Quality Control Chart Part 2
Janpu Hou
August 31, 2017
- Quality Control Charts Part 2
- Temperature readings from the eight configured burners on a boiler.
- Operating Characteristic Function
- Orange juice data
- Orange juice data - Part 2
- Pareto chart
- Personal computer manufacturer data
- Piston rings data
- Process capability analysis
- Quality Control Charts
- Grouping data based on a sample indicator
- Set or return options for the ‘qcc’ package.
- Overdispersion test for binomial and poisson data
- Functions specifying rules for Shewhart charts
- Functions to plot Shewhart c chart
- Statistics used in computing and drawing a Shewhart g chart
- Statistics used in computing and drawing a Shewhart np chart
- Statistics used in computing and drawing a Shewhart p chart
- Statistics used in computing and drawing a Shewhart R chart
- Functions to plot Shewhart S chart
- Statistics used in computing and drawing the Hotelling T^2 chart for subgrouped data
- Statistics used in computing and drawing the Hotelling T^2 chart for individual observations data
- Statistics used in computing and drawing a Shewhart u chart
- Statistics used in computing and drawing a Shewhart xbar chart
- Statistics used in computing and drawing a Shewhart xbar chart for one-at-time data
Quality Control Charts Part 2
Shewhart quality control charts for continuous, attribute and count data. Cusum and EWMA charts. Operating characteristic curves. Process capability analysis. Pareto chart and cause-and-effect chart. Multivariate control charts.
Temperature readings from the eight configured burners on a boiler.
library(qcc)## Package 'qcc' version 2.7## Type 'citation("qcc")' for citing this R package in publications.data(boiler)
summary(boiler)## t1 t2 t3 t4
## Min. :507 Min. :509.0 Min. :527.0 Min. :512.0
## 1st Qu.:520 1st Qu.:512.0 1st Qu.:537.0 1st Qu.:518.0
## Median :527 Median :514.0 Median :540.0 Median :523.0
## Mean :525 Mean :513.6 Mean :538.9 Mean :521.7
## 3rd Qu.:530 3rd Qu.:515.0 3rd Qu.:542.0 3rd Qu.:525.0
## Max. :536 Max. :518.0 Max. :546.0 Max. :530.0
## t5 t6 t7 t8
## Min. :497.0 Min. :508.0 Min. :471.0 Min. :472.0
## 1st Qu.:502.0 1st Qu.:511.0 1st Qu.:476.0 1st Qu.:476.0
## Median :504.0 Median :512.0 Median :480.0 Median :477.0
## Mean :503.8 Mean :512.4 Mean :478.7 Mean :477.2
## 3rd Qu.:507.0 3rd Qu.:514.0 3rd Qu.:482.0 3rd Qu.:478.0
## Max. :509.0 Max. :517.0 Max. :483.0 Max. :481.0boxplot(boiler)
Operating Characteristic Function
data(pistonrings)
attach(pistonrings)
diameter <- qcc.groups(diameter, sample)
beta <- oc.curves.xbar(qcc(diameter, type="xbar", nsigmas=3, plot=FALSE))
print(round(beta, 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# or to identify points on the plot use
## Not run: oc.curves.xbar(qcc(diameter, type="xbar", nsigmas=3, plot=FALSE), identify=TRUE)
detach(pistonrings)
data(orangejuice)
attach(orangejuice)
beta <- oc.curves(qcc(D[trial], sizes=size[trial], type="p", plot=FALSE))## Warning in oc.curves.p(object, ...): Some computed values for the type
