Controle Estatístico de Processos - Métodos e Filosofia

library(ggplot2)
set.seed(3)
mu0 <- 74; sigma <- 0.01
df_dist <- do.call(rbind, lapply(1:4, function(i)
  data.frame(x=rnorm(300,mu0,sigma), tempo=paste0("T",i))))
ggplot(df_dist,aes(x=x,fill=tempo)) +
  geom_density(alpha=.5) +
  scale_fill_manual(values=c("#7ecff7","#a8f77e","#f7c87e","#c87ef7")) +
  geom_vline(xintercept=c(mu0-3*sigma, mu0, mu0+3*sigma),
             color=c("#f07050","white","#f07050"),
             linetype=c("dashed","solid","dashed"),linewidth=.9) +
  labs(title="Sob controle: distribuições idênticas nos quatro instantes",
       x="Diametro (mm)",y="Densidade",fill="Instante") +
  theme_minimal(base_size=13)

library(ggplot2); library(patchwork)
set.seed(4)
mu0 <- 74; sigma <- 0.01
d1a <- data.frame(x=rnorm(300,mu0,sigma), g="Sob controle")
d1b <- data.frame(x=rnorm(300,mu0+.02,sigma), g="Média deslocada")
d2a <- data.frame(x=rnorm(300,mu0,sigma),     g="Sob controle")
d2b <- data.frame(x=rnorm(300,mu0,sigma*2.5), g="Variância inflada")
p1 <- ggplot(rbind(d1a,d1b),aes(x=x,fill=g)) +
  geom_density(alpha=.6) +
  scale_fill_manual(values=c("#7ecff7","#f07050")) +
  geom_vline(xintercept=c(mu0-3*.0045,mu0+3*.0045),
             color="#f07050",linetype="dashed",linewidth=1) +
  labs(title="Deslocamento de média",x="mm",y="",fill="") +
  theme_minimal(base_size=11)
p2 <- ggplot(rbind(d2a,d2b),aes(x=x,fill=g)) +
  geom_density(alpha=.6) +
  scale_fill_manual(values=c("#7ecff7","#a8f77e")) +
  geom_vline(xintercept=c(mu0-3*.0045,mu0+3*.0045),
             color="#f07050",linetype="dashed",linewidth=1) +
  labs(title="Aumento de variância",x="mm",y="",fill="") +
  theme_minimal(base_size=11)
p1 + p2

library(ggplot2); library(patchwork)
set.seed(42)
# Processo sob controle
y_ctrl <- rnorm(20, 74, 0.0045)
# Causa atribuível: deslocamento de média a partir do ponto 11
y_atrib <- c(rnorm(10, 74, 0.0045), rnorm(10, 74.015, 0.0045))
# Causa atribuível: aumento da variância a partir do ponto 11
y_var   <- c(rnorm(10, 74, 0.0045), rnorm(10, 74, 0.012))

lm_ <- 74; lsc <- 74 + 3*0.0045; lic <- 74 - 3*0.0045
mk <- function(y, titulo, cor) {
  df <- data.frame(t=1:20, y=y, fora=y>lsc|y<lic)
  ggplot(df, aes(t,y)) +
    geom_line(color="white", linewidth=.6) +
    geom_point(aes(color=fora), size=2.5) +
    scale_color_manual(values=c("FALSE"=cor,"TRUE"="#f07050"),guide="none") +
    geom_hline(yintercept=c(lsc,lm_,lic),
               color=c("#f07050","#a8f77e","#f07050"),
               linetype=c("dashed","solid","dashed"), linewidth=.8) +
    labs(title=titulo, x="Amostra", y=expression(bar(x))) +
    theme_minimal(base_size=11)
}
mk(y_ctrl, "Sob controle", "#7ecff7") +
mk(y_atrib,"Causa atrib.:\ndeslocamento de média","#f7c87e") +
mk(y_var,  "Causa atrib.:\naumento de variância","#c87ef7")

