0. Introducción.

Los datos utilizados son tomados del libro Control estadístico de la calidad de Douglas C. Montgomery.

1. Cartas de control \(\bar{x}\) y R.

Página 213.

muestra<-rep(1:40,each=5,len=200)
diametros<-c(74.030,74.002,74.019,73.992,74.008,73.995,73.992,74.001,74.011,74.004,73.988,74.024,74.021,74.005,74.002,74.002,73.996,73.993,74.015,74.009,73.992,74.007,74.015,73.989,74.014,74.009,73.994,73.997,73.985,73.993,73.995,74.006,73.994,74.000,74.005,73.985,74.003,73.993,74.015,73.988,74.008,73.995,74.009,74.005,74.004,73.998,74.000,73.990,74.007,73.995,73.994,73.998,73.994,73.995,73.990,74.004,74.000,74.007,74.000,73.996,73.983,74.002,73.998,73.997,74.012,74.006,73.967,73.994,74.000,73.984,74.012,74.014,73.998,73.999,74.007,74.000,73.984,74.005,73.998,73.996,73.994,74.012,73.986,74.005,74.007,74.006,74.010,74.018,74.003,74.000,73.984,74.002,74.003,74.005,73.997,74.000,74.010,74.013,74.020,74.003,73.988,74.001,74.009,74.005,73.996,74.004,73.999,73.990,74.006,74.009,74.010,73.989,73.990,74.009,74.014,74.015,74.008,73.993,74.000,74.010,73.982,73.984,73.995,74.017,74.013,74.012,74.015,74.030,73.986,74.000,73.995,74.010,73.990,74.015,74.001,73.987,73.999,73.985,74.000,73.990,74.008,74.010,74.003,73.991,74.006,74.003,74.000,74.001,73.986,73.997,73.994,74.003,74.015,74.020,74.004,74.008,74.002,74.018,73.995,74.005,74.001,74.004,73.990,73.996,73.998,74.015,74.000,74.016,74.025,74.000,74.030,74.005,74.000,74.016,74.012,74.001,73.990,73.995,74.010,74.024,74.015,74.020,74.024,74.005,74.019,74.035,74.010,74.012,74.015,74.026,74.017,74.013,74.036,74.025,74.026,74.010,74.005,74.029,74.000,74.020)
dia<-qcc.groups(diametros,muestra);dia

##      [,1]   [,2]   [,3]   [,4]   [,5]
## 1  74.030 74.002 74.019 73.992 74.008
## 2  73.995 73.992 74.001 74.011 74.004
## 3  73.988 74.024 74.021 74.005 74.002
## 4  74.002 73.996 73.993 74.015 74.009
## 5  73.992 74.007 74.015 73.989 74.014
## 6  74.009 73.994 73.997 73.985 73.993
## 7  73.995 74.006 73.994 74.000 74.005
## 8  73.985 74.003 73.993 74.015 73.988
## 9  74.008 73.995 74.009 74.005 74.004
## 10 73.998 74.000 73.990 74.007 73.995
## 11 73.994 73.998 73.994 73.995 73.990
## 12 74.004 74.000 74.007 74.000 73.996
## 13 73.983 74.002 73.998 73.997 74.012
## 14 74.006 73.967 73.994 74.000 73.984
## 15 74.012 74.014 73.998 73.999 74.007
## 16 74.000 73.984 74.005 73.998 73.996
## 17 73.994 74.012 73.986 74.005 74.007
## 18 74.006 74.010 74.018 74.003 74.000
## 19 73.984 74.002 74.003 74.005 73.997
## 20 74.000 74.010 74.013 74.020 74.003
## 21 73.988 74.001 74.009 74.005 73.996
## 22 74.004 73.999 73.990 74.006 74.009
## 23 74.010 73.989 73.990 74.009 74.014
## 24 74.015 74.008 73.993 74.000 74.010
## 25 73.982 73.984 73.995 74.017 74.013
## 26 74.012 74.015 74.030 73.986 74.000
## 27 73.995 74.010 73.990 74.015 74.001
## 28 73.987 73.999 73.985 74.000 73.990
## 29 74.008 74.010 74.003 73.991 74.006
## 30 74.003 74.000 74.001 73.986 73.997
## 31 73.994 74.003 74.015 74.020 74.004
## 32 74.008 74.002 74.018 73.995 74.005
## 33 74.001 74.004 73.990 73.996 73.998
## 34 74.015 74.000 74.016 74.025 74.000
## 35 74.030 74.005 74.000 74.016 74.012
## 36 74.001 73.990 73.995 74.010 74.024
## 37 74.015 74.020 74.024 74.005 74.019
## 38 74.035 74.010 74.012 74.015 74.026
## 39 74.017 74.013 74.036 74.025 74.026
## 40 74.010 74.005 74.029 74.000 74.020

