Grficos de Controle Controle deQualidadeProf. MIRKO S. C. GUTIERREZ

Causas de variabilidade dos processosLinha de produo pequenas variabilidades

Ex: saquinhos de leite Mdia = 1000mL, pouca variabilidade

1000mL valor alvo da varivel X (qtde de leite, V)

Tabela 1 Valores da varivel X (volumes dos saquinho de leite de um mesmo lote)Valor alvo

X = 999,8

998,8994,91001,01005,11004,81006,9991,3999,11004,4995,7997,2993,2992,6996,1996,9991,5997,7998,41000,5995,7998,7998,51005,4999,7999,3997,91007,91003,51009,5997,41006,6993,61002,21003,61007,7999,7997,91002,7998,51003,0994,2996,6993,9998,5999,91000,1998,71008,8993,0997,1989,71005,8994,9997,41003,01001,91003,51002,4994,5995,51002,81001,3996,2999,01000,51002,21000,6996,41007,51001,91000,31003,31003,4997,5996,31004,4995,2993,81002,81002,61008,81005,81005,21000,51000,01001,8999,9995,8992,91003,31001,81002,51000,9995,91005,0998,8996,6996,7998,3998,2

Figura 1 Histograma dos valores de X da Tabela 1Densidade de probabilidade normal

Grfico3

1

9

25

32

25

8

0

Freqncia

X

Freqncia

Plan1

998.8994.91001.01005.11004.81006.9991.3999.11004.4995.7

997.2993.2992.6996.1996.9991.5997.7998.41000.5998.5

998.7998.51005.4999.7999.3997.91007.91003.51009.5997.4

1006.6993.61002.21003.61007.7999.7997.91002.7998.51003.0

994.2996.6993.9998.5999.91000.1998.71008.8993.0997.1

989.71005.8994.9997.41003.01001.91003.51002.4994.5995.5

1002.81001.3996.2999.01000.51002.21000.6996.41007.51001.9

1000.31003.31003.4997.5996.31004.4995.2993.81002.81002.6

1008.81005.81005.21000.51000.01001.8999.9995.8992.91003.3

1001.81002.51000.9995.91005.0998.8996.6996.7998.3998.2BlocoFreqncia

9881

9909929

mdia=999.899499625

Desvio=4.32998100032

1002100425

1015.2498762671007.31554453321008.83959389991005.19307493761008.7634691934992.13170329111008.9316711435999.36640622561011.25263795781014.0241866372100610088

1020.5366780191005.04563675151004.01628883791011.17091985881008.14855982551008.3335146681022.61760189661010.30147930371008.83217242311024.642573660210100

1004.95412339461020.16909664031009.87729097481009.48466211211022.88124622081012.901051631013.49647052641008.11900124771015.46661794941009.4509198586

1004.11138560391001.21973814911011.62960532181002.1492963041025.51663444841008.9822754287997.29894286951007.31748175691017.65785443951006.9362397678

1004.7690866975999.06892869851012.52892277791008.69032762941014.57002897751004.9010089041007.23057953821012.28750650421007.35176970721011.6977719497

990.20939528941009.44908267941011.97487679541026.9319537235997.7981463214997.5309367781991.56185029071019.37801814871028.99490598591006.8801967043

1001.99328158281014.38394636151015.27190422871003.18346453951016.4743289841015.28179953111008.340390448997.61479218961018.10221536081016.1074752011

1007.19611878391004.47371010321016.90137312631012.77462277151014.45023033541026.68711774981012.186952771001.14672391441013.83705810241000.1716910244

1014.52471795141008.74798049861012.39097062151012.85665919361011.05043000081007.8244886734999.22106897231026.96658728181022.78156560151018.390579751

998.17602318011001.06154064071014.26141923531010.58834302761009.92809534891011.2898271962994.94640749411007.94616087461002.49650500131002.0194932201

mdia=1009.7

Desvio=8.01

Plan1

Freqncia

X

Freqncia

Plan2

Plan3

Figura 2 Processo isento de causas especiaisProcesso onde atuam somente causas aleatriasDist. Probabilidade estvel (mdia e disperso)Processo sob controle

EMBED Equation.2

EMBED Equation.2

f(X)

EMBED Equation.2

Tempo

f(X)

