# In control
# equivalência entre lambda e p0
lamb_x_in=0.8
lamb_x_out=1.4
n=105
d=3  #até 3 não conformidades é boa
p0=1-sum(dpois(0:d, lamb_x_in)); "p0";p0

[1] "p0"
[1] 0.009079858

LSC_np=n*p0 + 3*sqrt(n*p0*(1-p0)); LSC_np=round(LSC_np,0)
alfa_np = 1-(sum(dbinom(0:LSC_np,n,p0))); "alfa_np"; round(alfa_np,4)

[1] "alfa_np"
[1] 0.0028

ARLo_np=1/(alfa_np); "ARLo_np"; ARLo_np

[1] "ARLo_np"
[1] 355.5593

# Out of control
# equivalência entre lambda e p1
p1=1-sum(dpois(0:d, lamb_x_out)); "p1";p1

[1] "p1"
[1] 0.05372525

beta_np = sum(dbinom(0:LSC_np,n,p1))
poder_np=1-beta_np; "poder_np"; round(poder_np,4)

[1] "poder_np"
[1] 0.6708

ARL1_np=1/(1-beta_np); "ARL1_np"; ARL1_np

[1] "ARL1_np"
[1] 1.490653

#in control
n=5
lamb_x_in <- n*0.80 # valor de c
LSC_c=lamb_x_in + 3*sqrt(lamb_x_in) ;  "LSC_c"; LSC_c  

[1] "LSC_c"
[1] 10

alfa_c = 1-(sum(dpois(0:LSC_c, lamb_x_in))); "alfa_c"; round(alfa_c,4)

[1] "alfa_c"
[1] 0.0028

ARLo_c=1/(alfa_c); "ARLo_c"; ARLo_c

[1] "ARLo_c"
[1] 352.1417

# Out of control
lamb_x_out <-  n*1.4 # valor de c com shift
beta_c = sum(dpois(0:LSC_c, lamb_x_out))
poder_c=(1-beta_c); "Poder_c"; round(poder_c,4)

[1] "Poder_c"
[1] 0.0985

ARL1_c=1/(1-beta_c); "ARL1_c"; ARL1_c

[1] "ARL1_c"
[1] 10.15014

"ARLo_np"; ARLo_np

[1] "ARLo_np"
[1] 355.5593

"ARLo_c";ARLo_c

[1] "ARLo_c"
[1] 352.1417

"ARL1_np";ARL1_np

[1] "ARL1_np"
[1] 1.490653

"ARL1_c";ARL1_c

[1] "ARL1_c"
[1] 10.15014

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