1.1. Carta R.

xrango<-qcc(dia[1:25,], type="R")

summary(xrango)

## 
## Call:
## qcc(data = dia[1:25, ], type = "R")
## 
## R chart for dia[1:25, ] 
## 
## Summary of group statistics:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00800 0.01800 0.02100 0.02276 0.02600 0.03900 
## 
## Group sample size:  5
## Number of groups:  25
## Center of group statistics:  0.02276
## Standard deviation:  0.009785039 
## 
## Control limits:
##  LCL        UCL
##    0 0.04812533

1.2. Carta \(\bar{x}\).

xbarra <- qcc(dia[1:25,], type="xbar")

summary(xbarra)

## 
## Call:
## qcc(data = dia[1:25, ], type = "xbar")
## 
## xbar chart for dia[1:25, ] 
## 
## Summary of group statistics:
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## 73.99020 73.99820 74.00080 74.00118 74.00420 74.01020 
## 
## Group sample size:  5
## Number of groups:  25
## Center of group statistics:  74.00118
## Standard deviation:  0.009785039 
## 
## Control limits:
##       LCL     UCL
##  73.98805 74.0143

1.3. Capacidad del proceso.

process.capability(xbarra, spec.limits=c(73.95,74.05),confidence.level = 0.95)

## 
## Process Capability Analysis
## 
## Call:
## process.capability(object = xbarra, spec.limits = c(73.95, 74.05),     confidence.level = 0.95)
## 
## Number of obs = 125          Target = 74
##        Center = 74              LSL = 73.95
##        StdDev = 0.009785        USL = 74.05
## 
## Capability indices:
## 
##       Value   2.5%  97.5%
## Cp    1.703  1.491  1.915
## Cp_l  1.743  1.555  1.932
## Cp_u  1.663  1.483  1.844
## Cp_k  1.663  1.448  1.878
## Cpm   1.691  1.480  1.902
## 
## Exp<LSL 0%    Obs<LSL 0%
## Exp>USL 0%    Obs>USL 0%

1.4. Monitoreo.

qcc(dia[1:25,], type="xbar", newdata=dia[26:40,], nsigmas=2)

## List of 15
##  $ call        : language qcc(data = dia[1:25, ], type = "xbar", newdata = dia[26:40, ], nsigmas = 2)
##  $ type        : chr "xbar"
##  $ data.name   : chr "dia[1:25, ]"
##  $ data        : num [1:25, 1:5] 74 74 74 74 74 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ statistics  : Named num [1:25] 74 74 74 74 74 ...
##   ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
##  $ sizes       : Named int [1:25] 5 5 5 5 5 5 5 5 5 5 ...
##   ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
##  $ center      : num 74
##  $ std.dev     : num 0.00979
##  $ newstats    : Named num [1:15] 74 74 74 74 74 ...
##   ..- attr(*, "names")= chr [1:15] "26" "27" "28" "29" ...
##  $ newdata     : num [1:15, 1:5] 74 74 74 74 74 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ newsizes    : Named int [1:15] 5 5 5 5 5 5 5 5 5 5 ...
##   ..- attr(*, "names")= chr [1:15] "26" "27" "28" "29" ...
##  $ newdata.name: chr "dia[26:40, ]"
##  $ nsigmas     : num 2
##  $ limits      : num [1, 1:2] 74 74
##   ..- attr(*, "dimnames")=List of 2
##  $ violations  :List of 2
##  - attr(*, "class")= chr "qcc"

qcc(dia[1:25,], type="R", newdata=dia[26:40,])