X

X

X

X

EMBED Equation.2

f(X)

f(X)

_1091263583.unknown

_1106661628.unknown

_1107593979.unknown

_1120116452.unknown

_1120116675.unknown

_1120116678.unknown

_1120116694.unknown

_1120116659.unknown

_1120116445.unknown

_1120116448.unknown

_1120116426.unknown

_1107593201.unknown

_1107593881.unknown

_1107593115.unknown

_1106661617.unknown

_1106661619.unknown

_1106661614.unknown

_1041585545.unknown

_1091263577.unknown

_1091263580.unknown

_1091263565.unknown

_1041585467.unknown

_1041585514.unknown

_1041585413.unknown

Figura 3 Causa especial altera a mdia do processoCausas especiaisMudana da mdia e/ou aumento da disperso

EMBED Equation.2

EMBED Equation.2

EMBED Equation.2

EMBED Equation.2

Tempo

f(X)

X

X

X

X

f(X)

f(X)

f(X)

_1091263745.unknown

_1104064440.unknown

_1120117009.unknown

_1120117022.unknown

_1120117024.unknown

_1120117025.unknown

_1120117992.unknown

_1120117023.unknown

_1120117012.unknown

_1120117002.unknown

_1120117005.unknown

_1106661375.unknown

_1091264137.unknown

_1104064433.unknown

_1104064437.unknown

_1104064406.unknown

_1091263762.unknown

_1091263766.unknown

_1091263760.unknown

_1041585545.unknown

_1091263615.unknown

_1091263668.unknown

_1091263612.unknown

_1041585467.unknown

_1041585514.unknown

_1041585413.unknown

Figura 4 Causa especial altera a mdia e aumenta a variabilidade do processoCausas especiaisMudana da mdia e/ou aumento da disperso

f(X)

EMBED Equation.2

EMBED Equation.2

EMBED Equation.2

EMBED Equation.2

X

X

X

X

Tempo

_1120209110.unknown

_1120209113.unknown

_1120209117.unknown

_1120209106.unknown

Alterao indesejada de presso de operao nas tubulaes do sistema de empacotamento de leiteExemplo causa especial

Tabela 2 Valores da varivel X processo sob influncia de causas especiaisNova mdia

X = 1004,9

1010,2

1002,3

1003,8

1000,2

1008,8

992,1

1008,9

999,4

1011,3

1014,0

1010,5

995,0

994,0

1011,2

1008,1

1008,3

1017,6

1005,3

1003,8

1019,6

995,0

1010,2

999,9

1009,5

1017,9

1012,9

1008,5

1003,1

1010,5

1009,5

994,1

991,2

1001,6

1002,1

1010,5

1009,0

992,3

1002,3

1012,7

1006,9

994,8

989,1

1002,5

1008,7

1014,6

1004,9

1002,2

1007,3

1002,4

1011,7

980,2

999,4

1002,0

1011,9

997,8

997,5

986,6

1014,4

1024,0

1006,9

992,0

1004,4

1005,3

1003,2

1016,5

1015,3

1003,3

992,6

1013,1

1016,1

997,2

994,5

1006,9

1012,8

1014,5

1021,7

1007,2

996,1

1008,8

1000,2

1004,5

998,7

1002,4

1012,9

1011,1

1007,8

994,2

1012,0

1017,8

1018,4

988,2

991,1

1004,3

1010,6

1009,9

1011,3

989,9

1002,9

997,5

1002,0

Figura 5 Histograma dos valores de X da Tabela 2Presena de causas especiais Processo fora de controle

Grfico1

5

12

10

22

19

22

8

2

0

Freqncia

X

Freqncia

Plan1

998.8994.91001.01005.11004.81006.9991.3999.11004.4995.7

997.2993.2992.6996.1996.9991.5997.7998.41000.5998.5

998.7998.51005.4999.7999.3997.91007.91003.51009.5997.4

1006.6993.61002.21003.61007.7999.7997.91002.7998.51003.0

994.2996.6993.9998.5999.91000.1998.71008.8993.0997.1

989.71005.8994.9997.41003.01001.91003.51002.4994.5995.5

1002.81001.3996.2999.01000.51002.21000.6996.41007.51001.9

1000.31003.31003.4997.5996.31004.4995.2993.81002.81002.6

1008.81005.81005.21000.51000.01001.8999.9995.8992.91003.3

1001.81002.51000.9995.91005.0998.8996.6996.7998.3998.2BlocoFreqncia

9881

9909929

mdia=999.899499625

Desvio=4.32998100032

1002100425

1015.2498762671007.31554453321008.83959389991005.19307493761008.7634691934992.13170329111008.9316711435999.36640622561011.25263795781014.0241866372100610088

