capacidaddeprocesos-140424114529-phpapp02.pptx

Capacidad de procesos

1Laura Marcela Bernal lmbernals@ut.edu.co

REPASO GRAFICOS DE CONTROLControl Estadstico de ProcesosEl control estadstico de procesos (CEP) es una poderosa coleccin de herramientas para la solucin de problemas usadas para lograr la estabilidad del proceso y la mejora de la capacidad a travs de la reduccin de la variabilidad.

Objetivo

Reducir la variabilidadAumentar su capacidad para cumplir estndares.

Esto se logra monitoreando y controlando el proceso a travs del tiempo. Una caracterstica importante es que el SPC es reactivo y no correctivo.

Laura Marcela Bernal lmbernals@ut.edu.co

Control Estadstico de ProcesosLaura Marcela Bernal lmbernals@ut.edu.co

Son pocas, pero cuando aparecenproducen variaciones importantesAparecen espordicamenteFciles de identificar (y, por tanto,fciles de eliminar)No previsibles estadsticamente

Son muchas, cada una producepequeas variacionesSon parte permanente del procesoDifciles de eliminar Previsible estadsticamente

Control Estadstico de Procesos, VariabilidadLaura Marcela Bernal lmbernals@ut.edu.co

Vibraciones de la mquina Fluctuaciones de temperatura Fluctuaciones en los materiales Variaciones humanas en el controlControl Estadstico de ProcesosCausas comunesde variacinLaura Marcela Bernal lmbernals@ut.edu.co

Control Estadstico de Procesos, VariabilidadLaura Marcela Bernal lmbernals@ut.edu.co

Variabilidad

Grficos de ControlUsoVariables Continuas: Temperatura horno PesosVariables discretas: # de individuos con un atributo Proporcin de individuos con un atributoNmero de veces que ocurre un fenmeno por unidad de medidaIdem grafico C, pero n no constanteLaura Marcela Bernal lmbernals@ut.edu.co

Grficos de Control, Bandas de VariacinLaura Marcela Bernal lmbernals@ut.edu.co

Grficos de Control, AlertasLaura Marcela Bernal lmbernals@ut.edu.co

Grficos de Control, Alertas

17Primero estable y luego capaz Laura Marcela Bernal lmarcela@yahoo.com

Capacidad de un proceso: Laura Marcela Bernal lmarcela@yahoo.com

Consiste en conocer la amplitud de la variacin natural del proceso para una caracterstica de calidad dada, ya que esto permitir saber en que medida tal caracterstica es satisfactoria (cumple especificaciones)Porque medir la capacidad de un proceso: Laura Marcela Bernal lmarcela@yahoo.com

El nuevo modelo de aceptacin de proceso:La variacin resulta en prdida financiera.

21Capacidad de Proceso La principal razn para cuantificar la capacidad de un proceso es la de calcular la habilidad del proceso para mantener dentro de las especificaciones del producto. Para procesos que estn bajo control estadstico, una comparacin de la variacin de 6 con los lmites de especificaciones permite un fcil clculo del porcentaje de defectuosos mediante la tolerancia estadstica convencional.

Como ayuda a la prediccin: Es este proceso capaz de cumplir permanentemente con las especificaciones del producto?

Como ayuda al anlisis: Por qu este proceso no cumple con las especificaciones establecidas?Laura Marcela Bernal lmarcela@yahoo.com

21ndice de capacidad potencial del proceso

Laura Marcela Bernal lmarcela@yahoo.com

Capacidad de Proceso: CpVariacin toleradaVariacin realLaura Marcela Bernal lmbernals@ut.edu.co

Capacidad de Proceso: Cp

Capacidad de Procesos, Indice CpLaura Marcela Bernal lmarcela@yahoo.com

Capacidad de Proceso: CpValor ndice CpCategora del procesoInterpretacinCp 2Clase mundialSe tiene calidad seis sigmaCp > 1.331Adecuado

1 < Cp < 1.332Parcialmente adecuado, requiere control estricto

0.67 < Cp < 13No adecuado para el trabajo. Es necesario anlisis del proceso. Requiere modificaciones serias para alcanzar calidad satisfactoriaCp < 0.674No adecuado para el trabajo. Requiere modificaciones muy seriasTABLA 5.1