## List of 15
##  $ call        : language qcc(data = dia[1:25, ], type = "R", newdata = dia[26:40, ])
##  $ type        : chr "R"
##  $ data.name   : chr "dia[1:25, ]"
##  $ data        : num [1:25, 1:5] 74 74 74 74 74 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ statistics  : Named num [1:25] 0.038 0.019 0.036 0.022 0.026 ...
##   ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
##  $ sizes       : Named int [1:25] 5 5 5 5 5 5 5 5 5 5 ...
##   ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
##  $ center      : num 0.0228
##  $ std.dev     : num 0.00979
##  $ newstats    : Named num [1:15] 0.044 0.025 0.015 0.019 0.017 ...
##   ..- attr(*, "names")= chr [1:15] "26" "27" "28" "29" ...
##  $ newdata     : num [1:15, 1:5] 74 74 74 74 74 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ newsizes    : Named int [1:15] 5 5 5 5 5 5 5 5 5 5 ...
##   ..- attr(*, "names")= chr [1:15] "26" "27" "28" "29" ...
##  $ newdata.name: chr "dia[26:40, ]"
##  $ nsigmas     : num 3
##  $ limits      : num [1, 1:2] 0 0.0481
##   ..- attr(*, "dimnames")=List of 2
##  $ violations  :List of 2
##  - attr(*, "class")= chr "qcc"

1.5. Curva característica de operación.

beta1 <- oc.curves.xbar(qcc(dia, type="xbar", nsigmas=3, plot=TRUE))

print(round(beta1, digits=4))