1020.5366780191005.04563675151004.01628883791011.17091985881008.14855982551008.3335146681022.61760189661010.30147930371008.83217242311024.642573660210100

1004.95412339461020.16909664031009.87729097481009.48466211211022.88124622081012.901051631013.49647052641008.11900124771015.46661794941009.4509198586

1004.11138560391001.21973814911011.62960532181002.1492963041025.51663444841008.9822754287997.29894286951007.31748175691017.65785443951006.9362397678

1004.7690866975999.06892869851012.52892277791008.69032762941014.57002897751004.9010089041007.23057953821012.28750650421007.35176970721011.6977719497

990.20939528941009.44908267941011.97487679541026.9319537235997.7981463214997.5309367781991.56185029071019.37801814871028.99490598591006.8801967043

1001.99328158281014.38394636151015.27190422871003.18346453951016.4743289841015.28179953111008.340390448997.61479218961018.10221536081016.1074752011

1007.19611878391004.47371010321016.90137312631012.77462277151014.45023033541026.68711774981012.186952771001.14672391441013.83705810241000.1716910244

1014.52471795141008.74798049861012.39097062151012.85665919361011.05043000081007.8244886734999.22106897231026.96658728181022.78156560151018.390579751

998.17602318011001.06154064071014.26141923531010.58834302761009.92809534891011.2898271962994.94640749411007.94616087461002.49650500131002.0194932201

mdia=1009.7

Desvio=8.01

1010.2498762671002.31554453321003.83959389991000.19307493761008.7634691934992.13170329111008.9316711435999.36640622561011.25263795781014.0241866372

1010.536678019995.0456367515994.01628883791011.17091985881008.14855982551008.3335146681017.61760189661005.30147930371003.83217242311019.6425736602

994.95412339461010.1690966403999.87729097481009.48466211211017.88124622081012.901051631008.49647052641003.11900124771010.46661794941009.4509198586BlocoFreqncia

994.1113856039991.21973814911001.62960532181002.1492963041010.51663444841008.9822754287992.29894286951002.31748175691012.65785443951006.93623976789905

994.7690866975989.06892869851002.52892277791008.69032762941014.57002897751004.9010089041002.23057953821007.28750650421002.35176970721011.697771949799512

980.2093952894999.44908267931001.97487679541011.9319537235997.7981463214997.5309367781986.56185029071014.37801814871023.99490598591006.8801967043100010

991.99328158281004.38394636151005.27190422871003.18346453951016.4743289841015.28179953111003.340390448992.61479218961013.10221536081016.1074752011990100522

997.1961187839994.47371010321006.90137312631012.77462277151014.45023033541021.68711774981007.18695277996.14672391441008.83705810241000.1716910244995101019

1004.5247179514998.74798049861002.39097062151012.85665919361011.05043000081007.8244886734994.22106897231011.96658728181017.78156560151018.3905797511000101522

988.1760231801991.06154064071004.26141923531010.58834302761009.92809534891011.2898271962989.94640749411002.9461608746997.49650500131002.0194932201100510208

101010252

10150

1020

1025

Plan1

Freqncia

X

Freqncia

Plan2

Freqncia

X

Freqncia

Plan3

Monitoramento dos processos por grficos de controleProcesso devem sempre ser monitorados para deteco da presena de causas especiais.Exemplo leite: monitoramento constante ocorrncia de excessos (sacos estourados, manuseio transporte), falta (multas por volume inferior)Grficos de controlePrincipal ferramenta utilizada para monitorar os processos e sinalizar a presena de causas especiais

Monitoramento dos processos por grficos de controleOs grficos de controle servem para monitorar processos cuja caracterstica de qualidade de interesse X uma grandeza mensurvel.

