Desempenho do gráfico de controle c. Exemplo do livro: MONTGOMERY, D. C. Introdução ao Controle Estatístico da Qualidade. 4. ed. Rio de Janeiro: LTC, 2004. Tópico 6.3.4 Página 203

library(knitr)

In contol

#in control
lamb_x_in <- 20 # valor de c
LSC=(33.22); "LSC"; LSC

[1] "LSC"
[1] 33.22

LIC=(6.48); "LIC"; LIC

[1] "LIC"
[1] 6.48

prob=data.frame(0)
beta<-0
pr=0
for (x in 0:LSC) {
  prob[x+1] <- dpois(x, lamb_x_in)
if (x>= LIC && x<=LSC ) { 
pr=prob[x+1]
beta=beta+pr
                  }
                    }
round(beta,3)

ARLo=1/(1-beta); "ARLo"; ARLo

[1] "ARLo"

#print(prob)

Out of control

# out of control
lamb_x_out <- c(1.0*lamb_x_in, 1.05*lamb_x_in, 1.10*lamb_x_in, 1.15*lamb_x_in, 1.20*lamb_x_in, 1.25*lamb_x_in, 1.30*lamb_x_in, 1.40*lamb_x_in, 1.50*lamb_x_in, 2*lamb_x_in)  # valor de c com shift
n=length(lamb_x_out)
prob=data.frame(0)
beta<-0
pr=0
posicao=1
for (posicao in 1:n) {
  for (x in 0:LSC) {
    prob[x+1] <- dpois(x, lamb_x_out[posicao])
      if (x>= LIC && x<=LSC ) { 
        pr=prob[x+1]
        beta=beta+pr
                              }
                  }
                    #print(round(beta,3))
  ARL=1/(1-beta)
  print("shift"); 
  print(lamb_x_out[posicao]/lamb_x_in);
  print("c");
  print(lamb_x_out[posicao]);
  print("ARL");
  print(ARL);
  beta=0; pr=0  #zerar
}

[1] "shift"
[1] 1
[1] "c"
[1] 20
[1] "ARL"

[1] "shift"
[1] 1.05
[1] "c"
[1] 21
[1] "ARL"

[1] "shift"
[1] 1.1
[1] "c"
[1] 22
[1] "ARL"

[1] "shift"
[1] 1.15
[1] "c"
[1] 23
[1] "ARL"

[1] "shift"
[1] 1.2
[1] "c"
[1] 24
[1] "ARL"

[1] "shift"
[1] 1.25
[1] "c"
[1] 25
[1] "ARL"

[1] "shift"
[1] 1.3
[1] "c"
[1] 26
[1] "ARL"

[1] "shift"
[1] 1.4
[1] "c"
[1] 28
[1] "ARL"

[1] "shift"
[1] 1.5
[1] "c"
[1] 30
[1] "ARL"

[1] "shift"
[1] 2
[1] "c"
[1] 40
[1] "ARL"

  
#print(prob)