## II error have been rounded due to the discreteness of the binomial
## distribution. Thus, some ARL values might be meaningless.
print(round(beta, digits=4))## 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
## 0.0000 0.0894 0.2642 0.4447 0.5995 0.7206 0.8100 0.8735 0.9173 0.9468
## 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19
## 0.9662 0.9788 0.9869 0.9920 0.9951 0.9971 0.9983 0.9990 0.9993 0.9995
## 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29
## 0.9995 0.9993 0.9987 0.9978 0.9962 0.9937 0.9900 0.9845 0.9768 0.9662
## 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39
## 0.9522 0.9343 0.9118 0.8844 0.8518 0.8139 0.7711 0.7236 0.6722 0.6176
## 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49
## 0.5610 0.5035 0.4461 0.3901 0.3365 0.2862 0.2398 0.1980 0.1609 0.1287
## 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59
## 0.1013 0.0784 0.0596 0.0446 0.0327 0.0235 0.0166 0.0115 0.0078 0.0052
## 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69
## 0.0034 0.0021 0.0013 0.0008 0.0005 0.0003 0.0002 0.0001 0.0000 0.0000
## 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## 1
## 0.0000# or to identify points on the plot use
## Not run: oc.curves(qcc(D[trial], sizes=size[trial], type="p", plot=FALSE), identify=TRUE)
detach(orangejuice)
data(circuit)
attach(circuit)
q <- qcc(x[trial], sizes=size[trial], type="c", plot=FALSE)
beta <- oc.curves(q)## Warning in oc.curves.c(object, ...): Some computed values for the
## type II error have been rounded due to the discreteness of the Poisson
## distribution. Thus, some ARL values might be meaningless.
print(round(beta, digits=4))## 0 1 2 3 4 5 6 7 8 9
## 0.0000 0.0006 0.0166 0.0839 0.2149 0.3840 0.5543 0.6993 0.8088 0.8843
## 10 11 12 13 14 15 16 17 18 19
## 0.9329 0.9625 0.9797 0.9893 0.9945 0.9972 0.9986 0.9991 0.9992 0.9986
## 20 21 22 23 24 25 26 27 28 29
## 0.9972 0.9945 0.9895 0.9813 0.9686 0.9502 0.9249 0.8918 0.8505 0.8011
## 30 31 32 33 34 35 36 37 38 39
## 0.7444 0.6818 0.6150 0.5461 0.4772 0.4102 0.3470 0.2888 0.2365 0.1907
## 40 41 42 43 44 45 46 47 48 49
## 0.1514 0.1184 0.0912 0.0693 0.0519 0.0383 0.0280 0.0201 0.0143 0.0101
## 50 51 52 53 54 55 56 57 58 59
## 0.0070 0.0048 0.0033 0.0022 0.0015 0.0010 0.0006 0.0004 0.0003 0.0002
## 60 61 62 63 64 65
## 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000# or to identify points on the plot use
## Not run: oc.curves(qcc(x[trial], sizes=size[trial], type="c", plot=FALSE), identify=TRUE)
detach(circuit)Orange juice data
data(orangejuice)
orangejuice$d <- orangejuice$D/orangejuice$size
attach(orangejuice)
summary(orangejuice)## sample D size trial
## Min. : 1.00 Min. : 2.000 Min. :50 Mode :logical
## 1st Qu.:14.25 1st Qu.: 5.000 1st Qu.:50 FALSE:24
## Median :27.50 Median : 7.000 Median :50 TRUE :30
## Mean :27.50 Mean : 8.889 Mean :50
## 3rd Qu.:40.75 3rd Qu.:12.000 3rd Qu.:50
## Max. :54.00 Max. :24.000 Max. :50
## d
## Min. :0.0400
## 1st Qu.:0.1000
## Median :0.1400
## Mean :0.1778
## 3rd Qu.:0.2400
## Max. :0.4800boxplot(d ~ trial)
mark <- ifelse(trial, 1, 2)
plot(sample, d, type="b", col=mark, pch=mark)
detach(orangejuice)Orange juice data - Part 2
data(orangejuice2)
orangejuice2$d <- orangejuice2$D/orangejuice2$size
attach(orangejuice2)
summary(orangejuice2)## sample D size trial
## Min. :31.00 Min. : 1.000 Min. :50 Mode :logical
## 1st Qu.:46.75 1st Qu.: 4.000 1st Qu.:50 FALSE:40
## Median :62.50 Median : 5.000 Median :50 TRUE :24
## Mean :62.50 Mean : 5.484 Mean :50
## 3rd Qu.:78.25 3rd Qu.: 7.000 3rd Qu.:50
## Max. :94.00 Max. :12.000 Max. :50
## d
## Min. :0.0200
## 1st Qu.:0.0800
## Median :0.1000
## Mean :0.1097
## 3rd Qu.:0.1400
## Max. :0.2400boxplot(d ~ trial)
mark <- ifelse(trial, 1, 2)
plot(sample, d, type="b", col=mark, pch=mark)
detach(orangejuice2)Pareto chart
defect <- c(80, 27, 66, 94, 33)
names(defect) <- c("price code", "schedule date", "supplier code", "contact num.", "part num.")