Distribucin normalLaura Marcela Bernal lmarcela@yahoo.com

Ley normalLaura Marcela Bernal lmarcela@yahoo.com

Prueba de normalidadpermite determinar si los datos provienen de una distribucin normalSu importancia radica en la metodologa de inferencia estadsticaAlgunas pruebas de normalidad:Kolmogorov-smirnovAnderson-darlingJi-cuadradoShapiro-wilks

Prueba de normalidadLaura Marcela Bernal lmarcela@yahoo.com

Datos taller No 1 grupo del viernesCaso: Concentracin Nitrito de sodio Datos taller No 1 grupo del juevesCaso: Peso costales con arena

ndice Cr: Razn de capacidad potencialRepresenta la proporcin de la banda de especificaciones que es cubierta por el proceso

Ej: Cr: 0.90 indica que la variacin del proceso potencialmente cubre el 90% de la banda del especificaciones

ndice Cpi, Cps: ndice de capacidad para la especificacin inferior y superior Laura Marcela Bernal lmarcela@yahoo.com

Estos ndices a diferencia de Cp y Cr si toman en cuenta el centrado del proceso.Para interpretar estos ndices se usa la tabla 5.1; no obstante para considerar que el proceso es adecuado el valor de Cpi y Cps debe ser mayor de 1.25 en lugar de 1.33

ndice Cpk: ndice de capacidad real del procesoEs considerada una versin corregida de CpToma en cuenta el centrado del procesoSi Cpk es < 1 el proceso no cumple con por lo menos una de las especificacionesCpk > 1,25 es satisfactorio

Capacidad de Procesos, Indice CpkLaura Marcela Bernal lmarcela@yahoo.com

ndice Cpk: interpretacin

ndice K: ndice de centrado de procesoIndicador de que tan centrada est la distribucin de un proceso con respecto a las especificaciones de una caracterstica dada

Indica el grado porcentual de desviacinSi el signo de K es positivo significa que la media del proceso es mayor que el valor nominalValores de K menores a 20% en trminos absolutos se consideran como aceptables El valor N es la calidad objetivo y ptima, cualquier desviacin respecto a este valor lleva a un detrimento de la calidad

La mejora de un proceso debe orientarse a reducir su variabilidad alrededor del valor N y no solo a cumplir con las especificaciones

Cpm < 1: el proceso no cumple especificaciones ya sea por centrado o variabilidad

Cpm > 1: el proceso cumple especificaciones y la media del proceso esta dentro de la tercera parte central de la banda de especificaciones

Cpm > 1.33: el proceso cumple especificaciones pero ademas la media del proceso esta dentro de la quinta parte del rango central de especificaciones

ndice Cpm: ndice de TaguchiLaura Marcela Bernal lmarcela@yahoo.com

40Capacidad de Proceso

Anlisis de capacidad de proceso por Minitab

En un modelo de llanta para automvil la longitud de cada una debe ser 780 mm con una tolerancia de +/-10 mm. Para detectar la posible presencia de causas especiales de variacin y en general para monitorear el correcto funcionamiento del proceso de corte, cada hora se toman cinco capas y se miden. De acuerdo a las mediciones realizadas en el ltimo mes el proceso ha estado trabajando de forma estable, se tiene que : 783 y : 3Analizar el proceso de acuerdo a:Lmites realesIndices de capacidad Cp, Cpk, Cps, Cpi, K, CpmLaura Marcela Bernal lmarcela@yahoo.com

Ejercicio 1Laura Marcela Bernal lmarcela@yahoo.com

Ejercicio 1

Grafica del ejercicio 1En las pantas de tratamiento de aguas residuales una forma de medir la eficacia del tratamiento biolgico aerobio de clarificacin secundaria y de la filtracin, es mediante los slidos suspendidos totales SST. En una planta en particular, se tiene que los SST no deben ser mayores a ES=30 para considerar que el proceso fue satisfactorio.Por lo tanto, esta variable es de tipo entre mas pequea, mejor De acuerdo con datos histricos se tiene que la media y la desviacin estndar de SST son 10.2 y 5.1 respectivamente. Se considera que el proceso es capaz?

Ejercicio 2Respuesta:En este caso no es posible calcular el indice Cp ya que solo se cuenta con la especificacion superior. Por lo tanto se hace el calculo para determinar Cps

Cps = 1.29

De acuerdo con la tabla 5.2 tiene un porcentaje fuera de especificaciones cercano a 0,0048% que se considera adecuado a menos que se tenga una exigencia aun mayor.

