controle estatístico de qualidade aplicado à agricultura - a10 até a12
TRANSCRIPT
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Introduction to Statistical Quality Control, 4th Edition
CAPACIDADE DO PROCESSO
UNIVERSIDADE FEDERAL DO CEARÁ
CENTRO DE CIÊNCIAS AGRÁRIAS
PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA AGRÍCOLA
FORTALEZA – CE
Prof. Dr. Daniel Albiero
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Introduction to Statistical Quality Control, 4th Edition
7-1. Introduction • Process capability refers to the uniformity of the process.• Variability in the process is a measure of the uniformity of
output.• Two types of variability:
– Natural or inherent variability (instantaneous)– Variability over time
• Assume that a process involves a quality characteristic that follows a normal distribution with mean , and standard deviation, . The upper and lower natural tolerance limits of the process are
UNTL = + 3LNTL = - 3
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Introduction to Statistical Quality Control, 4th Edition
7-1. Introdução
Processo Incapaz
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Introduction to Statistical Quality Control, 4th Edition
Estimating the Process Standard Deviation• The process standard deviation can be estimated
using a function of the sample average range.
• This is an unbiased estimator of
Rd2
7-1. Introdução
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Introduction to Statistical Quality Control, 4th Edition
5-2. Control Charts for and R
Estimating Process Capability
• The x-bar and R charts give information about the capability of the process relative to its specification limits.
• Assumes a stable process.• We can estimate the fraction of nonconforming items for
any process where specification limits are involved.• Assume the process is normally distributed, and x is
normally distributed, the fraction nonconforming can be found by solving:
P(x < LSL) + P(x > USL)
x
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Introduction to Statistical Quality Control, 4th Edition
Process-Capability Ratios (Cp)• Used to express process capability.• For processes with both upper and lower control limits, Use an estimate of if it is unknown.
• If Cp > 1, then a low # of nonconforming items will be produced (.
• If Cp = 1, (assume norm. dist) then we are producing about 0.27% nonconforming.
• If Cp < 1, then a large number of nonconforming items are being produced.
6
LSLUSLCp
7-1. Introdução
LNTL=Lower Normal Tolerance Limit
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Introduction to Statistical Quality Control, 4th Edition
Process-Capability Ratios (Cp)• The percentage of the specification band that the
process uses up is denoted by
**The Cp statistic assumes that the process mean is centered at the midpoint of the specification band – it measures potential capability.
%100C1P
p
7-1. Introdução
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Introduction to Statistical Quality Control, 4th Edition
7-1. Introduction
• Process capability analysis is an engineering study to estimate process capability.
• In a product characterization study, the distribution of the quality characteristic is estimated.
Processo de Desenvolvimento
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Introduction to Statistical Quality Control, 4th Edition
7-1. Introduction Major uses of data from a process capability analysis
1. Predicting how well the process will hold the tolerances.2. Assisting product developers/designers in selecting or
modifying a process.3. Assisting in Establishing an interval between sampling for
process monitoring.4. Specifying performance requirements for new equipment.5. Selecting between competing vendors.6. Planning the sequence of production processes when there
is an interactive effect of processes on tolerances7. Reducing the variability in a manufacturing process.
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Introduction to Statistical Quality Control, 4th Edition
Techniques used in process capability analysis
• Histograms or probability plots
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Introduction to Statistical Quality Control, 4th Edition
Control Charts
Techniques used in process capability analysis
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Introduction to Statistical Quality Control, 4th Edition
Techniques used in process capability analysis
Experimental Design
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Introduction to Statistical Quality Control, 4th Edition
7-2. Process Capability Analysis Using a Histogram or a Probability Plot
7-2.1 Using a Histogram• The histogram along with the sample mean and
sample standard deviation provides information about process capability.
– The process capability can be estimated as– The shape of the histogram can be determined (such
as if it follows a normal distribution) – Histograms provide immediate, visual impression of
process performance.
s3x
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Introduction to Statistical Quality Control, 4th Edition
7-2.2 Probability Plotting
• Probability plotting is useful for
– Determining the shape of the distribution
– Determining the center of the distribution
– Determining the spread of the distribution.
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Introduction to Statistical Quality Control, 4th Edition
7-3. Process Capability Ratios
7-3.1 Use and Interpretation of Cp
• Recall
where LSL and USL are the lower and upper specification limits, respectively.
