<LIC)
α = P(Z>Z2) + P(Z<Z1)
Z2= 3.0010313047Z1= -3.001031305P(Z>3)= 0.001349898P(Z<-3)= 0.001349898 0.0026998
0.0026998
Proporción de botellas defectuosas
p = P(X>LSE) + P(X<LIE) LSE 2199LIE 2167
p = P(Z>Z2) + P(Z<Z1)
Z1= -17.86969101
α=P(Z>3)+P(Z<-3)=
Z2= 16.9767509
P(Z>16,98)= 0P(Z<-17,87)= 1.009972E-71
p= 1.009972E-71
La proporción de defectuosos es demasiado pequeña para ser calculadapor lo que decimos que el proceso tiene una baja variabilidad
Probabilidad de cometer un error tipo II
2184.7874721
β = P(LIC<X<LSC) LIC 2182.17753LSC 2184.64247
Z1= -6.355133271Z2= -0.353070662
β = P(Z1<Z<Z2) = P(Z<Z2) - P(Z<Z1)P(Z<-6,35)= 1.076575E-10 0.36316935P(Z<-0,35)= 0.3631693488
β= 0.3631693487
Probabilidad de detectarlo en la segunda muestra despues del cambio
p= 0.2312773729
Probabilidad de detectarlo antes de la tercera muestra despues del cambio
p= 0.5944467216 0.86810802
Muestras que hay que sacar en promedio para detectar el cambio
1.5702761762 Se necesitan alrededor de 2 muestras en promedio para detectar el cambio
µ=
σ=
APL1=
Ri Si3.2 1.287245122.2 1.007885581.5 0.661059761.2 0.506951671.8 0.793200274.3 1.669730521.6 0.683373984.1 1.828387272.2 0.840832922.2 0.888819441.6 0.751664822.6 1.121605992.1 0.746324331.6 0.683373981.9 0.75960516
3 1.132254392.2 0.951314881.8 0.817312673.7 1.377316231.7 0.610737261.5 0.738241151.4 0.531977441.7 0.772657751.1 0.43931765 CARTA X Y S1.2 0.47116876
2.136 0.88289436
CARTA DE CONTROL X
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 252180.5
2181
2181.5
2182
2182.5
2183
2183.5
2184
2184.5
2185
CARTA X
LSCLCLICXi
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
CARTA S
LSCLCLICSi
CARTA X Y R
CARTA DE CONTROL X
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
CARTA S
LSCLCLICSi
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 252180.5
2181
2181.5
2182
2182.5
2183
2183.5
2184
2184.5
2185
CARTA X
LSCLCLICXi
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 252180.5
2181
2181.5
2182
2182.5
2183
2183.5
2184
2184.5
2185
CARTA X
LSCLCLICXi
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
CARTA R
LSCLCLICRi
RCP es mayor a 1,33 de modo que tiene alta capacidad
0.91831470
Probabilidad de detectarlo en la segunda muestra despues del cambio
Probabilidad de detectarlo antes de la tercera muestra despues del cambio
Muestras que hay que sacar en promedio para detectar el cambio
Se necesitan alrededor de 2 muestras en promedio para detectar el cambio
CARTA X Y S
CARTA DE CONTROL S
CARTA X Y R
CARTA DE CONTROL R
n= 5LSC= 508LIC= 507 µ= 507.5LSE= 507.9 µ= 507.5LIE= 507.1σ= 2.5
Proporción de defectuosos
p = P(X>LSE) + P(X<LIE)
p = P(Z>Z2) + P(Z<Z1)
Z1= -0.160Z2= 0.160
P(Z>0,16)= 0.43644054P(Z<-0,16)= 0.43644054
p= 0.87288107
12870 426 muetras= 30
Xmedia= 429
Smedia= 14.2
n= 7c4= 0.9594B3= 0.118B4= 1.882
14.80
429
LSC de S 26.7244LC de S 14.2LIC de S 1.6756
ΣX = ΣS =
σ =
μ =