Volume do leite em saquinhoTeor de Vit. C polpa de frutasPeso unitrio de salgadinhos

Monitoramento dos processos por grficos de controleMonitoramento feito atravs da anlise peridica de amostras.Ex: a cada intervalo de tempo h retira-se uma amostra de n itens para anliseSaquinhos de leiteh = 30 minn = 5

Cada amostra calcula-se mdia amostral (X) e amplitude amostral ( R)Valores so graficados

Monitoramento dos processos por grficos de controleTabela 3 Valores de Xij, Xi e Ri

Amostra (i)Elemento (j) da amostra (i)11001,71004,01004,8996,31004,31002,28,42999,71000,31003,2993,9998,9999,29,23990,91004,01003,01004,01002,01000,813,141000,71007,3998,1995,5994,9999,312,451000,7998,3998,9997,81001,9999,54,16998,6993,71002,8995,5994,19979,171002,71010,5990,5992,51003,0999,819,981000,41004,01003,0999,8997,21000,96,89999,91005,6996,11005,5998,110019,610994,3993,21005,8996,4996,7997,312,611997,4997,1998,0995,61005,8998,810,1121003,5992,31000,81000,01001,2999,611,2131003,41004,61001,3997,31005,81002,58,514997,71004,6997,01001,01003,91000,87,6151012,01007,01002,71008,01005,01006,99,3

Monitoramento dos processos por grficos de controleFigura 6 Grficos de controle de X e R

