cep_trab_prac_2
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Carta de control S para la variabilidad Desviaciones estandares LC LSC LIC Mediciones Desv. estandar
description
cep_trab_prac_2
Transcript of cep_trab_prac_2
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Carta de control S para la variabilidad
Desviaciones estandares
LC
LSC
LIC
Mediciones
Des
v. e
stan
dar
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2181
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2185
Carta x media con el rango
Medias muestrales
LC
LSC
LIC
Medias muestrales
Diá
me
tro
s
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Carta R para los diametros
Rangos medios muestrales
LC
LSC
LIC
Numero de medición
Ran
go
s m
edio
s m
ues
tral
es
1 2 3 4 5 MEDIAS DESV.EST C42184.1 2183.1 2184.2 2181 2183.2 2183.12 1.28724512 0.942184.3 2182.5 2183.6 2184 7 2182.1 2183.125 1.007885582184.6 2183.9 2184.7 2183.2 2184.7 2184.22 0.661059762183.2 2183.4 2184.3 2183.1 2183.9 2183.58 0.506951672184.3 2182.5 2183.6 2184 7 2182.9 2183.325 0.793200272184.2 2181 2183.2 2184.6 2185.3 2183.66 1.669730522184.6 2183.9 2184.7 2183.1 2184.6 2184.18 0.683373982184.1 2181 2185 2185.1 2182.1 2183.46 1.828387272183.2 2182.5 2183.6 2184.7 2182.9 2183.38 0.840832922183.9 2183.2 2182.1 2181.7 2183.1 2182.8 0.888819442183.2 2184.6 2183.9 2184.7 2183.1 2183.9 0.751664822184.3 2182.5 2183.6 2184.7 2182.1 2183.44 1.121605992184.1 2183.1 2184.2 2184.3 2185.2 2184.18 0.746324332184.6 2183.9 2184.7 2183.1 2184.6 2184.18 0.683373982183.4 2183.9 2183.2 2184.3 2185.1 2183.98 0.759605162182.5 2183.6 2184.7 2181.7 2183.1 2183.12 1.132254392182.5 2183.6 2184.7 2183.1 2184.6 2183.7 0.951314882184.3 2182.5 2183.1 2183.9 2182.5 2183.26 0.817312672183.9 2184.7 2183.1 2181 2183.2 2183.18 1.377316232183.2 2182.5 2183.2 2183.1 2184.2 2183.24 0.610737262183.4 2181.9 2183.1 2183.2 2181.9 2182.7 0.738241152182.5 2183 2181.6 2182.1 2182.6 2182.36 0.531977442182.1 2181.9 2183.6 2183.1 2183.4 2182.82 0.772657752183.5 2183.1 2183.4 2182.4 2182.9 2183.06 0.439317652182.9 2183.2 2183.1 2183.1 2184.1 2183.28 0.47116876
2183.41 0.88289436
0.93924932
LSC sigma LIC sigma LIC sigma aprox.1.84423795 -0.07844923 0
σ =
LSC LC LIC B42184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.0892184.67013519473 2183.41 2182.14986480527 2.089
CARTA DE CONTROL S
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2180.52181
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2182.52183
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CARTA DE CONTROL DE X MEDIA
MEDIAS
LSC
LC
LIC
NUMERO DE MEDICIONES
VA
LO
RE
S D
E E
SP
ES
OR
CARTA DE CONTROL R
B3 LC LSC LIC Mayor Carta x-R Menor Carta x-R0 0.8823 1.84436632 0 2184.2 21810 0.8823 1.84436632 0 2184.3 2182.10 0.8823 1.84436632 0 2184.7 2183.20 0.8823 1.84436632 0 2184.3 2183.10 0.8823 1.84436632 0 2184.3 2182.50 0.8823 1.84436632 0 2185.3 21810 0.8823 1.84436632 0 2184.7 2183.10 0.8823 1.84436632 0 2185.1 21810 0.8823 1.84436632 0 2184.7 2182.50 0.8823 1.84436632 0 2183.9 2181.70 0.8823 1.84436632 0 2184.7 2183.10 0.8823 1.84436632 0 2184.7 2182.10 0.8823 1.84436632 0 2185.2 2183.10 0.8823 1.84436632 0 2184.7 2183.10 0.8823 1.84436632 0 2185.1 2183.20 0.8823 1.84436632 0 2184.7 2181.70 0.8823 1.84436632 0 2184.7 2182.50 0.8823 1.84436632 0 2184.3 2182.50 0.8823 1.84436632 0 2184.7 21810 0.8823 1.84436632 0 2184.2 2182.50 0.8823 1.84436632 0 2183.4 2181.90 0.8823 1.84436632 0 2183 2181.60 0.8823 1.84436632 0 2183.6 2181.90 0.8823 1.84436632 0 2183.5 2182.40 0.8823 1.84436632 0 2184.1 2182.9