library(ggplot2)
set.seed(7)
n <- 40
sem <- numeric(n); sem[1] <- rnorm(1,0,1)
for(i in 2:n) sem[i] <- sem[i-1] + rnorm(1,0,1)
com <- numeric(n); com[1] <- rnorm(1,0,1)
for(i in 2:n) com[i] <- com[i-1] + rnorm(1, -com[i-1]*0.9, 1)
df <- data.frame(t=rep(1:n,2),
                 y=c(sem,com),
                 tipo=rep(c("Sem ajuste (correto)","Com ajuste excessivo"),each=n))
ggplot(df, aes(t,y,color=tipo)) +
  geom_line(linewidth=1.1) + geom_point(size=1.5) +
  scale_color_manual(values=c("Sem ajuste (correto)"="#7ecff7",
                               "Com ajuste excessivo"="#f07050")) +
  labs(title="Ajuste excessivo amplifica a variabilidade do processo",
       x="Tempo", y="Desvio em relação ao alvo", color="") +
  theme_minimal(base_size=13)

library(ggplot2)
Ls     <- seq(1, 5, by=0.1)
alphas <- 1-(pnorm(Ls)-pnorm(-Ls))
ARL0s  <- 1/alphas
df_L   <- data.frame(L=Ls, alpha=alphas, ARL0=ARL0s)
library(patchwork)
p1 <- ggplot(df_L,aes(L,alpha)) +
  geom_line(color="#f07050",linewidth=1.3) +
  geom_vline(xintercept=3,color="#f7c87e",linetype="dashed",linewidth=1) +
  annotate("text",x=3.1,y=.03,label="L=3\nalpha=0.0027",
           color="#f7c87e",size=3.5,hjust=0) +
  labs(title="alpha vs L",x="L (sigmas)",y="Probabilidade de falso alarme") +
  theme_minimal(base_size=11)
p2 <- ggplot(df_L,aes(L,ARL0)) +
  geom_line(color="#7ecff7",linewidth=1.3) +
  geom_vline(xintercept=3,color="#f7c87e",linetype="dashed",linewidth=1) +
  annotate("text",x=3.1,y=100,label="L=3\nARL0=370",
           color="#f7c87e",size=3.5,hjust=0) +
  scale_y_log10() +
  labs(title="ARL0 vs L (escala log)",x="L (sigmas)",y="ARL0") +
  theme_minimal(base_size=11)
p1 + p2

library(ggplot2)
set.seed(11)
mu0 <- 74; sigma <- 0.01; n <- 5; s_xb <- sigma/sqrt(n)
medias <- c(rnorm(15, mu0, s_xb), rnorm(5, mu0+0.01, s_xb))
df <- data.frame(t=1:20, xbar=medias,
                 fora=medias > mu0+3*s_xb | medias < mu0-3*s_xb)
ggplot(df, aes(t, xbar)) +
  geom_line(color="white", linewidth=.7) +
  geom_point(aes(color=fora), size=3) +
  scale_color_manual(values=c("FALSE"="#7ecff7","TRUE"="#f07050"),
                     labels=c("Sob controle","Fora de controle"), name="") +
  geom_hline(yintercept=c(mu0+3*s_xb, mu0, mu0-3*s_xb),
             color=c("#f07050","#a8f77e","#f07050"),
             linetype=c("dashed","solid","dashed"), linewidth=1) +
  annotate("text",x=20.4,y=mu0+3*s_xb,label="LSC",color="#f07050",size=3.5,hjust=0) +
  annotate("text",x=20.4,y=mu0,        label="LM", color="#a8f77e",size=3.5,hjust=0) +
  annotate("text",x=20.4,y=mu0-3*s_xb,label="LIC",color="#f07050",size=3.5,hjust=0) +
  labs(title="Gráfico de Controle: Diametro de Aneis de Pistao",
       x="Amostra (hora)", y="Média amostral (mm)") +
  theme_minimal(base_size=13)

library(ggplot2)
x  <- seq(-4,4,length.out=500)
df <- data.frame(x=x, y=dnorm(x))
ggplot(df,aes(x,y)) +
  geom_line(color="white",linewidth=1.2) +
  geom_area(data=subset(df,x< -3),fill="#f07050",alpha=.6) +
  geom_area(data=subset(df,x>  3),fill="#f07050",alpha=.6) +
  geom_area(data=subset(df,x>=-3&x<=-2),fill="#f7c87e",alpha=.35) +
  geom_area(data=subset(df,x>= 2&x<= 3),fill="#f7c87e",alpha=.35) +
  geom_area(data=subset(df,x>= -2&x<= 2),fill="cyan",alpha=.2) +
  geom_vline(xintercept=c(-3,3),color="#f07050",linetype="dashed",linewidth=1.1) +
  annotate("text",x=0,y=.18,label="99.73%\n(não alarme)",color="forestgreen",size=4) +
  annotate("text",x=3.6,y=.04,label="alpha/2",color="#f07050",size=3.5) +
  labs(title="Distribuição de X-barra com limites 3-sigma",x="Z",y="f(Z)") +
  theme_minimal(base_size=13)

