Código fonte para avaliar o desempenho conjunto do GC X_barra e R

definição do erro tipo I e constantes dos LC de X_bar e R

# função para achar a contante de abertura dos LC de R
# adotar LIC_R=0
GCR <- function (n,alfa) {
Fnw=0; ws=0
while (Fnw<=1-alfa)  {
ws=ws+0.01   
integrando <- function(z) {((1/(sqrt(2*pi)))*exp(-(z^2)/2))*(pnorm(z+ws)-pnorm(z))^(n-1)}
Fnw=integrate(integrando, lower=-Inf, upper=Inf) 
Fnw=n*as.numeric(Fnw[1])
}
print(ws)
}
#n=4
#alfa=.0012
#GCR(n,alfa)

# escolha do erro alfa  -> NMAo
# alfa < 0.0027  => NMAo >= 370.4
n=4
alfa_r=0.0012
alfa_xbar=0.0012
alfa=alfa_xbar+alfa_r - alfa_xbar*alfa_r
NMAo=1/alfa

#alfa=0.0012
# contantes dos limites de controle 
k=-qnorm(alfa_xbar/2)
w=GCR(n,alfa)

[1] 4.99

print("NMAo"); NMAo

[1] "NMAo"
[1] 416.9168

print("contante para x_bar"); k

[1] "contante para x_bar"
[1] 3.23888

print("contante para R"); w

[1] "contante para R"
[1] 4.99

Cálculo do Poder/desempenho do GC X_barra e R

# GC de X_bar
# calculo do poder de X_bar
#n= ;k=
delta=0.0 # desvio na média; 
lambda= 1 #desvio no desvio-padrão
i=1    

result_xbar=matrix(c(NA),77,4)
while(lambda <= 2.1) {
   while (delta <= 3) {
exp1 <- -(k+delta*sqrt(n))/lambda
exp2 <- (-k+delta*sqrt(n))/lambda
poder=pnorm(exp1)+pnorm(exp2)
result_xbar[i,1] <-delta; 
result_xbar[i,2] <-lambda; 
result_xbar[i,3] <-poder #poder  
result_xbar[i,4] <-1/poder #NMA
i=i+1;
#print(i)
delta=delta+0.5  }
delta=0.0
lambda=lambda+0.1 }

colnames(result_xbar) <- c("delta","lambda", "Poder", "NMA")
kableExtra::kable(round(result_xbar,4))