LSE= 2199LIE= 2167
RCP= 5.67829353384764RCP es mayor a 1,33 de modo que tiene alta capacidad
Probabilidad de hallar una falsa alarma
P(X>2184,64247)=P(X<2182,17753)=Z1= 2.93414231700571Z2= -2.9341423170057P(Z>2,934)= 0.001665P(Z<-2,934)= 0.001665
α=P(Z>2,934)+P(Z<-2,934)=
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CARTA DE CONTROL DE X MEDIA
MEDIAS
LSC
LC
LIC
NUMERO DE MEDICIONES
VA
LO
RE
S D
E E
SP
ES
OR
Rango Carta x-R LC Carta x A2 Rango medioLSC carta x LIC carta x D43.19999999999982 2183.41 0.577 2.136 2184.64247 2182.17753 2.1152.20000000000027 2183.41 0.577 2.136 2184.64247 2182.17753 2.115
1.5 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.20000000000027 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.80000000000018 2183.41 0.577 2.136 2184.64247 2182.17753 2.1154.30000000000018 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.59999999999991 2183.41 0.577 2.136 2184.64247 2182.17753 2.1154.09999999999991 2183.41 0.577 2.136 2184.64247 2182.17753 2.1152.19999999999982 2183.41 0.577 2.136 2184.64247 2182.17753 2.1152.20000000000027 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.59999999999991 2183.41 0.577 2.136 2184.64247 2182.17753 2.1152.59999999999991 2183.41 0.577 2.136 2184.64247 2182.17753 2.1152.09999999999991 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.59999999999991 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.90000000000009 2183.41 0.577 2.136 2184.64247 2182.17753 2.115
3 2183.41 0.577 2.136 2184.64247 2182.17753 2.1152.19999999999982 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.80000000000018 2183.41 0.577 2.136 2184.64247 2182.17753 2.1153.69999999999982 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.69999999999982 2183.41 0.577 2.136 2184.64247 2182.17753 2.115
1.5 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.40000000000009 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.69999999999982 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.09999999999991 2183.41 0.577 2.136 2184.64247 2182.17753 2.1151.19999999999982 2183.41 0.577 2.136 2184.64247 2182.17753 2.115
Proporción de botellas defectuosas
Z1= -17.4713994Z2= 16.5983618
RCP es mayor a 1,33 de modo que tiene alta capacidadP(Z<-17,4713994)=P(Z>16,5983618)=
p=P(Z<-17,4713994)+P(Z>16,5983618)=
La proporción de defectuosos es demasiado pequeña para ser calculadapor lo que decimos que el proceso tiene una baja variabilidad
0.00333
LSC carta R D3 LIC carta R4.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 04.51764 0 0
La proporción de defectuosos es demasiado pequeña para ser calculada
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LSC carta RLIC carta RRango medioRango Carta x-R
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2181
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LSC carta xLIC carta xLC Carta xMEDIAS
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LSC carta RLIC carta RRango medioRango Carta x-R
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2181
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2182
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2183
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LSC carta xLIC carta xLC Carta xMEDIAS
0 0 0.99730020393674 1 210 0.1 0.9966187800872 2184.1 2183.120 0.2 0.994373549251788 2184.3 2182.530 0.3 0.989954337001374 2184.6 2183.940 0.4 0.982330046150928 2183.2 2183.450 0.5 0.970060578772435 2184.3 2182.560 0.6 0.951370436956018 2184.2 218170 0.7 0.924318674512519 2184.6 2183.980 0.8 0.887079361002365 2184.1 218190 0.9 0.838310450444301 2183.2 2182.5