EMBED Equation.3

_1106669470.unknown

_1120211317.unknown

_1120211483.xls

Grfico1

099410001006

1002.2299410001006

999.299410001006

1000.7899410001006

999.399410001006

999.5299410001006

996.9499410001006

999.8499410001006

1000.8899410001006

1001.0499410001006

997.2899410001006

998.7899410001006

999.5699410001006

1002.4899410001006

1000.8499410001006

1006.9499410001006

1699410001006

1799410001006

1899410001006

1999410001006

2099410001006

2199410001006

LSC

LIC

LM

Nmero da amostra

Plan1

1001.710041004.8996.31004.30994100010068.5

999.71000.31003.2993.9998.911002.22994100010069.3

990.910041003100410022999.29941000100613.1

1000.71007.3998.1995.5994.931000.789941000100612.4

1000.7998.3998.9997.81001.94999.3994100010064.1

998.6993.71002.8995.5994.15999.52994100010069.1

1002.71010.5990.5992.510036996.949941000100620

1000.410041003999.8997.27999.84994100010066.8

999.91005.6996.11005.5998.181000.88994100010069.5

994.3993.21005.8996.4996.791001.049941000100612.6

997.4997.1998995.61005.810997.289941000100610.2

1003.5992.31000.810001001.211998.789941000100611.2

1003.41004.61001.3997.31005.812999.56994100010068.5

997.71004.699710011003.9131002.48994100010067.6

101210071002.710081005141000.84994100010069.3

151006.9499410001006

1699410001006

1799410001006

1899410001006

1999410001006

2099410001006

2199410001006

Plan1

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

LSC

LIC

LM

Nmero da amostra

Xbarra

Plan2

Plan3

_1120211635.xls

Grfico2

8.510.522.21

9.310.522.21

13.110.522.21

12.410.522.21

4.110.522.21

9.110.522.21

2010.522.21

6.810.522.21

9.510.522.21

12.610.522.21

10.210.522.21

11.210.522.21

8.510.522.21

7.610.522.21

9.310.522.21

1510.522.21

1610.522.21

1710.522.21

1810.522.21

1910.522.21

2010.522.21

2110.522.21

LSC

LM

LIC=0

Nmero da amostra

R

Plan1

1001.710041004.8996.31004.309941000100608.510.522.21

999.71000.31003.2993.9998.911002.229941000100619.310.522.21

990.910041003100410022999.299410001006213.110.522.21

1000.71007.3998.1995.5994.931000.7899410001006312.410.522.21

1000.7998.3998.9997.81001.94999.39941000100644.110.522.21

998.6993.71002.8995.5994.15999.529941000100659.110.522.21

1002.71010.5990.5992.510036996.949941000100662010.522.21

1000.410041003999.8997.27999.849941000100676.810.522.21

999.91005.6996.11005.5998.181000.889941000100689.510.522.21

994.3993.21005.8996.4996.791001.0499410001006912.610.522.21

997.4997.1998995.61005.810997.28994100010061010.210.522.21

1003.5992.31000.810001001.211998.78994100010061111.210.522.21

1003.41004.61001.3997.31005.812999.5699410001006128.510.522.21

997.71004.699710011003.9131002.4899410001006137.610.522.21

101210071002.710081005141000.8499410001006149.310.522.21

151006.94994100010061510.522.21

16994100010061610.522.21

17994100010061710.522.21

18994100010061810.522.21

19994100010061910.522.21

20994100010062010.522.21

21994100010062110.522.21

Plan1

LSC

LIC

LM

Nmero da amostra

Xbarra

Plan2

LSC

LM

LIC=0

Nmero da amostra

Amplitude R

Plan3

_1106669495.xls

Grfico1

099410001006

1002.2299410001006

999.299410001006

1000.7899410001006

999.399410001006

999.5299410001006

996.9499410001006

999.8499410001006

1000.8899410001006

1001.0499410001006

997.2899410001006

998.7899410001006

999.5699410001006

1002.4899410001006

1000.8499410001006

1006.9499410001006

1699410001006

1799410001006

1899410001006

1999410001006

2099410001006

2199410001006

LSC

LIC

LM

Nmero da amostra

Plan1

1001.710041004.8996.31004.30994100010068.5

999.71000.31003.2993.9998.911002.22994100010069.3

990.910041003100410022999.29941000100613.1

1000.71007.3998.1995.5994.931000.789941000100612.4

1000.7998.3998.9997.81001.94999.3994100010064.1

998.6993.71002.8995.5994.15999.52994100010069.1

1002.71010.5990.5992.510036996.949941000100620

1000.410041003999.8997.27999.84994100010066.8

999.91005.6996.11005.5998.181000.88994100010069.5

994.3993.21005.8996.4996.791001.049941000100612.6

997.4997.1998995.61005.810997.289941000100610.2

1003.5992.31000.810001001.211998.789941000100611.2

1003.41004.61001.3997.31005.812999.56994100010068.5

997.71004.699710011003.9131002.48994100010067.6

101210071002.710081005141000.84994100010069.3

151006.9499410001006

1699410001006

1799410001006

1899410001006

1999410001006

2099410001006

2199410001006

Plan1

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

LSC

LIC

LM

Nmero da amostra

Xbarra

Plan2

Plan3

_1106662322.xls

Grfico2

8.510.522.21

9.310.522.21

13.110.522.21

12.410.522.21

4.110.522.21

9.110.522.21

2010.522.21

6.810.522.21

9.510.522.21

12.610.522.21

10.210.522.21

11.210.522.21

8.510.522.21

7.610.522.21

9.310.522.21

1510.522.21

1610.522.21

1710.522.21

1810.522.21

1910.522.21

2010.522.21

2110.522.21

LSC

LM

LIC=0

Nmero da amostra

R

Plan1

1001.710041004.8996.31004.309941000100608.510.522.21

999.71000.31003.2993.9998.911002.229941000100619.310.522.21

990.910041003100410022999.299410001006213.110.522.21

1000.71007.3998.1995.5994.931000.7899410001006312.410.522.21

1000.7998.3998.9997.81001.94999.39941000100644.110.522.21

998.6993.71002.8995.5994.15999.529941000100659.110.522.21

1002.71010.5990.5992.510036996.949941000100662010.522.21

1000.410041003999.8997.27999.849941000100676.810.522.21

999.91005.6996.11005.5998.181000.889941000100689.510.522.21

994.3993.21005.8996.4996.791001.0499410001006912.610.522.21

997.4997.1998995.61005.810997.28994100010061010.210.522.21

1003.5992.31000.810001001.211998.78994100010061111.210.522.21

1003.41004.61001.3997.31005.812999.5699410001006128.510.522.21

997.71004.699710011003.9131002.4899410001006137.610.522.21

101210071002.710081005141000.8499410001006149.310.522.21

151006.94994100010061510.522.21

16994100010061610.522.21

17994100010061710.522.21

18994100010061810.522.21

19994100010061910.522.21

20994100010062010.522.21

21994100010062110.522.21

Plan1

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

LSC

LIC

LM

Nmero da amostra

Xbarra

Plan2

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

LSC

LM

LIC=0

Nmero da amostra

Amplitude R

Plan3

Condies para construo e uso dos grficos de controleComo so determinados os limites dos grficos de controle?LSC e LIC so determinados com base na mdia e no desvio-padro da distribuio da varivel X quando o processo est isento de causas especiais.A mdia deve sempre coincidir com o valor alvo especificado (Ex: valor alvo leite em saquinho o valor nominal: 1000mL)Estimar o desvio-padro do processo