6
LSLUSLCp
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Introduction to Statistical Quality Control, 4th Edition
7-3.1 Use and Interpretation of Cp
The estimate of Cp is given by
Where the estimate can be calculated using the sample standard deviation, S, or
ˆ6LSLUSLCp
2d/R
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Introduction to Statistical Quality Control, 4th Edition
7-3.1 Use and Interpretation of Cp
Piston ring diameter in Example 5-1• The estimate of Cp is
68.1
)0099.0(695.7305.74Cp
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Introduction to Statistical Quality Control, 4th Edition
7-3.1 Use and Interpretation of Cp
One-Sided Specifications
These indices are used for upper specification and lower specification limits, respectively
3LSLC
3USLC
pl
pu
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Introduction to Statistical Quality Control, 4th Edition
7-3.1 Use and Interpretation of Cp
AssumptionsThe quantities presented here (Cp, Cpu, Clu) have some very
critical assumptions:1. The quality characteristic has a normal distribution.2. The process is in statistical control3. In the case of two-sided specifications, the process mean
is centered between the lower and upper specification limits.
If any of these assumptions are violated, the resulting quantities may be in error.
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Introduction to Statistical Quality Control, 4th Edition
7-3.2 Process Capability Ratio an Off-Center Process
• Cp does not take into account where the process mean is located relative to the specifications. (Measure only dispersion).
• A process capability ratio that does take into account centering is Cpk defined as
Cpk = min(Cpu, Cpl)
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Introduction to Statistical Quality Control, 4th Edition
Cpk x Falhas
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Introduction to Statistical Quality Control, 4th Edition
Cp X Cpk
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Introduction to Statistical Quality Control, 4th Edition
7-3.3 Normality and the Process Capability Ratio
• The normal distribution of the process output is an important assumption.
• If the distribution is nonnormal, Luceno (1996) introduced the index, Cpc, defined as
TXE
LSLUSLC pc
.2
6
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Introduction to Statistical Quality Control, 4th Edition
7-3.3 Normality and the Process Capability Ratio
• A capability ratio involving quartiles of the process distribution is given by
• In the case of the normal distribution Cp(q) reduces to Cp
00135.099865.0p xx
LSLUSL)q(C
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Introduction to Statistical Quality Control, 4th Edition
MAS E QUANDO OS PROCESSOS NÃO SÃO NORMAIS??
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Introduction to Statistical Quality Control, 4th Edition
8-2. MÉDIA MÓVEL EXPONENCIALMENTE PONDERADA (OBSERVAÇÕES INDIVIDUAIS).
The Exponentially Weighted Moving Average Control Chart Monitoring the Process Mean
• The exponentially weighted moving average (EWMA) is defined as
where 0 < 1 is a constant.z0 = 0 (sometimes z0 = )
1iii z)1(xz
x
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Introduction to Statistical Quality Control, 4th Edition
8-2. MÉDIA MÓVEL EXPONENCIALMENTE PONDERADA (MMEP).
A MMEP é uma média ponderada de todas as médias de amostras anteriores.
O limite acompanha a
média das médias
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Introduction to Statistical Quality Control, 4th Edition
8-2. MÉDIA MÓVEL EXPONENCIALMENTE PONDERADA (MMEP).
O peso decresce geometricamente com as observações (média móvel).
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Introduction to Statistical Quality Control, 4th Edition
8-2.1 The Exponentially Weighted Moving Average Control Chart Monitoring the Process Mean• The control limits for the EWMA control chart are
where L is the width of the control limits.
i20
0
i20
)1(1)2(
LLCL
CL
)1(1)2(
LUCL
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Introduction to Statistical Quality Control, 4th Edition
8-2.1 The Exponentially Weighted Moving Average Control Chart Monitoring the Process Mean
• As i gets larger, the term [1- (1 - )2i] approaches infinity.
• This indicates that after the EWMA control chart has been running for several time periods, the control limits will approach steady-state values given by
)2(LLCL
CL)2(
LUCL
0
0
0
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Introduction to Statistical Quality Control, 4th Edition
8-2.2 Design of an EWMA Control Chart
• The design parameters of the chart are L and .• The parameters can be chosen to give desired ARL
performance.• In general, 0.05 0.25 works well in practice.• L = 3 works reasonably well (especially with the larger
value of .• L between 2.6 and 2.8 is useful when 0.1• Similar to the cusum, the EWMA performs well against
small shifts but does not react to large shifts as quickly as the Shewhart chart.
• EWMA is often superior to the cusum for larger shifts particularly if > 0.1
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Introduction to Statistical Quality Control, 4th Edition
8-2.4 Robustness of the EWMA to Non-normality
• Individuals control chart is sensitive to non-normality.
• A properly designed EWMA is less sensitive to the normality assumption.
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Introduction to Statistical Quality Control, 4th Edition
EXEMPLO: Análise do Processo de Semeadura (Profundiade de sementes).
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Introduction to Statistical Quality Control, 4th Edition
EXEMPLO: Análise do Processo de Semeadura (Profundiade de sementes).
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Introduction to Statistical Quality Control, 4th Edition
EXEMPLO: Análise do Processo de Semeadura (Profundiade de sementes).