##                sample size
## shift (std.dev)    n=5    n=1   n=10   n=15   n=20
##            0    0.9973 0.9973 0.9973 0.9973 0.9973
##            0.05 0.9971 0.9973 0.9970 0.9968 0.9966
##            0.1  0.9966 0.9972 0.9959 0.9952 0.9944
##            0.15 0.9957 0.9970 0.9940 0.9920 0.9900
##            0.2  0.9944 0.9968 0.9909 0.9869 0.9823
##            0.25 0.9925 0.9964 0.9864 0.9789 0.9701
##            0.3  0.9900 0.9960 0.9798 0.9670 0.9514
##            0.35 0.9866 0.9956 0.9708 0.9500 0.9243
##            0.4  0.9823 0.9950 0.9586 0.9266 0.8871
##            0.45 0.9769 0.9943 0.9426 0.8957 0.8383
##            0.5  0.9701 0.9936 0.9220 0.8562 0.7775
##            0.55 0.9616 0.9927 0.8963 0.8078 0.7055
##            0.6  0.9514 0.9916 0.8649 0.7505 0.6243
##            0.65 0.9390 0.9905 0.8275 0.6853 0.5371
##            0.7  0.9243 0.9892 0.7842 0.6137 0.4481
##            0.75 0.9071 0.9877 0.7351 0.5379 0.3616
##            0.8  0.8871 0.9860 0.6809 0.4608 0.2817
##            0.85 0.8642 0.9842 0.6225 0.3851 0.2115
##            0.9  0.8383 0.9821 0.5612 0.3136 0.1527
##            0.95 0.8094 0.9798 0.4983 0.2485 0.1059
##            1    0.7775 0.9772 0.4355 0.1913 0.0705
##            1.05 0.7428 0.9744 0.3743 0.1431 0.0450
##            1.1  0.7055 0.9713 0.3161 0.1038 0.0275
##            1.15 0.6659 0.9678 0.2622 0.0730 0.0161
##            1.2  0.6243 0.9641 0.2134 0.0497 0.0090
##            1.25 0.5812 0.9599 0.1703 0.0328 0.0048
##            1.3  0.5371 0.9554 0.1333 0.0209 0.0024
##            1.35 0.4925 0.9505 0.1022 0.0129 0.0012
##            1.4  0.4481 0.9452 0.0768 0.0077 0.0006
##            1.45 0.4043 0.9394 0.0564 0.0045 0.0002
##            1.5  0.3616 0.9332 0.0406 0.0025 0.0001
##            1.55 0.3206 0.9265 0.0286 0.0013 0.0000
##            1.6  0.2817 0.9192 0.0197 0.0007 0.0000
##            1.65 0.2453 0.9115 0.0133 0.0003 0.0000
##            1.7  0.2115 0.9032 0.0088 0.0002 0.0000
##            1.75 0.1806 0.8943 0.0056 0.0001 0.0000
##            1.8  0.1527 0.8849 0.0036 0.0000 0.0000
##            1.85 0.1278 0.8749 0.0022 0.0000 0.0000
##            1.9  0.1059 0.8643 0.0013 0.0000 0.0000
##            1.95 0.0869 0.8531 0.0008 0.0000 0.0000
##            2    0.0705 0.8413 0.0004 0.0000 0.0000
##            2.05 0.0566 0.8289 0.0002 0.0000 0.0000
##            2.1  0.0450 0.8159 0.0001 0.0000 0.0000
##            2.15 0.0353 0.8023 0.0001 0.0000 0.0000
##            2.2  0.0275 0.7881 0.0000 0.0000 0.0000
##            2.25 0.0211 0.7734 0.0000 0.0000 0.0000
##            2.3  0.0161 0.7580 0.0000 0.0000 0.0000
##            2.35 0.0121 0.7422 0.0000 0.0000 0.0000
##            2.4  0.0090 0.7257 0.0000 0.0000 0.0000
##            2.45 0.0066 0.7088 0.0000 0.0000 0.0000
##            2.5  0.0048 0.6915 0.0000 0.0000 0.0000
##            2.55 0.0034 0.6736 0.0000 0.0000 0.0000
##            2.6  0.0024 0.6554 0.0000 0.0000 0.0000
##            2.65 0.0017 0.6368 0.0000 0.0000 0.0000
##            2.7  0.0012 0.6179 0.0000 0.0000 0.0000
##            2.75 0.0008 0.5987 0.0000 0.0000 0.0000
##            2.8  0.0006 0.5793 0.0000 0.0000 0.0000
##            2.85 0.0004 0.5596 0.0000 0.0000 0.0000
##            2.9  0.0002 0.5398 0.0000 0.0000 0.0000
##            2.95 0.0002 0.5199 0.0000 0.0000 0.0000
##            3    0.0001 0.5000 0.0000 0.0000 0.0000
##            3.05 0.0001 0.4801 0.0000 0.0000 0.0000
##            3.1  0.0000 0.4602 0.0000 0.0000 0.0000
##            3.15 0.0000 0.4404 0.0000 0.0000 0.0000
##            3.2  0.0000 0.4207 0.0000 0.0000 0.0000
##            3.25 0.0000 0.4013 0.0000 0.0000 0.0000
##            3.3  0.0000 0.3821 0.0000 0.0000 0.0000
##            3.35 0.0000 0.3632 0.0000 0.0000 0.0000
##            3.4  0.0000 0.3446 0.0000 0.0000 0.0000
##            3.45 0.0000 0.3264 0.0000 0.0000 0.0000
##            3.5  0.0000 0.3085 0.0000 0.0000 0.0000
##            3.55 0.0000 0.2912 0.0000 0.0000 0.0000
##            3.6  0.0000 0.2743 0.0000 0.0000 0.0000
##            3.65 0.0000 0.2578 0.0000 0.0000 0.0000
##            3.7  0.0000 0.2420 0.0000 0.0000 0.0000
##            3.75 0.0000 0.2266 0.0000 0.0000 0.0000
##            3.8  0.0000 0.2119 0.0000 0.0000 0.0000
##            3.85 0.0000 0.1977 0.0000 0.0000 0.0000
##            3.9  0.0000 0.1841 0.0000 0.0000 0.0000
##            3.95 0.0000 0.1711 0.0000 0.0000 0.0000
##            4    0.0000 0.1587 0.0000 0.0000 0.0000
##            4.05 0.0000 0.1469 0.0000 0.0000 0.0000
##            4.1  0.0000 0.1357 0.0000 0.0000 0.0000
##            4.15 0.0000 0.1251 0.0000 0.0000 0.0000
##            4.2  0.0000 0.1151 0.0000 0.0000 0.0000
##            4.25 0.0000 0.1056 0.0000 0.0000 0.0000
##            4.3  0.0000 0.0968 0.0000 0.0000 0.0000
##            4.35 0.0000 0.0885 0.0000 0.0000 0.0000
##            4.4  0.0000 0.0808 0.0000 0.0000 0.0000
##            4.45 0.0000 0.0735 0.0000 0.0000 0.0000
##            4.5  0.0000 0.0668 0.0000 0.0000 0.0000
##            4.55 0.0000 0.0606 0.0000 0.0000 0.0000
##            4.6  0.0000 0.0548 0.0000 0.0000 0.0000
##            4.65 0.0000 0.0495 0.0000 0.0000 0.0000
##            4.7  0.0000 0.0446 0.0000 0.0000 0.0000
##            4.75 0.0000 0.0401 0.0000 0.0000 0.0000
##            4.8  0.0000 0.0359 0.0000 0.0000 0.0000
##            4.85 0.0000 0.0322 0.0000 0.0000 0.0000
##            4.9  0.0000 0.0287 0.0000 0.0000 0.0000
##            4.95 0.0000 0.0256 0.0000 0.0000 0.0000
##            5    0.0000 0.0228 0.0000 0.0000 0.0000