Ejercicio 2Los siguientes datos representan las mediciones de viscosidad de los ltimos tres meses de un producto lcteo. El objetivo es tener viscosidad de 80 10 cpsLos datos se adjuntan en excelConstruya una grafica de capacidad de este proceso (histograma con tolerancias) y de una primera opinin sobre su capacidad Calcule la media y desviacin estndar y estime los indices de Cp, Cpk, Cpm y K e interpretelos.Con base en la tabla 5.2 estime el porcentaje fuera de especificaciones

Ejercicio 3

El peso neto (onzas) de un producto blanqueador en polvo va a monitorearse con cartas de control X-R utilizando un tamao de muestra n=5 Los datos de 20 muestras preliminares se adjuntan en archivo de excel

Establecer las cartas de control X-R usando los datos adjuntos. El proceso manifiesta control estadistico?El peso de llenado parece seguir una distribucion normal?Si las especificaciones son 16.2 0.5 que conclusiones saca de la capacidad del proceso?

Ejercicio 4

Recoger una muestra representativa de al menos 50 unidades (seguidas para estudios a corto plazo y espaciadas para estudios a largo plazo)

2. Chequear que los datos no evidencien un proceso o mquina fuera de control estadstico

3. Chequear que los datos no evidencien una distribucin no normal

4. Realizar el estudioCapacidad de Procesos, EtapasLaura Marcela Bernal lmarcela@yahoo.com

LIELIELSELSELaura Marcela Bernal lmarcela@yahoo.com

5253LIELIELSELSELaura Marcela Bernal lmarcela@yahoo.com

53Ejemplos de defectos segn el nivel SigmaNivel 3 sigma

5.000 cirugas sin xito en la semana.2 aterrizajes forzosos al da en los principales aeropuertos200.000 recetas medicas erradas al ao

Nivel 6 sigma

1,7 cirugas sin xito a la semana1 aterrizaje forzoso cada 5 aos68 recetas erradas al ao

Estado de un proceso: Capacidad y estabilidadLaura Marcela Bernal lmarcela@yahoo.com

Estado de un proceso: Capacidad y estabilidadCapacidad para cumplir especificaciones Cpk2,5AB21,51CD0,50-0,5-1036912151821Estabilidad de la variabilidad a traves del tiempo StLaura Marcela Bernal lmarcela@yahoo.com

Estado de un proceso: Capacidad y estabilidadEl proceso es estable? Herramientas: Cartas de control e indice de inestabilidadSINOEl proceso es capaz? Herramientas: estudios de capacidad e indices Cp y CpkSIAB estable y capazcapaz pero inestableNOC D estable y incapazincapaze inestableLaura Marcela Bernal lmarcela@yahoo.com

Estado de un proceso: Capacidad y estabilidadDelimitar datos historicos Recoger datos que reflejen la realidad del proceso, en lapso de tiempo considerable donde no se hayan realizado grandes modificaciones al proceso procesos masivos: 3-4 semanas- 300 a 500 puntos procesos lentos: 100 a 200 puntos Analizar estabilidad analizar los datos historicos: comportamiento de los puntos.patrones especiales de variacion, y calcular St. Si da S alto (ej >10% ) alta inestabilidad. Si St=1-3 Proceso estable Estudiar la capacidad Con los datos historicos hacer analisis de SCP incluye Cp Cpk histograma identifica si hay problemas de capacidad por centrado y/o exceso de variacion

Capacidad y estabilidad Proceso tipo D (inestable e incapaz)Laura Marcela Bernal lmarcela@yahoo.com

Capacidad y estabilidad Proceso tipo C (estable e incapaz)Laura Marcela Bernal lmarcela@yahoo.com

Capacidad y estabilidad Proceso tipo B (inestable pero capaz)Similar el ejercicio 1 en otro modelo de llantas para automovil se tiene que la longitud de capa debe ser de 550 mm con una tolerancia de 8 mm. Para detectar la posible presencia de causas especiales de variacion y en general para monitorear el correcto funcionamiento del proceso de corte, cada hora, se toman 5 capas y se miden.

Cual es el comportamiento de la tendencia central y variabilidad de los datos?Establecer si el proceso manifiesta control estadistico?Cuales son los limites reales del proceso?Que conclusiones saca de la capacidad del proceso?