Estimar a mdia do processo isento de causas especiais

Etapa inicial: conhecendo, estabilizando e ajustando o processoPara monitorar o processo necessrio conhecer bem o processo

Conhecimento dos fatores que afetam as caractersticas de qualidade X

Etapa rdua grandes melhorias do processo

Etapa inicial: conhecendo, estabilizando e ajustando o processoFigura 7 Volume dos saquinhos de leite (processo instvel)

Grfico9

0985101510001

100098510151000

100198510151000

100298510151000

100698510151000

100398510151000

101298510151000

100498510151000

102098510151000

99898510151000

99798510151000

99898510151000

99798510151000

99698510151000

99898510151000

99698510151000

99098510151000

98298510151000

100098510151000

100198510151000

100398510151000

100298510151000

100598510151000

1020.398510151000

100898510151000

101798510151000

101298510151000

99898510151000

100298510151000

99798510151000

100398510151000

100098510151000

99598510151000

100698510151000

99998510151000

99598510151000

99098510151000

98898510151000

98398510151000

98898510151000

98598510151000

Limites de especificao

Limites de especificao

Nmero das observaes

X (mL)

Plan1

098510151000

1100098510151000

2100198510151000

3100298510151000

4100698510151000

5100398510151000

6101298510151000

7100498510151000

8102098510151000

999898510151000

1099798510151000

1199898510151000

1299798510151000

1399698510151000

1499898510151000

1599698510151000

1699098510151000

1798298510151000

18100098510151000

19100198510151000

20100398510151000

21100298510151000

22100598510151000

231020.398510151000

24100898510151000

25101798510151000

26101298510151000

2799898510151000

28100298510151000

2999798510151000

30100398510151000

31100098510151000

3299598510151000

33100698510151000

3499998510151000

3599598510151000

3699098510151000

3798898510151000

3898398510151000

3998898510151000

4098598510151000

Plan1

1

Limites de especificao

Limites de especificao

Nmero das observaes

X (ml)

Plan2

Plan3

Etapa inicial: conhecendo, estabilizando e ajustando o processoFigura 8 Distribuio do volume dos saquinhos de leite ao longo do tempo (processo instvel)

EMBED Equation.2

EMBED Equation.2

EMBED Equation.2

EMBED Equation.2

Tempo

f(X)

X

EMBED Equation.2

X

X

X

_1089555979.unknown

_1089556108.unknown

_1120212854.unknown

_1120213463.unknown

_1120213466.unknown

_1120213473.unknown

_1120213452.unknown

_1120212803.unknown

_1120212850.unknown

_1120212764.unknown

_1089556101.unknown

_1089556105.unknown

_1089556019.unknown

_1041585545.unknown

_1084182631.unknown

_1084192525.unknown

_1084176721.unknown

_1041585467.unknown

_1041585514.unknown

_1041585413.unknown

Etapa inicial: conhecendo, estabilizando e ajustando o processoAntes de construir os grficos preciso identificar e eliminar as causas especiais que esto fazendo o processo sair do estado de controle estatstico Pessoas diretamente envolvidas no processoColeta de informaes qualitativas e quantitativas (ex: viscosidade do leite, fornecedor, presso da tubulao, T, n do bocal, etc...)