2. Carta de control para \(\bar{x}\) y S.

xdes<-qcc(dia[1:25,], type="S")

summary(xdes)

## 
## Call:
## qcc(data = dia[1:25, ], type = "S")
## 
## S chart for dia[1:25, ] 
## 
## Summary of group statistics:
##        Min.     1st Qu.      Median        Mean     3rd Qu.        Max. 
## 0.002863564 0.007314369 0.008467585 0.009240037 0.011928956 0.016177144 
## 
## Group sample size:  5
## Number of groups:  25
## Center of group statistics:  0.009240037
## Standard deviation:  0.009829977 
## 
## Control limits:
##  LCL        UCL
##    0 0.01930242

2.1. Monitoreo.

qcc(dia[1:25,], type="S", newdata=dia[26:40,])

## List of 15
##  $ call        : language qcc(data = dia[1:25, ], type = "S", newdata = dia[26:40, ])
##  $ type        : chr "S"
##  $ data.name   : chr "dia[1:25, ]"
##  $ data        : num [1:25, 1:5] 74 74 74 74 74 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ statistics  : Named num [1:25] 0.01477 0.0075 0.01475 0.00908 0.01222 ...
##   ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
##  $ sizes       : Named int [1:25] 5 5 5 5 5 5 5 5 5 5 ...
##   ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
##  $ center      : num 0.00924
##  $ std.dev     : num 0.00983
##  $ newstats    : Named num [1:15] 0.01655 0.01033 0.00691 0.0075 0.00673 ...
##   ..- attr(*, "names")= chr [1:15] "26" "27" "28" "29" ...
##  $ newdata     : num [1:15, 1:5] 74 74 74 74 74 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ newsizes    : Named int [1:15] 5 5 5 5 5 5 5 5 5 5 ...
##   ..- attr(*, "names")= chr [1:15] "26" "27" "28" "29" ...
##  $ newdata.name: chr "dia[26:40, ]"
##  $ nsigmas     : num 3
##  $ limits      : num [1, 1:2] 0 0.0193
##   ..- attr(*, "dimnames")=List of 2
##  $ violations  :List of 2
##  - attr(*, "class")= chr "qcc"