Ejercicio 5

Grfico10.00000002710.00000002990.0000000330.00000003630.000000040.0000000440.00000004840.00000005330.00000005860.00000006440.00000007080.00000007780.00000008540.00000009380.0000001030.00000011310.00000012410.00000013620.00000014930.00000016380.00000017950.00000019670.00000021550.0000002360.00000025840.00000028290.00000030960.00000033870.00000037040.0000004050.00000044270.00000048380.00000052860.00000057730.00000063030.00000068810.00000075090.00000081920.00000089350.00000097430.0000010620.00000115740.00000126090.00000137340.00000149540.00000162780.00000177150.00000192740.00000209630.00000227940.00000247790.00000269280.00000292560.00000317770.00000345050.00000374560.00000406490.00000441020.00000478350.0000051870.00000562290.00000609370.00000660220.0000071510.00000774340.00000838250.00000907180.00000981510.00001061640.00001147980.00001241010.0000134120.00001449070.00001565190.00001690140.00001824560.00001969130.00002124560.00002291620.00002471130.00002663960.00002871040.00003093360.00003331970.00003587980.0000386260.00004157080.00004472770.00004811090.00005173570.00005561810.00005977530.00006422530.00006898750.00007408220.00007953110.0000853570.00009158420.00009823840.00010534690.00011293830.00012104320.00012969370.00013892380.00014876940.00015926860.00017046140.00018239010.00019509930.00020863620.00022305040.00023839420.00025472270.0002720940.00029056930.00031021290.00033109250.00035327920.00037684810.00040187760.00042845060.00045665370.00048657820.00051831960.00055197830.00058765950.00062547340.00066553560.00070796710.00075289470.00080045110.0008507750.00090401150.00096031250.00101983660.00108274930.00114922390.00121944080.00129358850.00137186370.00145447120.00154162460.00163354660.00173046880.00183263250.00194028880.00205369860.00217313350.00229887560.0024312180.0025704650.00271693250.00287094820.00303285220.00320299660.00338174680.00356948080.00376659020.00397348030.00419057020.00441829330.00465709740.00490744520.00516981450.00544469840.00573260550.00603406040.00634960350.00667979180.00702519860.0073864140.00776404520.00815871610.00857106820.00900176030.00945146870.00992088740.0104107280.01092172010.01145461120.01201016630.01258916870.01319241930.0138207370.01447495840.01515593750.01586454610.01660167310.01736822470.01816512380.018993310.01985373930.02074738360.02167523030.02263828210.02363755630.02467408450.02574891190.02686309690.02801771010.02921383420.03045256260.03173499920.03306225730.03443545880.03585573340.03732421720.03884205230.04041038530.04203036650.04370314850.0454298850.04721172960.04904983460.05094534950.05289941970.05491318480.05698777740.05912432140.06132393030.06358770580.0659167360.06831209340.07077483370.07330599330.07590658810.07857761120.0813200310.08413478930.08702279950.08998494420.09302207350.09613500260.09932451010.10259133560.10593617750.10935969130.11286248690.11644512680.12010812390.12385193930.127676980.13158359720.13557208350.13964267160.14379553140.14803076850.1523484220.15674846230.16123078950.16579523130.17044154090.17516939560.17997839470.18486805780.18983782350.19488704750.20001500120.205220870.21050375270.21586265940.22129651090.22680413740.23238427740.23803557740.24375659050.24954577610.25540149930.26132203060.26730554560.27335012450.27945375260.28561432010.29182962250.29809736080.30441514230.3107804810.31719079840.3236434250.33013560050.33666447590.34322711450.34982049350.35644150580.36308696170.36975359120.37643804580.38313690110.38984665940.39656375160.40328454090.4100053250.41672233940.42343176080.43012970980.43681225510.44347541650.45011516880.45672744570.46330814360.46985312570.47635822620.48281925460.48923199970.49559223450.50189572030.50813821160.51431546070.52042322230.52645725820.53241334250.53828726610.54407484170.54977190860.55537433820.56087803790.56627895720.57157309170.57675648860.58182525140.58677554460.59160359880.59630571530.60087827080.60531772210.60962061070.61378356720.61780331560.6216766780.62540057820.62897204620.63238822190.63564635910.63874382920.64167812430.64444686130.64704778450.6494787690.65173782330.65382309240.65573286020.65746555150.65901973480.66039412370.66158757910.66259911040.66342787720.66407319020.66453451230.66481145930.66490380070.66481145930.66453451230.66407319020.66342787720.66259911040.66158757910.66039412370.65901973480.65746555150.65573286020.65382309240.65173782330.6494787690.64704778450.64444686130.64167812430.63874382920.63564635910.63238822190.62897204620.62540057820.6216766780.61780331560.61378356720.60962061070.60531772210.60087827080.59630571530.59160359880.58677554460.58182525140.57675648860.57157309170.56627895720.56087803790.55537433820.54977190860.54407484170.53828726610.53241334250.52645725820.52042322230.51431546070.50813821160.50189572030.49559223450.48923199970.48281925460.47635822620.46985312570.46330814360.45672744570.45011516880.44347541650.43681225510.43012970980.42343176080.41672233940.4100053250.40328454090.39656375160.38984665940.38313690110.37643804580.36975359120.36308696170.35644150580.34982049350.3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yProceso 6 sigma