Observacion Concentracion Rango movil LSC de x LC de x LIC de x1 94.8 105.10 99.10 93.092 98.3 3.5 105.10 99.10 93.093 98.4 0.1 105.10 99.10 93.094 102 3.6 105.10 99.10 93.095 102 0 105.10 99.10 93.096 98.5 3.5 105.10 99.10 93.097 99 0.5 105.10 99.10 93.098 101.1 2.1 105.10 99.10 93.099 98.4 2.7 105.10 99.10 93.09
10 97 1.4 105.10 99.10 93.0911 97.7 0.7 105.10 99.10 93.0912 100 2.3 105.10 99.10 93.0913 101.3 1.3 105.10 99.10 93.0914 98.7 2.6 105.10 99.10 93.0915 101.4 2.7 105.10 99.10 93.0916 97.2 4.2 105.10 99.10 93.0917 101 3.8 105.10 99.10 93.0918 98.1 2.9 105.10 99.10 93.0919 96.7 1.4 105.10 99.10 93.0920 100.3 3.6 105.10 99.10 93.09
99.10 2.26
d2 (n=1) = 1.128D3 (n=1) = 0D4 (n=1) = 3.267
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2085.00
90.00
95.00
100.00
105.00
110.00
Carta X
LSC de xLC de xLIC de xConcentracion
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
1
2
3
4
5
6
7
8
Carta de MR
LSC de MRLC de MRLIC de MRRango movil
µ= 99.10σ= 2.00167973
LSE 100LIE 98
CP= 0.16652681 menor que 1,33 por lo que habra muchos defectuosos; se debe disminuir la variabilidad del proceso
Horas de produccion deficiente
p = P(x<LIE) + P(x>LSE)
p = P(Z<Z1) + P(Z>Z2)
Z1= -0.54704055944Z2= 0.45212027972
P(Z<-0,547)= 0.29218936606P(Z>0,452)= 0.32563449122
p= 0.61782385728 Aproximadamente cada 100 horas 62 serán deficientes
LSC de MR LC de MR LIC de MR7.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 07.37654211 2.26 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
1
2
3
4
5
6
7
8
Carta de MR
LSC de MRLC de MRLIC de MRRango movil
menor que 1,33 por lo que habra muchos defectuosos; se debe disminuir la variabilidad del proceso
Número de muestra X R LSC de X LC de X LiC de X1 103 4 106.85 104.2 101.552 102 5 106.85 104.2 101.553 104 2 106.85 104.2 101.554 105 11 106.85 104.2 101.555 104 4 106.85 104.2 101.556 106 4 106.85 104.2 101.557 103 7 106.85 104.2 101.558 105 2 106.85 104.2 101.559 106 4 106.85 104.2 101.55
10 104 3 106.85 104.2 101.55
Xmedia= 104.2Rmedio= 4.6d2 (n=5)= 2.326σ= 1.978A2 (n=5)= 0.577D3 (n=5)= 0
D4 (n=5)= 2.115
1 2 3 4 5 6 7 8 9 1098.0099.00
100.00101.00102.00103.00104.00105.00106.00107.00108.00
Carta X
LSC de XLC de XLiC de XX
1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
Carta R
LSC de RLC de RLIC de RR
Si el tamaño de la muestra cambia a 9 utilizaríamos la carta X-S porque la muestra es mayor a aunque el ejercicio sería más fácil aplicarlo si se dispone del uso de un software ya que esto sería demasiado tedioso para un cálculo manual.
1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
Carta R
LSC de RLC de RLIC de RR
LSC de R LC de R LIC de R9.729 4.6 09.729 4.6 09.729 4.6 09.729 4.6 09.729 4.6 09.729 4.6 09.729 4.6 09.729 4.6 09.729 4.6 09.729 4.6 0
CARTA X Y R
CARTA DE CONTROL XCARTA DE CONTROL R
CARTA X Y R
CARTA DE CONTROL R
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