3. Tamaño de muestra variable.

Datos tomados de la página 245.

muestra2<-c(rep(1,5),rep(2,3),rep(3:5,each=5,length=15),rep(6:7,each=4,length=8),rep(8,5),rep(9,4),rep(10:12,each=5,length=15),rep(13,3),rep(14,5),rep(15,3),rep(16,5),rep(17,4),rep(18:19,each=5,length=10),rep(20,3),rep(21:25,each=5,length=25))
muestra2

##   [1]  1  1  1  1  1  2  2  2  3  3  3  3  3  4  4  4  4  4  5  5  5  5  5  6  6
##  [26]  6  6  7  7  7  7  8  8  8  8  8  9  9  9  9 10 10 10 10 10 11 11 11 11 11
##  [51] 12 12 12 12 12 13 13 13 14 14 14 14 14 15 15 15 16 16 16 16 16 17 17 17 17
##  [76] 18 18 18 18 18 19 19 19 19 19 20 20 20 21 21 21 21 21 22 22 22 22 22 23 23
## [101] 23 23 23 24 24 24 24 24 25 25 25 25 25

diametro2<-c(74.030,74.002,74.019,73.992,74.008,73.995,73.992,74.001,
73.988,74.024,74.021,74.005,74.002,74.002,73.996,73.993,74.015,74.009,
73.992,74.007,74.015,73.989,74.014,74.009,73.994,73.997,73.985,73.995,74.006,73.994,74.000,73.985,74.003,73.993,74.015,73.988,74.008,73.995,74.009,74.005,73.998,74.000,73.990,74.007,73.995,73.994,73.998,73.994,73.995,73.990,74.004,74.000,74.007,74.000,73.996,73.983,74.002,73.998,74.006,73.967,73.994,74.000,73.984,74.012,74.014,73.998,74.000,73.984,74.005,73.998,73.996,73.994,74.012,73.986,74.005,74.006,74.010,74.018,74.003,74.000,73.984,74.002,74.003,74.005,73.997,74.000,74.010,74.013,73.988,74.001,74.009,74.005,73.996,74.004,73.999,73.990,74.006,74.009,74.010,73.989,73.990,74.009,74.014,74.015,74.008,73.993,74.000,74.010,73.982,73.984,73.995,74.017,74.013)
diame<-qcc.groups(diametro2,muestra2)
diame

##      [,1]   [,2]   [,3]   [,4]   [,5]
## 1  74.030 74.002 74.019 73.992 74.008
## 2  73.995 73.992 74.001     NA     NA
## 3  73.988 74.024 74.021 74.005 74.002
## 4  74.002 73.996 73.993 74.015 74.009
## 5  73.992 74.007 74.015 73.989 74.014
## 6  74.009 73.994 73.997 73.985     NA
## 7  73.995 74.006 73.994 74.000     NA
## 8  73.985 74.003 73.993 74.015 73.988
## 9  74.008 73.995 74.009 74.005     NA
## 10 73.998 74.000 73.990 74.007 73.995
## 11 73.994 73.998 73.994 73.995 73.990
## 12 74.004 74.000 74.007 74.000 73.996
## 13 73.983 74.002 73.998     NA     NA
## 14 74.006 73.967 73.994 74.000 73.984
## 15 74.012 74.014 73.998     NA     NA
## 16 74.000 73.984 74.005 73.998 73.996
## 17 73.994 74.012 73.986 74.005     NA
## 18 74.006 74.010 74.018 74.003 74.000
## 19 73.984 74.002 74.003 74.005 73.997
## 20 74.000 74.010 74.013     NA     NA
## 21 73.988 74.001 74.009 74.005 73.996
## 22 74.004 73.999 73.990 74.006 74.009
## 23 74.010 73.989 73.990 74.009 74.014
## 24 74.015 74.008 73.993 74.000 74.010
## 25 73.982 73.984 73.995 74.017 74.013