Etapa inicial: conhecendo, estabilizando e ajustando o processoFigura 9 Diagrama de causa e efeito (causas especiais que afetam o volume de leite)

_1120213766.doc

ENTUPIMENTO DO BOCAL

ACMULO DE GORDURA

LQUIDO

IMPUREZAS

TUBULAO

VOLUME

DE

LEITE

Etapa inicial: conhecendo, estabilizando e ajustando o processoDiagnstico das causas especiais

Eliminao das causas especiais

Tabela 4: Causas Especiais e Medidas Corretivas/Preventivas

Causa especial

Medida corretiva/preventiva

Gordura na tubulao

Limpeza mensal da tubulao

Entupimento do bocal

Troca semanal do bocal

Impurezas no leite

Utilizao de filtros

Etapa inicial: conhecendo, estabilizando e ajustando o processoFigura 9 Volume dos saquinhos de leite (processo estvel e ajustado)

Grfico1

098510151000

998.011139723598510151000

1001.323787728398510151000

997.6585604698510151000

999.296114765598510151000

997.898510151000

1001.324115146498510151000

1007.074231689398510151000

994.580030033898510151000

993.37356712298510151000

1000.325781002298510151000

998.152579792198510151000

1002.185215635198510151000

998.562534528998510151000

997.456870914998510151000

1001.252565198298510151000

1005.056526788498510151000

991.598510151000

1004.308349161998510151000

1001.35550635698510151000

996.460564943898510151000

1003.753648343398510151000

1002.166771082698510151000

993.961955624498510151000

998.424236764598510151000

1004.080857252198510151000

997.898510151000

1001.51970198298510151000

1003.345339791898510151000

997.844206518598510151000

1000.909071786798510151000

1007.354210538398510151000

1002.165706973898510151000

999.102856236398510151000

999.302954165698510151000

1002.81935172198510151000

1002.425122147598510151000

995.08519977198510151000

995.935586412198510151000

1003.319792085798510151000

1009.477080311698510151000

especificaes

Nmero das observaes

X (mL)

Plan1

098510151000

1100098510151000

2100198510151000

3100298510151000

4100698510151000

5100398510151000

6101298510151000

7100498510151000

8102098510151000

999898510151000

1099798510151000

1199898510151000

1299798510151000

1399698510151000

1499898510151000

1599698510151000

1699098510151000

1798298510151000

18100098510151000

19100198510151000

20100398510151000

21100298510151000

22100598510151000

231020.398510151000

24100898510151000

25101798510151000

26101298510151000

2799898510151000

28100298510151000

2999798510151000

30100398510151000

31100098510151000

3299598510151000

33100698510151000

3499998510151000

3599598510151000

3699098510151000

3798898510151000

3898398510151000

3998898510151000

4098598510151000

Plan1

1

Limites de especificao

Limites de especificao

Nmero das observaes

X (ml)

Plan2

098510151000

1998.011139723598510151000

21001.323787728398510151000

3997.6585604698510151000

4999.296114765598510151000

5997.898510151000

61001.324115146498510151000

71007.074231689398510151000

8994.580030033898510151000

9993.37356712298510151000

101000.325781002298510151000

11998.152579792198510151000

121002.185215635198510151000

13998.562534528998510151000

14997.456870914998510151000

151001.252565198298510151000

161005.056526788498510151000

17991.598510151000

181004.308349161998510151000

191001.35550635698510151000

20996.460564943898510151000

211003.753648343398510151000

221002.166771082698510151000

23993.961955624498510151000

24998.424236764598510151000

251004.080857252198510151000

26997.898510151000

271001.51970198298510151000

281003.345339791898510151000

29997.844206518598510151000

301000.909071786798510151000

311007.354210538398510151000

321002.165706973898510151000

33999.102856236398510151000

34999.302954165698510151000

351002.81935172198510151000

361002.425122147598510151000

37995.08519977198510151000

38995.935586412198510151000

391003.319792085798510151000

401009.477080311698510151000

Plan2

especificaes

Nmero das observaes

X (ml)

Plan3

Processo estvel e sob controleConstruo dos grficos de controle para monitoramento do processo (X e R)Mdia () e desvio padro () do processo desconhecidosEstimativaAmostra de 100 saquinhos