delta	lambda	Poder	NMA
0.0	1.0	0.0012	833.3333
0.5	1.0	0.0126	79.4086
1.0	1.0	0.1077	9.2855
1.5	1.0	0.4056	2.4655
2.0	1.0	0.7767	1.2875
2.5	1.0	0.9609	1.0407
3.0	1.0	0.9971	1.0029
0.0	1.1	0.0032	309.0776
0.5	1.1	0.0210	47.6957
1.0	1.1	0.1300	7.6905
1.5	1.1	0.4140	2.4152
2.0	1.1	0.7555	1.3236
2.5	1.1	0.9453	1.0579
3.0	1.1	0.9940	1.0061
0.0	1.2	0.0070	143.8141
0.5	1.2	0.0312	32.0049
1.0	1.2	0.1509	6.6248
1.5	1.2	0.4211	2.3747
2.0	1.2	0.7370	1.3568
2.5	1.2	0.9289	1.0765
3.0	1.2	0.9893	1.0108
0.0	1.3	0.0127	78.6014
0.5	1.3	0.0431	23.2175
1.0	1.3	0.1703	5.8711
1.5	1.3	0.4271	2.3413
2.0	1.3	0.7209	1.3872
2.5	1.3	0.9122	1.0962
3.0	1.3	0.9832	1.0171
0.0	1.4	0.0207	48.3186
0.5	1.4	0.0561	17.8190
1.0	1.4	0.1882	5.3137
1.5	1.4	0.4323	2.3134
2.0	1.4	0.7067	1.4151
2.5	1.4	0.8958	1.1163
3.0	1.4	0.9757	1.0249
0.0	1.5	0.0308	32.4354
0.5	1.5	0.0701	14.2592
1.0	1.5	0.2047	4.8861
1.5	1.5	0.4368	2.2896
2.0	1.5	0.6941	1.4408
2.5	1.5	0.8798	1.1366
3.0	1.5	0.9672	1.0339
0.0	1.6	0.0429	23.2887
0.5	1.6	0.0849	11.7793
1.0	1.6	0.2199	4.5474
1.5	1.6	0.4407	2.2691
2.0	1.6	0.6829	1.4644
2.5	1.6	0.8645	1.1568
3.0	1.6	0.9578	1.0441
0.0	1.7	0.0568	17.6208
0.5	1.7	0.1002	9.9754
1.0	1.7	0.2341	4.2716
1.5	1.7	0.4442	2.2510
2.0	1.7	0.6728	1.4863
2.5	1.7	0.8499	1.1766
3.0	1.7	0.9478	1.0550
0.0	1.8	0.0720	13.8968
0.5	1.8	0.1160	8.6173
1.0	1.8	0.2474	4.0413
1.5	1.8	0.4475	2.2348
2.0	1.8	0.6638	1.5064
2.5	1.8	0.8361	1.1961
3.0	1.8	0.9375	1.0667
0.0	1.9	0.0883	11.3308
0.5	1.9	0.1322	7.5661
1.0	1.9	0.2601	3.8447
1.5	1.9	0.4505	2.2198
2.0	1.9	0.6557	1.5251
2.5	1.9	0.8230	1.2150
3.0	1.9	0.9269	1.0788
0.0	2.0	0.1054	9.4919
0.5	2.0	0.1485	6.7339
1.0	2.0	0.2722	3.6735
1.5	2.0	0.4534	2.2057
2.0	2.0	0.6484	1.5423
2.5	2.0	0.8107	1.2334
3.0	2.0	0.9163	1.0914

# GC de R
# calculo do poder do GC R

#k=3.24

Fnw=0; ws=0
while (Fnw<=1-alfa/2)  {
ws=ws+0.01   
integrando <- function(z) {((1/(sqrt(2*pi)))*exp(-(z^2)/2))*(pnorm(z+ws)-pnorm(z))^(n-1)}
Fnw=integrate(integrando, lower=-Inf, upper=Inf) 
Fnw=n*as.numeric(Fnw[1])
}

lambda=1.0;i=1                                                    
result_r=matrix(c(NA),11,3)
while (lambda<=2.1)  {
integrando <- function(z) {((1/(sqrt(2*pi)))*exp(-(z^2)/2))*(pnorm(z+ws/lambda)-pnorm(z))^(n-1)}
Fnw=integrate(integrando, lower=-Inf, upper=Inf)  #list
Fnw=1-n*as.numeric(Fnw[1]) # poder Pr[W>Ws|n=n0]

result_r[i,1] <-lambda
result_r[i,2] <-Fnw   #poder  
result_r[i,3] <-1/Fnw #NMA
i=i+1; lambda=lambda+0.1
}

colnames(result_r) <- c("lambda", "Poder", "NMA")
kableExtra::kable(round(result_r,4))

lambda	Poder	NMA
1.0	0.0012	850.0642
1.1	0.0041	243.0293
1.2	0.0107	93.8212
1.3	0.0223	44.8167
1.4	0.0400	25.0008
1.5	0.0639	15.6553
1.6	0.0934	10.7024
1.7	0.1277	7.8296
1.8	0.1656	6.0402
1.9	0.2058	4.8603
2.0	0.2472	4.0453