xbarra1 <- qcc(diame[1:25,], type="xbar")

xrango1<-qcc(diame[1:25,], type="R")

xdes1<-qcc(diame[1:25,], type="S")

process.capability(xbarra1, spec.limits=c(73.95,74.05),confidence.level = 0.95)

## 
## Process Capability Analysis
## 
## Call:
## process.capability(object = xbarra1, spec.limits = c(73.95, 74.05),     confidence.level = 0.95)
## 
## Number of obs = 113          Target = 74
##        Center = 74              LSL = 73.95
##        StdDev = 0.009857        USL = 74.05
## 
## Capability indices:
## 
##       Value   2.5%  97.5%
## Cp    1.691  1.470  1.912
## Cp_l  1.716  1.521  1.912
## Cp_u  1.665  1.475  1.856
## Cp_k  1.665  1.439  1.892
## Cpm   1.686  1.466  1.906
## 
## Exp<LSL 0%    Obs<LSL 0%
## Exp>USL 0%    Obs>USL 0%

4. Carta de control de Shewhart para mediciones individuales.

Datos tomados de la página 250.

x <- c(33.75, 33.05, 34, 33.81, 33.46, 34.02, 33.68, 33.27, 33.49, 33.20,33.62, 33.00, 33.54, 33.12, 33.84)

4.1. Carta \(\bar{x}\).

uno<-qcc(x, type="xbar.one",std.dev = "MR")

qcc(x, type="xbar.one", std.dev = "SD")

## List of 11
##  $ call      : language qcc(data = x, type = "xbar.one", std.dev = "SD")
##  $ type      : chr "xbar.one"
##  $ data.name : chr "x"
##  $ data      : num [1:15, 1] 33.8 33 34 33.8 33.5 ...
##   ..- attr(*, "dimnames")=List of 2
##  $ statistics: Named num [1:15] 33.8 33 34 33.8 33.5 ...
##   ..- attr(*, "names")= chr [1:15] "1" "2" "3" "4" ...
##  $ sizes     : int [1:15] 1 1 1 1 1 1 1 1 1 1 ...
##  $ center    : num 33.5
##  $ std.dev   : num 0.342
##  $ nsigmas   : num 3
##  $ limits    : num [1, 1:2] 32.5 34.5
##   ..- attr(*, "dimnames")=List of 2
##  $ violations:List of 2
##  - attr(*, "class")= chr "qcc"

4.2. Capacidad de proceso.

process.capability(uno, spec.limits=c(32,34),confidence.level = 0.95)

## 
## Process Capability Analysis
## 
## Call:
## process.capability(object = uno, spec.limits = c(32, 34), confidence.level = 0.95)
## 
## Number of obs = 15           Target = 33
##        Center = 33.52           LSL = 32
##        StdDev = 0.4262          USL = 34
## 
## Capability indices:
## 
##        Value    2.5%   97.5%
## Cp    0.7822  0.4960  1.0684
## Cp_l  1.1915  0.7950  1.5880
## Cp_u  0.3728  0.1899  0.5558
## Cp_k  0.3728  0.1548  0.5908
## Cpm   0.4939  0.2747  0.7137
## 
## Exp<LSL 0.018%    Obs<LSL 0%
## Exp>USL 13%   Obs>USL 6.7%

Paquete utilizado: qcc

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O.M.F.