100 1 0.777546041389625 2183.9 2183.2110 1.1 0.705513593433533 2183.2 2184.6120 1.2 0.62427136071352 2184.3 2182.5130 1.3 0.537092558872591 2184.1 2183.1140 1.4 0.448087337780567 2184.6 2183.9150 1.5 0.361631234186581 2183.4 2183.9160 1.6 0.281730380584622 2182.5 2183.6170 1.7 0.211474492039695 2182.5 2183.6180 1.8 0.152699911718046 2184.3 2182.5190 1.9 0.105918668766107 2183.9 2184.7200 2 0.0704920839469958 2183.2 2182.5210 2.1 0.0449673040962087 2183.4 2181.9220 2.2 0.0274700555171974 2182.5 2183230 2.3 0.0160583018315475 2182.1 2181.9240 2.4 0.00897705558930412 2183.5 2183.1250 2.5 0.00479642809227934 2182.9 2183.2260 2.6 0.00244816104390278270 2.7 0.00119320799881283280 2.8 0.000555119118725129290 2.9 0.000246439263508351300 3 0.000104367262710537
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Curva CO
Cantidad de desviacines es-tandar
Erro
r tipo
II
3 4 5 MEDIAS DESV.EST C4 A3 LSC de x2184.2 2181 2183.2 2183.12 1.28724512 0.94 0.63829787 2186.058682183.6 2184 7 2182.1 2183.125 1.00788558 2186.058682184.7 2183.2 2184.7 2184.22 0.66105976 2186.058682184.3 2183.1 2183.9 2183.58 0.50695167 2186.058682183.6 2184 7 2182.9 2183.325 0.79320027 2186.058682183.2 2184.6 2185.3 2183.66 1.66973052 2186.058682184.7 2183.1 2184.6 2184.18 0.68337398 2186.058682185 2185.1 2182.1 2183.46 1.82838727 2186.05868
2183.6 2184.7 2182.9 2183.38 0.84083292 2186.058682182.1 2181.7 2183.1 2182.8 0.88881944 2186.058682183.9 2184.7 2183.1 2183.9 0.75166482 2186.058682183.6 2184.7 2182.1 2183.44 1.12160599 2186.058682184.2 2184.3 2185.2 2184.18 0.74632433 2186.058682184.7 2183.1 2184.6 2184.18 0.68337398 2186.058682183.2 2184.3 2185.1 2183.98 0.75960516 2186.058682184.7 2181.7 2183.1 2183.12 1.13225439 2186.058682184.7 2183.1 2184.6 2183.7 0.95131488 2186.058682183.1 2183.9 2182.5 2183.26 0.81731267 2186.058682183.1 2181 2183.2 2183.18 1.37731623 2186.058682183.2 2183.1 2184.2 2183.24 0.61073726 2186.058682183.1 2183.2 2181.9 2182.7 0.73824115 2186.058682181.6 2182.1 2182.6 2182.36 0.53197744 2186.058682183.6 2183.1 2183.4 2182.82 0.77265775 2186.058682183.4 2182.4 2182.9 2183.06 0.43931765 2186.058682183.1 2183.1 2184.1 2183.28 0.47116876 2186.05868
2183.41 0.88289436
0.93924932
β=F(3-1*(0,939224932)^0,5)-F(-3-1*(0,939224932)^0,5)
F1= 2.03085124F2= -3.96914876β=F(2,03)-F(-3,97)=
F(2,03)= 0.97882F(-3,97)= 0.00004β= 0.97878 Probabilidad de no detectar el cambio1-β= 0.02122
σ =
241
432
4133 cc
SScSSSLSC
241
432
4133 cc
SScSSSLIC
nkLFnkLF
β*(1-β)= 0.02076971 Probabilidad de detectar el cambio en la segunda muestra
β+β*(1-β)= 0.99954971 Probabilidad de detectar el cambio antes de la tercera muestra
47.1253534 Se necesitan alrededor de 47 muestras en promedio para detectar el cambioAPL1=1/(1-β)=
LIC de x LC de x B3 B4 LSC de s LIC de s LC de s2180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.882894362180.76132 2183.41 0 2.0888546 1.84423795 0 0.88289436
1 3 5 7 9 11 13 15 17 19 21 23 252178
2179
2180
2181
2182
2183
2184
2185
2186
2187
LSC de xLIC de xLC de xMEDIAS
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LSC de sLIC de sLC de sDESV.EST
Se necesitan alrededor de 47 muestras en promedio para detectar el cambio
1 3 5 7 9 11 13 15 17 19 21 23 252178
2179
2180
2181
2182
2183
2184
2185
2186
2187
LSC de xLIC de xLC de xMEDIAS
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0.2
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LSC de sLIC de sLC de sDESV.EST
n= 5LSC= 508LIC= 507
LSE= 507.9LIE= 507.1
2.5σ=
α=P(X>LSC)+P(X<LIC)
Z=(X-μ)/(σ/n^0,5)