Poder Global X_bar e R

kableExtra::kable(round(result_xbar,4))

delta	lambda	Poder	NMA
0.0	1.0	0.0012	833.3333
0.5	1.0	0.0126	79.4086
1.0	1.0	0.1077	9.2855
1.5	1.0	0.4056	2.4655
2.0	1.0	0.7767	1.2875
2.5	1.0	0.9609	1.0407
3.0	1.0	0.9971	1.0029
0.0	1.1	0.0032	309.0776
0.5	1.1	0.0210	47.6957
1.0	1.1	0.1300	7.6905
1.5	1.1	0.4140	2.4152
2.0	1.1	0.7555	1.3236
2.5	1.1	0.9453	1.0579
3.0	1.1	0.9940	1.0061
0.0	1.2	0.0070	143.8141
0.5	1.2	0.0312	32.0049
1.0	1.2	0.1509	6.6248
1.5	1.2	0.4211	2.3747
2.0	1.2	0.7370	1.3568
2.5	1.2	0.9289	1.0765
3.0	1.2	0.9893	1.0108
0.0	1.3	0.0127	78.6014
0.5	1.3	0.0431	23.2175
1.0	1.3	0.1703	5.8711
1.5	1.3	0.4271	2.3413
2.0	1.3	0.7209	1.3872
2.5	1.3	0.9122	1.0962
3.0	1.3	0.9832	1.0171
0.0	1.4	0.0207	48.3186
0.5	1.4	0.0561	17.8190
1.0	1.4	0.1882	5.3137
1.5	1.4	0.4323	2.3134
2.0	1.4	0.7067	1.4151
2.5	1.4	0.8958	1.1163
3.0	1.4	0.9757	1.0249
0.0	1.5	0.0308	32.4354
0.5	1.5	0.0701	14.2592
1.0	1.5	0.2047	4.8861
1.5	1.5	0.4368	2.2896
2.0	1.5	0.6941	1.4408
2.5	1.5	0.8798	1.1366
3.0	1.5	0.9672	1.0339
0.0	1.6	0.0429	23.2887
0.5	1.6	0.0849	11.7793
1.0	1.6	0.2199	4.5474
1.5	1.6	0.4407	2.2691
2.0	1.6	0.6829	1.4644
2.5	1.6	0.8645	1.1568
3.0	1.6	0.9578	1.0441
0.0	1.7	0.0568	17.6208
0.5	1.7	0.1002	9.9754
1.0	1.7	0.2341	4.2716
1.5	1.7	0.4442	2.2510
2.0	1.7	0.6728	1.4863
2.5	1.7	0.8499	1.1766
3.0	1.7	0.9478	1.0550
0.0	1.8	0.0720	13.8968
0.5	1.8	0.1160	8.6173
1.0	1.8	0.2474	4.0413
1.5	1.8	0.4475	2.2348
2.0	1.8	0.6638	1.5064
2.5	1.8	0.8361	1.1961
3.0	1.8	0.9375	1.0667
0.0	1.9	0.0883	11.3308
0.5	1.9	0.1322	7.5661
1.0	1.9	0.2601	3.8447
1.5	1.9	0.4505	2.2198
2.0	1.9	0.6557	1.5251
2.5	1.9	0.8230	1.2150
3.0	1.9	0.9269	1.0788
0.0	2.0	0.1054	9.4919
0.5	2.0	0.1485	6.7339
1.0	2.0	0.2722	3.6735
1.5	2.0	0.4534	2.2057
2.0	2.0	0.6484	1.5423
2.5	2.0	0.8107	1.2334
3.0	2.0	0.9163	1.0914

kableExtra::kable(round(result_r,4))

lambda	Poder	NMA
1.0	0.0012	850.0642
1.1	0.0041	243.0293
1.2	0.0107	93.8212
1.3	0.0223	44.8167
1.4	0.0400	25.0008
1.5	0.0639	15.6553
1.6	0.0934	10.7024
1.7	0.1277	7.8296
1.8	0.1656	6.0402
1.9	0.2058	4.8603
2.0	0.2472	4.0453

NA