library(ggplot2)
set.seed(11)
dados <- data.frame(t=1:25, y=rnorm(25,50,1))
ggplot(dados, aes(t,y)) +
  geom_line(color="white",linewidth=.7) +
  geom_point(size=2.5, color="#7ecff7") +
  geom_hline(yintercept=c(48,52),color="#f7c87e",
             linetype="dotted",linewidth=1.1) +
  geom_hline(yintercept=c(47,53),color="#f07050",
             linetype="dashed",linewidth=1.1) +
  geom_hline(yintercept=50,color="#a8f77e",linewidth=1) +
  annotate("text",x=24,y=52.2,label="LSA (2sigma)",
           color="#f7c87e",size=3.2,hjust=0) +
  annotate("text",x=24,y=53.2,label="LSC (3sigma)",
           color="#f07050",size=3.2,hjust=0) +
  annotate("text",x=26,y=50.2,label="LM",
           color="#a8f77e",size=3.2,hjust=0) +
  labs(title="Gráfico de Controle com Limites de Ação (3s) e Alerta (2s)",
       x="Amostra",y=expression(bar(x))) +
  theme_minimal(base_size=13)

library(ggplot2)
L <- 3; k_vals <- seq(0,4,by=0.05)
ns    <- c(1,3,5,10,20)
cores <- c("#f07050","#f7c87e","#7ecff7","#a8f77e","#c87ef7")
df <- do.call(rbind, lapply(seq_along(ns), function(i){
  n <- ns[i]
  data.frame(k=k_vals,
             beta=pnorm(L-k_vals*sqrt(n))-pnorm(-L-k_vals*sqrt(n)),
             n=paste0("n=",n))
}))
ggplot(df, aes(k,beta,color=n)) +
  geom_line(linewidth=1.2) +
  scale_color_manual(values=cores) +
  labs(title="Curva CO: probabilidade beta vs deslocamento k (L=3)",
       x="Deslocamento k (multiplos de sigma)",
       y="beta (prob. de não detectar)",color="") +
  theme_minimal(base_size=13)

library(ggplot2)
k  <- 1; L <- 3; ns <- 1:25
ARL1_vals <- 1/(1-(pnorm(L-k*sqrt(ns))-pnorm(-L-k*sqrt(ns))))
ggplot(data.frame(n=ns,ARL1=ARL1_vals), aes(n,ARL1)) +
  geom_line(color="#7ecff7",linewidth=1.3) +
  geom_point(color="#7ecff7",size=2) +
  geom_hline(yintercept=2,color="#f7c87e",linetype="dashed") +
  annotate("text",x=20,y=3,label="ARL1 = 2",color="#f7c87e",size=4) +
  labs(title=sprintf("ARL1 vs tamanho n (deslocamento k=%g sigma, L=%g)", k, L),
       x="Tamanho da amostra n",
       y="ARL1 (amostras ate detectar)") +
  theme_minimal(base_size=13)

library(ggplot2); library(patchwork)
set.seed(99)
d1 <- data.frame(sg=rep(1:12,each=5),
                 y=c(rnorm(50,10,1),rnorm(10,16,1)))
medias1 <- aggregate(y~sg, d1, mean)
sig1    <- mean(aggregate(y~sg, d1, sd)$y)

d2 <- data.frame(sg=rep(1:12,each=5),
  y=unlist(lapply(1:12,function(i)
    if(i %in% 5:8) c(rnorm(2,10,1),rnorm(3,16,1)) else rnorm(5,10,1))))
medias2 <- aggregate(y~sg, d2, mean)
sig2    <- mean(aggregate(y~sg, d2, sd)$y)