Hoja1 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Hoja1 (2)

yProceso 6 sigma

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LSELIE

yProceso 3 sigma

LSELIEGrfico20.00087268270.00090372220.00093577220.00096886180.00100302130.00103828130.00107467330.00111222970.00115098340.00119096840.00123221920.00127477120.00131866090.00136392520.00141060230.00145873080.00150835060.00155950230.00161222750.00166656850.00172256890.0017802730.00183972620.00190097470.00196406590.00202904810.00209597060.00216488390.00223583940.00230888970.00238408820.00246148970.002541150.0026231260.00270747580.00279425840.00288353430.00297536510.00306981330.00316694290.00326681910.0033695080.00347507740.00358359590.00369513370.00380976210.00392755360.00404858220.0041729230.00430065250.00443184840.004566590.00470495750.00484703290.00499289920.00514264090.00529634390.00545409520.00561598360.00578209890.00595253240.00612737690.00630672640.00649067640.00667932370.00687276670.00707110490.00727443940.00748287250.00769650820.00791545160.00813980920.00836968920.00860520060.00884645440.00909356250.00934663840.00960579680.00987115380.01014282690.01042093480.01070559760.01099693660.01129507450.01160013510.01191224360.01223152640.01255811090.01289212610.01323370180.01358296920.01394006050.0143051090.01467824910.01505961630.01544934710.0158475790.01625445050.01667010080.01709467050.01752830050.0179711330.01842331060.01888497710.01935627670.01983735440.02032835570.0208294270.02134071490.02186236680.02239453030.02293735370.02349098540.02405557420.02463126930.02521821990.02581657550.02642648550.02704809950.02768156710.02832703770.02898466060.02965458480.03033695920.03103193220.03173965180.03246026560.03319392060.03394076320.0347009390.03547459280.03626186890.03706291020.0378778590.03870685610.03955004160.04040755390.04127953040.0421661070.04306741790.0439835960.04491477230.04586107630.04682263530.04779957490.04879201860.04980008770.05082390150.05186357670.05291922770.05399096650.05507890240.05618314190.05730378890.05844094430.05959470610.0607651690.06195242460.06315656140.06437766430.06561581480.06687109060.06814356610.06943331150.07074039350.07206487430.07340681260.07476626240.07614327370.0775378920.07895015830.08038010910.0818277760.08329318610.08477636130.08627731880.08779607060.08933262350.0908869790.09245913340.09404907740.09565679620.09728226930.09892547070.10058636840.10226492460.10396109530.10567483080.10740607510.10915476590.11092083470.11270420660.11450480030.11632252790.11815729510.12000900070.1218775370.12376278950.12566463680.12758295060.12951759570.13146842990.1334353040.13541806160.13741653930.13943056640.14145996520.14350455050.145564130.14763850410.14972746560.15183080040.15394828680.15607969560.15822479040.16038332730.16255505520.16473971540.16693704170.16914676090.1713685920.1736022470.17584743030.17810383910.18037116320.18264908540.1849372810.18723541820.18954315810.19186015470.1941860550.19652049890.19886311940.20121354270.20357138830.20593626870.208307790.21068555170.21306914680.21545816180.2178521770.22025076670.22265349880.22505993530.22746963250.22988214070.23229700470.23471376390.2371319520.23955109770.24197072450.24439035090.24680949060.24922765250.25164434110.25405905650.25647129440.25888054670.26128630120.26368804210.26608524990.26847740180.27086397180.27324443090.27561824720.27798488610.28034381080.28269448210.28503635850.2873688970.28969155280.29200377950.29430502980.2965947550.29887240580.30113743220.30338928380.305627410.30785126050.31006028480.31225393340.3144316570.31659290770.31873713850.32086380380.32297235970.32506226410.3271329770.32918396080.33121468020.33322460290.33521319950.33717994380.33912431320.34104578860.3429438550.34481800140.34666772130.34849251280.35029187860.35206532680.35381237050.35553252850.35722532520.3588902910.36052696250.36213488240.36371360040.36526267260.36678166240.36827014030.36972768410.37115387940.37254831930.37391060540.37524034690.37653716180.37780067650.37903052620.38022635480.38138781550.38251457070.38360629220.38466266130.38568336920.38666811680.38761661510.38852858530.38940375880.39024187760.3910426940.39180597120.39253148310.39321901460.39386836160.39447933090.39505174080.39558542080.39608021180.3965359660.39695254750.39732983160.39766770550