12870 426 14.8009172muestras 30
Xmedia 429 Smedia 14.2
n= 7C4 0.9594 LSC de s 26.7244A2 1.134 LIC de s 1.6756A3 1.182 LC de s 14.2B3 0.118B4 1.882
ΣX = ΣS = σ = μ =
429
Observación Concentración MR d2 D4 D3 LSC de mi LIC de mi1 94.8 1.128 3.267 0 105.100039 93.08996082 98.3 3.5 1.128 3.267 0 105.100039 93.08996083 98.4 0.1 1.128 3.267 0 105.100039 93.08996084 102 3.6 1.128 3.267 0 105.100039 93.08996085 102 0 1.128 3.267 0 105.100039 93.08996086 98.5 3.5 1.128 3.267 0 105.100039 93.08996087 99 0.5 1.128 3.267 0 105.100039 93.08996088 101.1 2.1 1.128 3.267 0 105.100039 93.08996089 98.4 2.7 1.128 3.267 0 105.100039 93.0899608
10 97 1.4 1.128 3.267 0 105.100039 93.089960811 97.7 0.7 1.128 3.267 0 105.100039 93.089960812 100 2.3 1.128 3.267 0 105.100039 93.089960813 101.3 1.3 1.128 3.267 0 105.100039 93.089960814 98.7 2.6 1.128 3.267 0 105.100039 93.089960815 101.4 2.7 1.128 3.267 0 105.100039 93.089960816 97.2 4.2 1.128 3.267 0 105.100039 93.089960817 101 3.8 1.128 3.267 0 105.100039 93.089960818 98.1 2.9 1.128 3.267 0 105.100039 93.089960819 96.7 1.4 1.128 3.267 0 105.100039 93.089960820 100.3 3.6 1.128 3.267 0 105.100039 93.0899608
MR medio 2.25789474 d2= 1.128X media 99.095σ= 2.00167973
LSE= 100LIE= 98
CPk= 0.16652681 CPk es menor a 1,33
Z1= -0.54704056 P(Z<Z1)= 0.42858Z2= 0.45212028 P(Z>Z2)= 0.44038
p= 0.86896Aproximadamente cada 100 horas 87 serán deficientes
LC de mi LSC de MR LIC de MR LC de MR99.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.2578947499.095 7.37654211 0 2.25789474
1 3 5 7 9 11 13 15 17 1980
85
90
95
100
105
110
LSC de miLIC de miLC de miMediciones Individuales
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
LSC de MRLIC de MRLC de MRMR
1 3 5 7 9 11 13 15 17 1980
85
90
95
100
105
110
LSC de miLIC de miLC de miMediciones Individuales
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
LSC de MRLIC de MRLC de MRMR
Número de muestra X R LSC de X LIC de X LC de X LSC de R1 103 4 106.8542 101.5458 104.2 9.7292 102 5 106.8542 101.5458 104.2 9.7293 104 2 106.8542 101.5458 104.2 9.7294 105 11 106.8542 101.5458 104.2 9.7295 104 4 106.8542 101.5458 104.2 9.7296 106 4 106.8542 101.5458 104.2 9.7297 103 7 106.8542 101.5458 104.2 9.7298 105 2 106.8542 101.5458 104.2 9.7299 106 4 106.8542 101.5458 104.2 9.729
10 104 3 106.8542 101.5458 104.2 9.729
X media= 104.2R medio= 4.6A2= 0.577D4= 2.115D3= 0n= 5d2= 2.326
1.97764402
LSE= 107LIE= 99
CPk= 0.6742029 El CPk es menor a 1,33 por lo que habrán muchos defectuosos
Z1= -2.6293913 P(Z<Z1)= 0.00427Z2= 1.41582609 P(Z>Z2)= 0.078535
p= 0.082805p es aproximadamente igual a 0,083Entonces decimos que cada 1000 productos 83 estarán fuera de especificación
Si el tamaño de la muestra cambia a 9 utilizaríamos la carta X-S porque la muestra es mayor aaunque el ejercicio sería más fácil aplicarlo si se dispone del uso de un software ya que esto sería demasiado tedioso para un cálculo manual.
σ=
LIC de R LC de R0 4.60 4.60 4.60 4.60 4.60 4.60 4.60 4.60 4.60 4.6
El CPk es menor a 1,33 por lo que habrán muchos defectuosos
Si el tamaño de la muestra cambia a 9 utilizaríamos la carta X-S porque la muestra es mayor aaunque el ejercicio sería más fácil aplicarlo si se dispone del uso de un software ya que esto
1 2 3 4 5 6 7 8 9 1098
99
100
101
102
103
104
105
106
107
108
LSC de XLIC de XLC de XX
1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
LSC de RLIC de RLC de RR
1 2 3 4 5 6 7 8 9 1098
99
100
101
102
103
104
105
106
107
108
LSC de XLIC de XLC de XX
1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
LSC de RLIC de RLC de RR