Grfico3

1

9

25

32

25

8

0

Freqncia

X

Freqncia

Plan1

998.8994.91001.01005.11004.81006.9991.3999.11004.4995.7

997.2993.2992.6996.1996.9991.5997.7998.41000.5998.5

998.7998.51005.4999.7999.3997.91007.91003.51009.5997.4

1006.6993.61002.21003.61007.7999.7997.91002.7998.51003.0

994.2996.6993.9998.5999.91000.1998.71008.8993.0997.1

989.71005.8994.9997.41003.01001.91003.51002.4994.5995.5

1002.81001.3996.2999.01000.51002.21000.6996.41007.51001.9

1000.31003.31003.4997.5996.31004.4995.2993.81002.81002.6

1008.81005.81005.21000.51000.01001.8999.9995.8992.91003.3

1001.81002.51000.9995.91005.0998.8996.6996.7998.3998.2BlocoFreqncia

9881

9909929

mdia=999.899499625

Desvio=4.32998100032

1002100425

1015.2498762671007.31554453321008.83959389991005.19307493761008.7634691934992.13170329111008.9316711435999.36640622561011.25263795781014.0241866372100610088

1020.5366780191005.04563675151004.01628883791011.17091985881008.14855982551008.3335146681022.61760189661010.30147930371008.83217242311024.642573660210100

1004.95412339461020.16909664031009.87729097481009.48466211211022.88124622081012.901051631013.49647052641008.11900124771015.46661794941009.4509198586

1004.11138560391001.21973814911011.62960532181002.1492963041025.51663444841008.9822754287997.29894286951007.31748175691017.65785443951006.9362397678

1004.7690866975999.06892869851012.52892277791008.69032762941014.57002897751004.9010089041007.23057953821012.28750650421007.35176970721011.6977719497

990.20939528941009.44908267941011.97487679541026.9319537235997.7981463214997.5309367781991.56185029071019.37801814871028.99490598591006.8801967043

1001.99328158281014.38394636151015.27190422871003.18346453951016.4743289841015.28179953111008.340390448997.61479218961018.10221536081016.1074752011

1007.19611878391004.47371010321016.90137312631012.77462277151014.45023033541026.68711774981012.186952771001.14672391441013.83705810241000.1716910244

1014.52471795141008.74798049861012.39097062151012.85665919361011.05043000081007.8244886734999.22106897231026.96658728181022.78156560151018.390579751

998.17602318011001.06154064071014.26141923531010.58834302761009.92809534891011.2898271962994.94640749411007.94616087461002.49650500131002.0194932201

mdia=1009.7

Desvio=8.01

Plan1

Freqncia

X

Freqncia

Plan2

Plan3

Se houvesse certeza absoluta que o processo permaneceu sob controle em todo intervalo de tempo em que foram retiradas as amostras, poderia ser adotado:X como estimativa de S2 como estimativa de 2Ser que durante a produo dos itens dos quais se obtiveram os valores da cq X, o processo realmente permaneceu isento de causas especiais?

Subgrupos RacionaisRetirada de pequenas amostras a intervalos de tempo regulares

Ao invs de retirar 100 saquinhos de uma s vez, retirada de amostras menores, distanciadas de tempo.

Ex: Amostras de 4 ou 5 unidades a cada hora

Cada amostra subgrupo racionalCaso ocorra perturbaes no processo em consequncia de alguma causa especial, dificilmente ela ocorrer durante a formao de um subgrupo minimiza-se a probabilidade de que uma amostra seja formada por elementos de populaes

Distribuio Normal Padro

Verificao de Produto Fabricado sob ControleX=valor da cq, determinado na amostra = valor mdio da cq, especificado na norma ou padro de qualidade = valor do desvio padro da cq, especificado na norma ou padro de qualidade do produto.f = frequncia com que o valor de x aparece nas diversas amostras colhidas na partida ou lote do produto avaliado.

Verificao de Produto Fabricado sob ControleNas condies extremas, para o produto fabricado sob controle:

No mximo: x- = 3

No mnimo: f =1,

Ficando z = (3 / ) . 1 = 3

Logo:

Para -3 x +3 fabricao do produto sob controlePara -3 x +3 fabricao do produto fora controle

ExemploUm suco de abacaxi tem como padro de acidez (expresso em g/L de cido ctrico) os valores: = 5,6 e = 0,1. Cinco amostras retiradas de um mesmo lote apresentaram o valor x = 5,75.

Verificar se o suco foi fabricado sob controle R = No

b) Quantas amostras poderiam apresentar o valor encontrado para que o processo de fabricao fosse considerado sob controle? R = 4

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