mk_cc <- function(med, sig, titulo, cor) {
  lsc_cc <- 10+3*sig/sqrt(5); lic_cc <- 10-3*sig/sqrt(5)
  med$fora <- med$y > lsc_cc | med$y < lic_cc
  ggplot(med, aes(sg,y)) +
    geom_line(color="white",linewidth=.6) +
    geom_point(aes(color=fora),size=2.5) +
    scale_color_manual(values=c("FALSE"=cor,"TRUE"="#f07050"),guide="none") +
    geom_hline(yintercept=c(lsc_cc,10,lic_cc),
               color=c("#f07050","#a8f77e","#f07050"),
               linetype=c("dashed","solid","dashed")) +
    labs(title=titulo, x="Subgrupo", y=expression(bar(x))) +
    theme_minimal(base_size=11)
}
mk_cc(medias1,sig1,"Abordagem 1: detecta salto (limites estreitos)","#7ecff7") +
mk_cc(medias2,sig2,"Abordagem 2: limites inflados, falha mascarada","#f7c87e")

library(ggplot2)
set.seed(12)
pts <- c(rnorm(9,0,1), rnorm(12,1.5,0.8))
df  <- data.frame(t=seq_along(pts), y=pts,
                  weco=c(rep("Normal",9),rep("Regra 4",12)))
ggplot(df, aes(t,y)) +
  annotate("rect",xmin=-Inf,xmax=Inf,ymin=2,ymax=3,
           fill="#f07050",alpha=.15) +
  annotate("rect",xmin=-Inf,xmax=Inf,ymin=-3,ymax=-2,
           fill="#f07050",alpha=.15) +
  annotate("rect",xmin=-Inf,xmax=Inf,ymin=1,ymax=2,
           fill="#f7c87e",alpha=.12) +
  annotate("rect",xmin=-Inf,xmax=Inf,ymin=-2,ymax=-1,
           fill="#f7c87e",alpha=.12) +
  geom_line(color="white",linewidth=.7)+
  geom_point(aes(color=weco),size=3)+
  scale_color_manual(values=c("Normal"="#7ecff7","Regra 4"="#f7c87e"))+
  geom_hline(yintercept=c(3,2,1,0,-1,-2,-3),
             color=c("#f07050","#f7c87e","#a8f77e","#a8f77e",
                     "#a8f77e","#f7c87e","#f07050"),
             linetype=c("dashed","dotted","dotted","solid",
                        "dotted","dotted","dashed"),linewidth=.8)+
  annotate("segment",x=10,xend=17,y=-0.5,yend=-0.5,
           color="#f7c87e",linewidth=1.2,
           arrow=arrow(ends="both",length=unit(.15,"cm")))+
  annotate("text",x=13.5,y=-0.85,
           label="8 pts acima da LM (Regra 4)",
           color="#f7c87e",size=3.5)+
  labs(title="Gráfico de Controle com Detecção da Regra 4",
       x="Amostra",y="Estatistica",color="")+
  theme_minimal(base_size=13)

library(ggplot2); library(patchwork)
set.seed(33)
f1 <- rnorm(20,50,1); f1[8] <- 56
f2 <- rnorm(15,50,1)
m_ok <- mean(f1[-8]); s_ok <- sd(f1[-8])
lsc_ok <- m_ok+3*s_ok; lic_ok <- m_ok-3*s_ok

mk_fase <- function(y, titulo, cor, extra=NULL){
  df <- data.frame(t=seq_along(y),y=y,fora=y>lsc_ok|y<lic_ok)
  p  <- ggplot(df,aes(t,y))+
    geom_line(color="white",linewidth=.6)+
    geom_point(aes(color=fora),size=2.5)+
    scale_color_manual(values=c("FALSE"=cor,"TRUE"="#f07050"),guide="none")+
    geom_hline(yintercept=c(lsc_ok,m_ok,lic_ok),
               color=c("#f07050","#a8f77e","#f07050"),
               linetype=c("dashed","solid","dashed"))+
    labs(title=titulo,x="Subgrupo",y="")+
    theme_minimal(base_size=11)
  if(!is.null(extra)) p <- p + extra
  p
}
p1 <- mk_fase(f1,"Fase I: Analise Retrospectiva","#7ecff7",
  annotate("point",x=8,y=56,color="#f07050",size=5,shape=4,stroke=2.5))
p2 <- mk_fase(f2,"Fase II: Monitoramento Prospectivo","#a8f77e")
p1 + p2