.39796606820.39822483020.39844391410.39862325420.39876279680.39886249990.39892233380.39894228040.39892233380.39886249990.39876279680.39862325420.39844391410.39822483020.39796606820.39766770550.39732983160.39695254750.3965359660.39608021180.39558542080.39505174080.39447933090.39386836160.39321901460.39253148310.39180597120.3910426940.39024187760.38940375880.38852858530.38761661510.38666811680.38568336920.38466266130.38360629220.38251457070.38138781550.38022635480.37903052620.37780067650.37653716180.37524034690.37391060540.37254831930.37115387940.36972768410.36827014030.36678166240.36526267260.36371360040.36213488240.36052696250.3588902910.35722532520.35553252850.35381237050.35206532680.35029187860.34849251280.34666772130.34481800140.3429438550.34104578860.33912431320.33717994380.33521319950.33322460290.33121468020.32918396080.3271329770.32506226410.32297235970.32086380380.31873713850.31659290770.3144316570.31225393340.31006028480.30785126050.305627410.30338928380.30113743220.29887240580.2965947550.29430502980.29200377950.28969155280.2873688970.28503635850.28269448210.28034381080.27798488610.27561824720.27324443090.27086397180.26847740180.26608524990.26368804210.26128630120.25888054670.25647129440.25405905650.25164434110.24922765250.24680949060.24439035090.24197072450.23955109770.2371319520.23471376390.23229700470.22988214070.22746963250.22505993530.22265349880.22025076670.2178521770.21545816180.21306914680.21068555170.208307790.20593626870.20357138830.20121354270.19886311940.19652049890.1941860550.19186015470.18954315810.18723541820.1849372810.18264908540.18037116320.17810383910.17584743030.1736022470.1713685920.16914676090.16693704170.16473971540.16255505520.16038332730.15822479040.15607969560.15394828680.15183080040.14972746560.14763850410.145564130.14350455050.14145996520.13943056640.13741653930.13541806160.1334353040.13146842990.12951759570.12758295060.12566463680.12376278950.1218775370.12000900070.11815729510.11632252790.11450480030.11270420660.11092083470.10915476590.10740607510.10567483080.10396109530.10226492460.10058636840.09892547070.09728226930.09565679620.09404907740.09245913340.0908869790.08933262350.08779607060.08627731880.08477636130.08329318610.0818277760.08038010910.07895015830.0775378920.07614327370.07476626240.07340681260.07206487430.07074039350.06943331150.06814356610.06687109060.06561581480.06437766430.06315656140.06195242460.0607651690.05959470610.05844094430.05730378890.05618314190.05507890240.05399096650.05291922770.05186357670.05082390150.04980008770.04879201860.04779957490.04682263530.04586107630.04491477230.0439835960.04306741790.0421661070.04127953040.04040755390.03955004160.03870685610.0378778590.03706291020.03626186890.03547459280.0347009390.03394076320.03319392060.03246026560.03173965180.03103193220.03033695920.02965458480.02898466060.02832703770.02768156710.02704809950.02642648550.02581657550.02521821990.02463126930.02405557420.02349098540.02293735370.02239453030.02186236680.02134071490.0208294270.02032835570.01983735440.01935627670.01888497710.01842331060.0179711330.01752830050.01709467050.01667010080.01625445050.0158475790.01544934710.01505961630.01467824910.0143051090.01394006050.01358296920.01323370180.01289212610.01255811090.01223152640.01191224360.01160013510.01129507450.01099693660.01070559760.01042093480.01014282690.00987115380.00960579680.00934663840.00909356250.00884645440.00860520060.00836968920.00813980920.00791545160.00769650820.00748287250.00727443940.00707110490.00687276670.00667932370.00649067640.00630672640.00612737690.00595253240.00578209890.00561598360.00545409520.00529634390.00514264090.00499289920.00484703290.00470495750.004566590.00443184840.00430065250.0041729230.00404858220.00392755360.00380976210.00369513370.00358359590.00347507740.0033695080.00326681910.00316694290.00306981330.00297536510.00288353430.00279425840.00270747580.0026231260.002541150.00246148970.00238408820.00230888970.00223583940.00216488390.00209597060.00202904810.00196406590.00190097470.00183972620.0017802730.00172256890.00166656850.00161222750.00155950230.00150835060.00145873080.00141060230.00136392520.00131866090.00127477120.00123221920.00119096840.00115098340.00111222970.00107467330.00103828130.00100302130.00096886180.00093577220.00090372220.0008726827

