From aaba2610a9f1e9787b344e9afaf9c41efec1d27d Mon Sep 17 00:00:00 2001 From: Walmes Zeviani <walmes@ufpr.br> Date: Mon, 18 Apr 2016 20:25:19 -0300 Subject: [PATCH] Adiciona slides das duas aulas. --- slides/as7ferr.org | 135 +++++++++++++++++++++++++++++++++++ slides/as7ferr.pdf | Bin 0 -> 177050 bytes slides/graf_contr_X_S.org | 144 ++++++++++++++++++++++++++++++++++++++ slides/graf_contr_X_S.pdf | Bin 0 -> 190874 bytes slides/img/X_MR-chart.png | Bin 0 -> 130378 bytes slides/img/X_S-chart.png | Bin 0 -> 60540 bytes 6 files changed, 279 insertions(+) create mode 100644 slides/as7ferr.org create mode 100644 slides/as7ferr.pdf create mode 100644 slides/graf_contr_X_S.org create mode 100644 slides/graf_contr_X_S.pdf create mode 100644 slides/img/X_MR-chart.png create mode 100644 slides/img/X_S-chart.png diff --git a/slides/as7ferr.org b/slides/as7ferr.org new file mode 100644 index 0000000..e451f4f --- /dev/null +++ b/slides/as7ferr.org @@ -0,0 +1,135 @@ +#+TITLE: As 7 Ferramentas do CEQ +#+AUTHOR: Prof. Walmes Zeviani +#+EMAIL: walmes@ufpr.br +#+DATE: +#+LANGUAGE: pt + +#+STARTUP: beamer +#+STARTUP: oddeven + +#+LaTeX_CLASS: beamer +#+LaTeX_CLASS_OPTIONS: [aspectratio=169, serif, professionalfont] + +#+BEAMER_THEME: default +#+COLUMNS: %40ITEM %10BEAMER_env(Env) %9BEAMER_envargs(Env Args) %4BEAMER_col(Col) %10BEAMER_extra(Extra) + +# PREAMBULO ------------------------------------------------------------ +#+LaTeX_HEADER: \usepackage[brazil]{babel} +#+LaTeX_HEADER: \usepackage[T1]{fontenc} +#+LaTeX_HEADER: \usepackage[utf8]{inputenc} +#+LaTeX_HEADER: \usepackage{mathpazo} +#+LaTeX_HEADER: \usepackage{eulervm} +#+LaTeX_HEADER: \usepackage{inconsolata} +#+LaTeX_HEADER: \usepackage{hyperref} +#+LaTeX_HEADER: \hypersetup{colorlinks, allcolors=., urlcolor=blue, runcolor=orange} + +# ---------------------------------------------------------------------- +# Para chunks R. +#+LaTeX_HEADER: \usepackage{listings} +#+LATEX_HEADER: \lstset{ +#+LATEX_HEADER: keywordstyle=\color{blue}, +#+LATEX_HEADER: commentstyle=\color{red}, +#+LATEX_HEADER: stringstyle=\color{green}, +#+LATEX_HEADER: basicstyle=\ttfamily\small, +#+LATEX_HEADER: columns=fullflexible, +#+LATEX_HEADER: basewidth={0.5em,0.4em} +#+LATEX_HEADER: } + +#+LATEX_HEADER: \RequirePackage{fancyvrb} +#+LATEX_HEADER: \DefineVerbatimEnvironment{verbatim}{Verbatim}{ +#+LATEX_HEADER: fontsize=\footnotesize, +#+LATEX_HEADER: formatcom={\color[rgb]{0,0,0.5}} +#+LATEX_HEADER: } + +#+OPTIONS: H:1 toc:nil + +# ---------------------------------------------------------------------- + +* As 7 Ferramentas do Controle Estatístico da Qualidade + + * Histogramas e Ramos-e-folhas + * Folha de Verificação + * Gráfico de Pareto + * Diagrama de Causa-e-efeito + * Diagrama de Concentração de Defeitos + * Diagrama de Dispersão + * Gráficos de Controle + +* Folha de Verificação + + - Registro de defeitos + - Resumo por período + - Orientado no tempo: tendências e padrões + - Deve conter + - Data + - Operador e envolvidos + - Identificações + - Condições de contorno + - Constante adaptação + +[[https://www.google.com.br/search?q=process+control+pareto+plot&client=ubuntu&hs=tsC&channel=fs&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiS7afTwZHMAhWGDJAKHb3IDUMQ_AUIBygB&biw=1863&bih=954#channel=fs&tbm=isch&q=check+sheet+in+quality+control][Exemplos +de Folha de Verificação]] + +* Gráfico de Pareto + + - Distribuição de frequências dos tipos de defeito + - A frequência diminui da esquerda para a direita + - Algumas adaptações consideram os custos e danos + - Frequência acumulada em outro eixo + - Aplicação em contextos não industriais + +[[https://www.google.com.br/search?q=process+control+pareto+plot&client=ubuntu&hs=tsC&channel=fs&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiS7afTwZHMAhWGDJAKHb3IDUMQ_AUIBygB&biw=1863&bih=954][Exemplos +de Gráfico de Pareto]] + +* Diagrama de Causa-e-efeito + + - Representa as causas, os meios e suas magnitudes + - Útil para ação de eliminar causas + - Requer sessões de /brainstorm/ + +[[https://www.google.com.br/search?client=ubuntu&hs=raX&channel=fs&biw=1863&bih=954&tbm=isch&q=cause+and+effect+diagram&revid=1089372911&sa=X&ved=0ahUKEwjtnJCiwpHMAhULCpAKHVQGCNYQ1QIIJw&dpr=1][Exemplos +de Diagrama de Causa-e-efeito]] + +* Diagrama de Concentração de Defeitos + + - Figura da unidade produzida com todas as vistas relevantes + - Pode se usar cores ou símbolos diferentes para sinalização + - Posição sistemática ou padrões de defeitos ajuda na busca da causa + +[[https://www.google.com.br/search?q=process+control+pareto+plot&client=ubuntu&hs=tsC&channel=fs&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiS7afTwZHMAhWGDJAKHb3IDUMQ_AUIBygB&biw=1863&bih=954#channel=fs&tbm=isch&q=defect+concentration+diagram][Exemplo +de Diagramas de Concentração de Defeitos]] + +* Diagrama de Dispersão + + - Relação entre pares de variáveis + - Correlação \neq causalidade + - Útil para ideias de otimização do processo + +* Gráfico de Controle para medidas individuais + + - Quando + - Inspeção automática, sistema informatizado + - Taxa de produção é lenta + - Medidas consecutivas tem variabilidade muito pequena + - X-chart: valores individuais + - $LC = \bar{X}$ + - $LIC = \bar{X} - 3 \frac{\bar{MR}}{d_{2}}$ + - $LSC = \bar{X} + 3 \frac{\bar{MR}}{d_{2}}$ + - $MR = |x_{i} - x_{i-1}|$ + - MR-chart: amplutude móvel + - $LC = \bar{MR}$ + - $LIC = \bar{MR} - 3 d_{3} \frac{\bar{MR}}{d_{2}} = D_{3} + \bar{MR}$ + - $LSC = \bar{MR} + 3 d_{3} \frac{\bar{MR}}{d_{2}} = D_{4} + \bar{MR}$ + - $D_{3} = 0$ se amplitude é com $n = 2$ + +* Um exemplo + + #+NAME: fig:SED-HR4049 + #+CAPTION: + #+ATTR_LATEX: :width 8cm + [[./img/X_MR-chart.png]] + + - Interpretação igual ao $\bar{X}$ e R-chart + - CUIDADO: amplitudes móveis não são independentes diff --git a/slides/as7ferr.pdf b/slides/as7ferr.pdf new file mode 100644 index 0000000000000000000000000000000000000000..73a9702b65b6ddc19a9ca2a27fe286eb000a4fd6 GIT binary patch literal 177050 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para $\bar{X}$ e $S$ +#+AUTHOR: Prof. Walmes Zeviani +#+EMAIL: walmes@ufpr.br +#+DATE: +#+LANGUAGE: pt + +#+STARTUP: beamer +#+STARTUP: oddeven + +#+LaTeX_CLASS: beamer +#+LaTeX_CLASS_OPTIONS: [aspectratio=169, serif, professionalfont] + +#+BEAMER_THEME: default +#+COLUMNS: %40ITEM %10BEAMER_env(Env) %9BEAMER_envargs(Env Args) %4BEAMER_col(Col) %10BEAMER_extra(Extra) + +# PREAMBULO ------------------------------------------------------------ +#+LaTeX_HEADER: \usepackage[brazil]{babel} +#+LaTeX_HEADER: \usepackage[T1]{fontenc} +#+LaTeX_HEADER: \usepackage[utf8]{inputenc} +#+LaTeX_HEADER: \usepackage{mathpazo} +#+LaTeX_HEADER: \usepackage{eulervm} +#+LaTeX_HEADER: \usepackage{inconsolata} +#+LaTeX_HEADER: \usepackage{hyperref} +#+LaTeX_HEADER: \hypersetup{colorlinks, allcolors=., urlcolor=blue, runcolor=orange} + +# ---------------------------------------------------------------------- +# Para chunks R. +#+LaTeX_HEADER: \usepackage{listings} +#+LATEX_HEADER: \lstset{ +#+LATEX_HEADER: keywordstyle=\color{blue}, +#+LATEX_HEADER: commentstyle=\color{red}, +#+LATEX_HEADER: stringstyle=\color{green}, +#+LATEX_HEADER: basicstyle=\ttfamily\small, +#+LATEX_HEADER: columns=fullflexible, +#+LATEX_HEADER: basewidth={0.5em,0.4em} +#+LATEX_HEADER: } + +#+LATEX_HEADER: \RequirePackage{fancyvrb} +#+LATEX_HEADER: \DefineVerbatimEnvironment{verbatim}{Verbatim}{ +#+LATEX_HEADER: fontsize=\footnotesize, +#+LATEX_HEADER: formatcom={\color[rgb]{0,0,0.5}} +#+LATEX_HEADER: } + +#+OPTIONS: H:1 toc:nil + +# ---------------------------------------------------------------------- + +* Quando usar + + #+ATTR_BEAMER: :overlay +- + - Há casos em que é melhor estimar $\sigma$ por $S$ do que por $R$ + - Indicado quando $n > 10$, pois o estimador baseado em $R$ perde + eficiência + - Quando o tamanho das amostras é variável (esquemas adaptativos) + - Ver script [[../scripts/03_S_distr.R][=03_S_distr.R=]]. + +* Gráfico de controle para $S$ e $\bar{X}$ + + #+ATTR_BEAMER: :overlay +- + - Mesma sequência de etapas de $\bar{X}$ e $R$ + - São baseados em $$\bar{X} = \frac{\sum X}{n} \quad \text{e} \quad + S = \sqrt{\frac{\sum (x - \bar{x})^2}{n-1}}$$ + - $S^2$ é estimador não viciado para $\sigma^2$ + - Mas $S$ não é um estimador não viciado para $\sigma$ + - Se $X$ é Normal, $S$ estima $c_4 \sigma$, ou seja + $E(S) = c_4 \sigma$ + - $c_4$ é uma constante de correção de viés que depende do $n$ + - O desvio-padrão do estimador $S$ é $\sigma \sqrt{1-c_4^2}$ + +* Linhas de Controle para S + + #+ATTR_BEAMER: :overlay +- + - $LC = c_4 \sigma$ + - $LIC = c_4 \sigma - 3\sigma \sqrt{1-c_4^2}$ + - $LSC = c_4 \sigma + 3\sigma \sqrt{1-c_4^2}$ + + #+LATEX: \pause Sem conhecer ou ter um valor adequado para $\sigma$, estimamos a partir + das $m$ amostras de tamnho $n$. + + #+ATTR_BEAMER: :overlay +- + - Se $E(S) = c_4 \sigma$, então $E(S/c_4) = \sigma$ + - $\bar{S} = \frac{1}{m} \sum S_i$ + - $LC = \bar{S}$ + - $LIC = \bar{S} - 3 \frac{\bar{S}}{c_4} \sqrt{1-c_4^2}, + \quad B_3 = 1 - \frac{3}{c_4} \sqrt{1 - c_4^2},\quad$ + assim $LIC = B_3 \bar{S}$ + - $LSC = \bar{S} + 3 \frac{\bar{S}}{c_4} \sqrt{1-c_4^2}, + \quad B_4 = 1 + \frac{3}{c_4} \sqrt{1 - c_4^2},\quad$ + assim $LSC = B_4 \bar{S}$ + +* Linhas de Controle para $\bar{X}$ + + #+ATTR_BEAMER: :overlay +- + - Agora os limites são função de $S$ e não de $R$ + - $LC = \bar{\bar{X}}$ + - $LIC = \bar{\bar{X}} - 3 \frac{\bar{S}}{c_4 \sqrt{n}}$ + - $LIC = \bar{\bar{X}} + 3 \frac{\bar{S}}{c_4 \sqrt{n}}$ + + #+LATEX: \pause + Se $A_3 = \frac{3}{c_4 \sqrt{n}}$, então + + #+ATTR_BEAMER: :overlay +- + - $LIC = \bar{\bar{X}} - A_3 \bar{S}$ + - $LIC = \bar{\bar{X}} + A_3 \bar{S}$ + +* Gráfico de Controle com $n$ variável + + #+ATTR_BEAMER: :overlay +- + - Os gráficos de $\bar{X}$ e $S$ são simple de adaptar + - Considerar pesos para os tamanhos de amostra (estimadores + ponderados) + - $\bar{\bar{X}} = \dfrac{\sum n_i \bar{X}_i}{\sum n_i}$ + - $\bar{S} = \sqrt{\dfrac{\sum (n_i -1) \bar{S}_i^2}{\sum n_i - m}}$ + - Com estes são traçadas as linhas centrais + - Os limites serão dependentes do $n$ alterando a constante $c_4$, por + consequência $A_3$, $B_3$ e $B_4$ + - O gráfico não tem limites de controle formando uma linha. + +# * Simulação +# +# # #+begin_src R :exports both :results graphics :file img/fig2.pdf ::: include=TRUE +# # #+begin_src R :exports code :results graphics :file img/fig2.pdf ::: echo=FALSE, results="markup" +# # #+begin_src R :exports results :results graphics :file img/fig2.pdf ::: fig=TRUE, echo=FALSE, results="hide" +# # #+begin_src R :exports results :results code :file img/fig2.pdf ::: exibe [[file:img/fig2.pdf]] +# +# # :exports {code,results,both,none} +# # :results {vector,scalar,file,raw,html,latex,code,graphics} +# +# #+name: fig2 +# #+header: :width 3 :height 3 +# #+begin_src R :exports results :results latex :file img/fig2.pdf +# runif(2) +# plot(cars) +# #+end_src +# +# #+ATTR_LaTeX: width=0.5\textwidth +# #+RESULTS: fig2 +# [[file:img/fig2.pdf]] + +* Exemplo + + 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