library(ggplot2)
set.seed(5)
dados <- data.frame(d=c(rnorm(90,74,.008), rnorm(10,74.02,.006)))
ggplot(dados, aes(x=d)) +
  geom_histogram(aes(y=after_stat(density)),bins=20,
                 fill="#7ecff7",color="black",alpha=.8)+
  stat_function(fun=dnorm,args=list(mean=74,sd=.008),
                color="#f07050",linewidth=1.3)+
  geom_vline(xintercept=c(74-3*.008,74,74+3*.008),
             color=c("#f07050","#a8f77e","#f07050"),
             linetype=c("dashed","solid","dashed"),linewidth=1)+
  annotate("text",x=74-3.5*.008+.001,y=20,label="LIC",
           color="#f07050",size=3.5,hjust=0)+
  annotate("text",x=74+3*.008+.001,y=20,label="LSC",
           color="#f07050",size=3.5,hjust=0)+
  labs(title="Histograma com Limites 3-sigma sobrepostos",
       x="Diametro (mm)",y="Densidade")+
  theme_minimal(base_size=13)

library(ggplot2)
defeitos <- data.frame(
  Falha   =factor(c("Vazamento","Ferrugem","Quebra","Furo"),
                  levels=c("Vazamento","Ferrugem","Quebra","Furo")),
  Contagem=c(140,40,15,5))
defeitos$Cum <- cumsum(defeitos$Contagem)/sum(defeitos$Contagem)
total <- sum(defeitos$Contagem)
ggplot(defeitos, aes(x=Falha)) +
  geom_col(aes(y=Contagem),fill="#7ecff7",color="black")+
  geom_line(aes(y=Cum*total,group=1),color="#f07050",linewidth=1.3)+
  geom_point(aes(y=Cum*total),color="#f07050",size=3)+
  geom_hline(yintercept=.8*total,color="#f7c87e",
             linetype="dashed",linewidth=.9)+
  annotate("text",x=3.5,y=.82*total,label="80%",color="#f7c87e",size=4)+
  scale_y_continuous(name="Frequencia",
    sec.axis=sec_axis(~./total,name="Frequencia Acumulada",
                      labels=scales::percent))+
  labs(title="Gráfico de Pareto: Defeitos em Valvulas",x="")+
  theme_minimal(base_size=13)

library(ggplot2)
set.seed(7)
loc <- data.frame(
  x    = c(runif(15,.6,.9), runif(5,.1,.4)),
  y    = c(runif(15,.3,.7), runif(5,.1,.9)),
  tipo = c(rep("Lateral direita (70%)",15), rep("Outras regioes (30%)",5))
)
ggplot(loc, aes(x,y,color=tipo)) +
  annotate("rect",xmin=0,xmax=1,ymin=0,ymax=1,
           fill="grey15",color="#7ecff7",linewidth=1.2)+
  geom_point(size=5,shape=4,stroke=2)+
  scale_color_manual(values=c("Lateral direita (70%)"="#f07050",
                               "Outras regioes (30%)"="#7ecff7"))+
  scale_x_continuous(breaks=c(0,1),labels=c("Esq.","Dir."))+
  scale_y_continuous(breaks=c(0,1),labels=c("Inf.","Sup."))+
  labs(title="Diagrama de Concentração de Defeitos (Vista Frontal)",
       x="",y="",color="")+
  theme_minimal(base_size=13)

library(ggplot2)
set.seed(88)
velocidade  <- runif(30,100,200)
nivelamento <- 5 + 0.05*velocidade + rnorm(30,0,1.5)
d <- data.frame(velocidade, nivelamento)
r <- cor(velocidade, nivelamento)
ggplot(d, aes(velocidade,nivelamento)) +
  geom_point(color="#7ecff7",size=3)+
  geom_smooth(method="lm",color="#f07050",
              linetype="dashed",linewidth=1.2,se=TRUE)+
  annotate("text",x=110,y=15,
           label=sprintf("r = %.3f",r),color="#f7c87e",size=5)+
  labs(title="Dispersao: Velocidade da Fresa vs Desvio de Nivelamento",
       x="Velocidade da fresa (rpm)",y="Desvio de nivelamento (mm)")+
  theme_minimal(base_size=13)

