Desempenho do gráfico de controle np. Exemplo do livro: MONTGOMERY, D. C. Introdução ao Controle Estatístico da Qualidade. 4. ed. Rio de Janeiro: LTC, 2004. Tópico 6.2.4 Página 192

library(knitr)

In contol

#in control
p0=0.20
n=50
LSC=0.3697; "LSC"; LSC

[1] "LSC"
[1] 0.3697

LIC=0.0303; "LIC"; LIC

[1] "LIC"
[1] 0.0303

Dinf=trunc(n*LIC,1)
Dsup=trunc(n*LSC,1)
beta = sum(dbinom(0:Dsup,n,p0)) - sum(dbinom(0:Dinf,n,p0))
round(beta,5)

[1] 0.9973

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

[1] "ARLo"
[1] 369.8387

#print(prob)

Out of control

# out of control
p1=c(1.00,1.05,1.10,1.15,1.20,1.25,1.30,1.40,1.50,2.00)*p0
#print(prob)
for (shift in 1:length(p1)) {
  
beta = sum(dbinom(0:Dsup,n,p1[shift])) - sum(dbinom(0:Dinf,n,p1[shift]))
ARL1=1/(1-beta); "ARL1"; ARL1
print("shift")
print(p1[shift]/p0)
print("p_out")
print(p1[shift])
print("ARL")
print(ARL1)
}

[1] "shift"
[1] 1
[1] "p_out"
[1] 0.2
[1] "ARL"
[1] 369.8387
[1] "shift"
[1] 1.05
[1] "p_out"
[1] 0.21
[1] "ARL"
[1] 219.2371
[1] "shift"
[1] 1.1
[1] "p_out"
[1] 0.22
[1] "ARL"
[1] 131.6029
[1] "shift"
[1] 1.15
[1] "p_out"
[1] 0.23
[1] "ARL"
[1] 81.53256
[1] "shift"
[1] 1.2
[1] "p_out"
[1] 0.24
[1] "ARL"
[1] 52.33865
[1] "shift"
[1] 1.25
[1] "p_out"
[1] 0.25
[1] "ARL"
[1] 34.79088
[1] "shift"
[1] 1.3
[1] "p_out"
[1] 0.26
[1] "ARL"
[1] 23.90272
[1] "shift"
[1] 1.4
[1] "p_out"
[1] 0.28
[1] "ARL"
[1] 12.35411
[1] "shift"
[1] 1.5
[1] "p_out"
[1] 0.3
[1] "ARL"
[1] 7.114385
[1] "shift"
[1] 2
[1] "p_out"
[1] 0.4
[1] "ARL"
[1] 1.505147

#print(prob)