yProceso 3 sigma

Hoja1 (2)03.1415926536sigma0.60.6649038007xyy1y2(x-)/2sigmaexp-3.50.0000000271-33-17.01388888890.0000000408-3.490.0000000299-33-16.91680555560.000000045-3.480.000000033-33-16.820.0000000496-3.470.0000000363-33-16.72347222220.0000000546-3.460.00000004-33-16.62722222220.0000000601-3.450.000000044-33-16.531250.0000000662-3.440.0000000484-33-16.43555555560.0000000728-3.430.0000000533-33-16.34013888890.0000000801-3.420.0000000586-33-16.2450.0000000881-3.410.0000000644-33-16.15013888890.0000000968-3.40.0000000708-33-16.05555555560.0000001065-3.390.0000000778-33-15.961250.000000117-3.380.0000000854-33-15.86722222220.0000001285-3.370.0000000938-33-15.77347222220.0000001411-3.360.000000103-33-15.680.000000155-3.350.0000001131-33-15.58680555560.0000001701-3.340.0000001241-33-15.49388888890.0000001867-3.330.0000001362-33-15.401250.0000002048-3.320.0000001493-33-15.30888888890.0000002246-3.310.0000001638-33-15.21680555560.0000002463-3.30.0000001795-33-15.1250.00000027-3.290.0000001967-33-15.03347222220.0000002958-3.280.0000002155-33-14.94222222220.0000003241-3.270.000000236-33-14.851250.000000355-3.260.0000002584-33-14.76055555560.0000003887-3.250.0000002829-33-14.67013888890.0000004254-3.240.0000003096-33-14.580.0000004656-3.230.0000003387-33-14.49013888890.0000005093-3.220.0000003704-33-14.40055555560.0000005571-3.210.000000405-33-14.311250.0000006091-3.20.0000004427-33-14.22222222220.0000006658-3.190.0000004838-33-14.13347222220.0000007276-3.180.0000005286-33-14.0450.0000007949-3.170.0000005773-33-13.95680555560.0000008682-3.160.0000006303-33-13.86888888890.000000948-3.150.0000006881-33-13.781250.0000010349-3.140.0000007509-33-13.69388888890.0000011293-3.130.0000008192-33-13.60680555560.0000012321-3.120.0000008935-33-13.520.0000013438-3.110.0000009743-33-13.43347222220.0000014653-3.10.000001062-33-13.34722222220.0000015973-3.090.0000011574-33-13.261250.0000017407-3.080.0000012609-33-13.17555555560.0000018964-3.070.0000013734-33-13.09013888890.0000020655-3.060.0000014954-33-13.0050.0000022491-3.050.0000016278-33-12.92013888890.0000024482-3.040.0000017715-33-12.83555555560.0000026643-3.030.0000019274-33-12.751250.0000028987-3.020.0000020963-33-12.66722222220.0000031528-3.010.0000022794-33-12.58347222220.0000034282-30.0000024779-33-12.50.0000037267-2.990.0000026928-33-12.41680555560.00000405-2.980.0000029256-33-12.33388888890.0000044001-2.970.0000031777-33-12.251250.0000047791-2.960.0000034505-33-12.16888888890.0000051894-2.950.0000037456-33-12.08680555560.0000056

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