library(ggplot2)
df_caso <- data.frame(
  y    = c(placa_antes, placa_apos),
  fase = rep(c("Antes do reparo","Apos o reparo"), each=10),
  obs  = rep(1:10, 2)
)
ggplot(df_caso, aes(x=obs,y=y,color=fase)) +
  geom_line(linewidth=1.1) + geom_point(size=3) +
  scale_color_manual(values=c("Antes do reparo"="#f07050",
                               "Apos o reparo"="#7ecff7"))+
  geom_hline(yintercept=mean(placa_antes),color="#f07050",
             linetype="dashed",linewidth=.8)+
  geom_hline(yintercept=mean(placa_apos),color="#7ecff7",
             linetype="dashed",linewidth=.8)+
  labs(title="Espessura de Cobre: Antes e Apos Reparo do Colorimetro",
       x="Observação",y="Espessura (unidades)",color="")+
  theme_minimal(base_size=13)

library(ggplot2)
ggplot(data.frame(v=fase_i),aes(sample=v)) +
  stat_qq(color="#7ecff7",size=2.5) +
  stat_qq_line(color="#f07050",linewidth=1.2) +
  labs(title="Q-Q Plot: Validação Normal dos Dados da Fase I",
       x="Quantis Teoricos",y="Quantis Amostrais") +
  theme_minimal(base_size=13)

library(ggplot2); library(patchwork)
set.seed(10)
# Dados "originais" com mudanca de nível em t=25
pop <- c(rnorm(24,10,1), rnorm(24,12,1))
# Subgrupos de n=3
sg3 <- tapply(pop, rep(1:16, each=3), mean)
# Subgrupos de n=8
sg8 <- tapply(pop, rep(1:6, each=8), mean)

mk_sg <- function(med, n_sg, titulo) {
  sig_p <- 1; lsc_p <- 10+3*sig_p/sqrt(n_sg); lic_p <- 10-3*sig_p/sqrt(n_sg)
  df <- data.frame(t=seq_along(med), y=med, fora=med>lsc_p|med<lic_p)
  ggplot(df,aes(t,y)) +
    geom_line(color="white",linewidth=.6) +
    geom_point(aes(color=fora),size=2.5) +
    scale_color_manual(values=c("FALSE"="#7ecff7","TRUE"="#f07050"),guide="none") +
    geom_hline(yintercept=c(lsc_p,10,lic_p),
               color=c("#f07050","#a8f77e","#f07050"),
               linetype=c("dashed","solid","dashed")) +
    labs(title=titulo, x="Subgrupo", y=expression(bar(x))) +
    theme_minimal(base_size=11)
}
mk_sg(sg3, 3, "n=3: detecta grandes mudancas") +
mk_sg(sg8, 8, "n=8: detecta mudancas menores")

library(ggplot2); library(patchwork)
set.seed(42); lm0 <- 0

# Regra 6: 15 pontos consecutivos dentro da Zona C (estratificação)
y6 <- rnorm(20, 0, 0.4)  # baixa variância → pontos colados na LM

# Regra 7: 14 pontos alternando acima/abaixo
y7 <- rep(c(1.2,-1.2), 10) + rnorm(20,0,.15)

mk3 <- function(y, titulo, cor="#7ecff7") {
  df <- data.frame(t=seq_along(y), y=y, fora=abs(y)>3)
  ggplot(df,aes(t,y)) +
    geom_line(color="white",linewidth=.5) +
    geom_point(aes(color=fora),size=2) +
    scale_color_manual(values=c("FALSE"=cor,"TRUE"="#f07050"),guide="none") +
    geom_hline(yintercept=c(3,2,1,0,-1,-2,-3),
               color=c("#f07050","#f7c87e","#a8f77e","#a8f77e",
                       "#a8f77e","#f7c87e","#f07050"),
               linetype=c("dashed","dotted","dotted","solid",
                          "dotted","dotted","dashed"),linewidth=.7) +
    labs(title=titulo,x="",y="") + theme_minimal(base_size=10)
}
mk3(y6, "Regra 6: 15 pts na Zona C (estratificação)", "#a8f77e") +
mk3(y7, "Regra 7: 14 pts alternando cima/baixo",      "#f7c87e")

library(ggplot2); library(patchwork)
set.seed(7)