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Introduction to Statistical Quality Control, 4th Edition
Fail Mode and Effects Analysis (FMEA)
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Introduction to Statistical Quality Control, 4th Edition
FMEAO FMEA é uma ferramenta que busca evitar FALHAS por meio da análise das falhas potenciais E propõe ações de melhoria para que estas falhas não ocorram no projeto de um produto ou processo. O objetivo básico desta metodologia é aumentar a confiabilidade
( diminuir a probabilidade de falha do produto/processo).
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Introduction to Statistical Quality Control, 4th Edition
Prioriza três linhas básicas:
1-Trabalha como ferramenta de prevenção de problemas e identificação das soluções mais eficazes;
2-É um procedimento que oferece estrutura para a avaliação, condução e a atualização no desenvolvimento de projetos;
3-Atua como diário que se inicia no planejamento do projeto ou processo e se mantém durante todo o período de utilização do produto.
FMEA
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Introduction to Statistical Quality Control, 4th Edition
Design-FMEA (DFMEA)O DFMEA é um método preventivo que tem como objetivo
assegurar que durante o projeto do produto, os modos de falhas potenciais e suas causas/mecanismos associados
sejam considerados e abordados.
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Introduction to Statistical Quality Control, 4th Edition
1-Deve ser iniciado antes ou na finalização do projeto conceitual e concluído quando na finalização do projeto detalhado e liberação para a ferramentaria;
2-O produto final, subsistemas, componentes e sistemas relacionados são os objetos de estudo nesta fase, que considera como “cliente”, além do usuário final, os engenheiros e equipes responsáveis pelo projeto.
DFMEA
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Introduction to Statistical Quality Control, 4th Edition
Process-FMEA (PFMEA)O PFMEA tem o mesmo objetivo que o DFMEA, porém seu
objeto de estudo é o processo de fabricação e o “cliente” pode ser o usuário final do produto ou ainda uma operação
de assistência técnica.
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Introduction to Statistical Quality Control, 4th Edition
O PFMEA de processo deve ser iniciado antes ou durante o estágio de viabilidade e antes do desenvolvimento das ferramentas para a produção. Deve-se considerar todas as operações do processo, desde a entrada de matéria prima até o produto final.
PFMEA
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Introduction to Statistical Quality Control, 4th Edition
Identificar os modos de falhas potenciais do processo relacionados ao produto;
Avaliar os efeitos potenciais da falha em relação ao cliente;
Identificar as causas potenciais de falha do processo de manufatura ou montagem e as variáveis que deverão ser controladas para redução da ocorrência ou melhoria da eficácia na detecção da falhas;
Classificar modos de falhas potenciais criando um sistema de priorização para as ações corretivas;
Documentar os resultados do processo de manufatura ou montagem.
PFMEA
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Introduction to Statistical Quality Control, 4th Edition
FMEA
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Introduction to Statistical Quality Control, 4th Edition
Fase do evento
Representação Gráfica
Descrição
Processo Processo ou operação executada
Resultado Dados de saída do processo
Avaliação Comparação de dados e tomada de decisão
Dados Informações ou dados de qualquer natureza
FMEAPrimeiro passo: Definir o Fluxograma do Projeto e ou Processo
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Introduction to Statistical Quality Control, 4th Edition
FMEASegundo passo: Estruturação do Formulário FMEA (QAI, 2009)
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Introduction to Statistical Quality Control, 4th Edition
FMEATerceiro passo: Escolha da Equipe FMEA
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Introduction to Statistical Quality Control, 4th Edition
Quarto passo: Cálculo do NPRFMEA
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Introduction to Statistical Quality Control, 4th Edition
Quinto passo: Interpretação dos ResultadosFMEA
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Introduction to Statistical Quality Control, 4th Edition
Quinto passo: Interpretação dos ResultadosFMEA
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Introduction to Statistical Quality Control, 4th Edition
FALHAS CRÍTICAS:1-A falha potencial com maior risco é em relação ao não funcionamento dos freios de mãoEsta falha ocorre principalmente a uma não conformidade de uso do sistema de freios, estes foram previstos para operação em auxílio a manobras de curva, mas em vez disto o operador pode usá-los como meio de parada da máquina Dependendo da situação de relevo em que a máquina se encontre (uma descida), o operador pode se valer dos freios de mão para parar o motocultor, nesta situação existe o sério risco de acidente com vítimas, pois o sistema de freios de mão não foi projetado para parar a máquina.
Sexto passo: Definição Falha CríticaFMEA
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Introduction to Statistical Quality Control, 4th Edition
RECOMENDAÇÕES DE AÇÕES CORRETIVAS1- Freios de mão não funcionam:
Reprojeto dos freios de mão para atuarem também como freios de parada.
Sétimo passo: Correção da Falha CríticaFMEA