# Mistura vs Estratificação
y_mist  <- c(rnorm(10,0,1) + rep(c(-1.8,1.8),5))
y_estra <- rnorm(20,0,0.3)

# Deslocamento vs Tendencia
y_desl <- c(rnorm(10,0,1), rnorm(10,2,1))
y_tend <- seq(0,3,length.out=20)+rnorm(20,0,.25)

mk3v <- function(y,titulo,cor="#7ecff7") {
  df <- data.frame(t=seq_along(y),y=y,fora=abs(y)>3)
  ggplot(df,aes(t,y)) +
    geom_line(color="white",linewidth=.5) +
    geom_point(aes(color=fora),size=2) +
    scale_color_manual(values=c("FALSE"=cor,"TRUE"="#f07050"),guide="none") +
    geom_hline(yintercept=c(3,0,-3),
               color=c("#f07050","#a8f77e","#f07050"),
               linetype=c("dashed","solid","dashed"),linewidth=.7) +
    labs(title=titulo,x="",y="") + theme_minimal(base_size=10)
}
(mk3v(y_mist,"Mistura: pontos nas bordas","#f07050") +
 mk3v(y_estra,"Estratificação: pontos no centro","#a8f77e")) /
(mk3v(y_desl,"Deslocamento: salto abrupto","#c87ef7") +
 mk3v(y_tend,"Tendencia: subida gradual","#f7c87e"))

library(ggplot2)
# Simulando a instabilidade da estimativa de sigma com poucos subgrupos
set.seed(22)
sigma_true <- 1
resultados <- sapply(5:40, function(m) {
  medias_R <- replicate(500, {
    dados <- matrix(rnorm(m*5, 0, sigma_true), nrow=m)
    R_bar <- mean(apply(dados,1,function(x) diff(range(x))))
    R_bar / 2.326  # d2 para n=5
  })
  c(media=mean(medias_R), dp=sd(medias_R))
})
df_m <- data.frame(m=5:40,
                   media=resultados["media",],
                   dp=resultados["dp",])
ggplot(df_m,aes(m,dp)) +
  geom_line(color="#7ecff7",linewidth=1.3) +
  geom_vline(xintercept=c(20,25),color=c("#f7c87e","#a8f77e"),
             linetype="dashed",linewidth=1) +
  annotate("text",x=21,y=.035,label="m=20",color="#f7c87e",size=3.5,hjust=0) +
  annotate("text",x=26,y=.035,label="m=25",color="#a8f77e",size=3.5,hjust=0) +
  labs(title="Variabilidade da estimativa de sigma vs numero de subgrupos m (n=5)",
       x="Numero de subgrupos m",y="DP da estimativa de sigma") +
  theme_minimal(base_size=13)

library(ggplot2); library(patchwork)
set.seed(8)
x_ind <- c(rnorm(18,50,2), rnorm(7,54,2))
MR    <- c(NA, abs(diff(x_ind)))
xbar  <- mean(x_ind[1:18]); MRbar <- mean(MR[2:19],na.rm=TRUE)
d2    <- 1.128
LSC_I <- xbar + 3*MRbar/d2; LIC_I <- xbar - 3*MRbar/d2
LSC_MR <- 3.267*MRbar

df_i  <- data.frame(t=seq_along(x_ind), y=x_ind,
                    fora=x_ind>LSC_I|x_ind<LIC_I)
df_mr <- data.frame(t=seq_along(MR),    y=MR,
                    fora=!is.na(MR)&MR>LSC_MR)

p1 <- ggplot(df_i,aes(t,y))+
  geom_line(color="white",linewidth=.6)+
  geom_point(aes(color=fora),size=2.5)+
  scale_color_manual(values=c("FALSE"="#7ecff7","TRUE"="#f07050"),guide="none")+
  geom_hline(yintercept=c(LSC_I,xbar,LIC_I),
             color=c("#f07050","#a8f77e","#f07050"),
             linetype=c("dashed","solid","dashed"))+
  labs(title="Gráfico I (Individuos)",x="",y="X")+theme_minimal(base_size=11)

p2 <- ggplot(df_mr,aes(t,y))+
  geom_line(color="white",linewidth=.6)+
  geom_point(aes(color=fora),size=2.5)+
  scale_color_manual(values=c("FALSE"="#a8f77e","TRUE"="#f07050"),guide="none")+
  geom_hline(yintercept=c(LSC_MR,MRbar,0),
             color=c("#f07050","#a8f77e","#a8f77e"),
             linetype=c("dashed","solid","solid"))+
  labs(title="Gráfico MR (Amplitude Móvel)",x="Observação",y="MR")+
  theme_minimal(base_size=11)
p1/p2

library(ggplot2)
set.seed(8)
dados_cap <- rnorm(200, 74, 0.008)
LIE <- 73.98; LSE <- 74.02
mu_h <- mean(dados_cap); sg_h <- sd(dados_cap)
x_seq <- seq(73.96,74.04,length.out=400)
df_cap <- data.frame(x=x_seq, y=dnorm(x_seq,mu_h,sg_h))
ggplot(df_cap,aes(x,y)) +
  geom_line(color="white",linewidth=1.3) +
  geom_area(data=subset(df_cap,x<LIE),fill="#f07050",alpha=.6) +
  geom_area(data=subset(df_cap,x>LSE),fill="#f07050",alpha=.6) +
  geom_area(data=subset(df_cap,x>LIE&x<LSE),fill="#7ecff7",alpha=.2) +
  geom_vline(xintercept=c(LIE,LSE),color="#f7c87e",
             linetype="dashed",linewidth=1.2) +
  geom_vline(xintercept=c(mu_h-3*sg_h,mu_h+3*sg_h),color="#7ecff7",
             linetype="dotted",linewidth=1) +
  annotate("text",x=LIE-.002,y=20,label="LIE",color="#f7c87e",size=4,hjust=1) +
  annotate("text",x=LSE+.002,y=20,label="LSE",color="#f7c87e",size=4,hjust=0) +
  labs(title=sprintf("Capacidade do Processo: Cp=%.2f, Cpk=%.2f",
                     (LSE-LIE)/(6*sg_h),
                     min((LSE-mu_h)/(3*sg_h),(mu_h-LIE)/(3*sg_h))),
       x="Diametro (mm)",y="Densidade") +
  theme_minimal(base_size=13)

library(ggplot2); library(patchwork)
set.seed(13)
m <- 20; n <- 5; mu0 <- 74; sigma0 <- 0.01
dados_xr <- matrix(rnorm(m*n, mu0, sigma0), nrow=m)
xbars <- apply(dados_xr,1,mean)
Rs    <- apply(dados_xr,1,function(x) diff(range(x)))
xbb   <- mean(xbars); Rbar  <- mean(Rs)
d2 <- 2.326; D3 <- 0; D4 <- 2.114; A2 <- 0.577

lsc_x <- xbb + A2*Rbar; lic_x <- xbb - A2*Rbar
lsc_r <- D4*Rbar;        lic_r <- D3*Rbar

df_x <- data.frame(t=1:m,y=xbars,fora=xbars>lsc_x|xbars<lic_x)
df_r <- data.frame(t=1:m,y=Rs,   fora=Rs>lsc_r|Rs<lic_r)

px <- ggplot(df_x,aes(t,y)) +
  geom_line(color="white",linewidth=.6) +
  geom_point(aes(color=fora),size=2.5) +
  scale_color_manual(values=c("FALSE"="#7ecff7","TRUE"="#f07050"),guide="none") +
  geom_hline(yintercept=c(lsc_x,xbb,lic_x),
             color=c("#f07050","#a8f77e","#f07050"),
             linetype=c("dashed","solid","dashed")) +
  labs(title=expression(paste("Gráfico ",bar(X))),x="",y=expression(bar(x))) +
  theme_minimal(base_size=11)

pr <- ggplot(df_r,aes(t,y)) +
  geom_line(color="white",linewidth=.6) +
  geom_point(aes(color=fora),size=2.5) +
  scale_color_manual(values=c("FALSE"="#a8f77e","TRUE"="#f07050"),guide="none") +
  geom_hline(yintercept=c(lsc_r,Rbar,lic_r),
             color=c("#f07050","#a8f77e","#a8f77e"),
             linetype=c("dashed","solid","solid")) +
  labs(title="Gráfico R",x="Subgrupo",y="R") +
  theme_minimal(base_size=11)
px/pr