pareto.chart(defect, ylab = "Error frequency")
##
## Pareto chart analysis for defect
## Frequency Cum.Freq. Percentage Cum.Percent.
## contact num. 94.00000 94.00000 31.33333 31.33333
## price code 80.00000 174.00000 26.66667 58.00000
## supplier code 66.00000 240.00000 22.00000 80.00000
## part num. 33.00000 273.00000 11.00000 91.00000
## schedule date 27.00000 300.00000 9.00000 100.00000pareto.chart(defect, ylab = "Error frequency", xlab = "Error causes", las=1)
##
## Pareto chart analysis for defect
## Frequency Cum.Freq. Percentage Cum.Percent.
## contact num. 94.00000 94.00000 31.33333 31.33333
## price code 80.00000 174.00000 26.66667 58.00000
## supplier code 66.00000 240.00000 22.00000 80.00000
## part num. 33.00000 273.00000 11.00000 91.00000
## schedule date 27.00000 300.00000 9.00000 100.00000pareto.chart(defect, ylab = "Error frequency", col=rainbow(length(defect)))
##
## Pareto chart analysis for defect
## Frequency Cum.Freq. Percentage Cum.Percent.
## contact num. 94.00000 94.00000 31.33333 31.33333
## price code 80.00000 174.00000 26.66667 58.00000
## supplier code 66.00000 240.00000 22.00000 80.00000
## part num. 33.00000 273.00000 11.00000 91.00000
## schedule date 27.00000 300.00000 9.00000 100.00000pareto.chart(defect, cumperc = seq(0, 100, by = 5), ylab2 = "A finer tickmarks grid")
##
## Pareto chart analysis for defect
## Frequency Cum.Freq. Percentage Cum.Percent.
## contact num. 94.00000 94.00000 31.33333 31.33333
## price code 80.00000 174.00000 26.66667 58.00000
## supplier code 66.00000 240.00000 22.00000 80.00000
## part num. 33.00000 273.00000 11.00000 91.00000
## schedule date 27.00000 300.00000 9.00000 100.00000Personal computer manufacturer data
data(pcmanufact)
attach(pcmanufact)
summary(pcmanufact)## x size
## Min. : 5.00 Min. :5
## 1st Qu.: 7.00 1st Qu.:5
## Median :10.00 Median :5
## Mean : 9.65 Mean :5
## 3rd Qu.:11.25 3rd Qu.:5
## Max. :16.00 Max. :5plot(x/size, type="b")
detach(pcmanufact)Piston rings data
data(pistonrings)
attach(pistonrings)## The following object is masked _by_ .GlobalEnv:
##
## diametersummary(pistonrings)## diameter sample trial
## Min. :73.97 Min. : 1.00 Mode :logical
## 1st Qu.:74.00 1st Qu.:10.75 FALSE:75
## Median :74.00 Median :20.50 TRUE :125
## Mean :74.00 Mean :20.50
## 3rd Qu.:74.01 3rd Qu.:30.25
## Max. :74.04 Max. :40.00boxplot(pistonrings$diameter ~ pistonrings$sample)
plot(sample, diameter, cex=0.7)
lines(tapply(diameter,sample,mean))
detach(pistonrings)Process capability analysis
data(pistonrings)
attach(pistonrings)## The following object is masked _by_ .GlobalEnv:
##
## diameterdiameter <- qcc.groups(diameter, sample)
q <- qcc(diameter[1:25,], type="xbar", nsigmas=3, plot=FALSE)
process.capability(q, spec.limits=c(73.95,74.05))
##
## Process Capability Analysis
##
## Call:
## process.capability(object = q, spec.limits = c(73.95, 74.05))
##
## Number of obs = 125 Target = 74
## Center = 74 LSL = 73.95
## StdDev = 0.01187 USL = 74.05
##
## Capability indices:
##
## Value 2.5% 97.5%
## Cp 1.405 1.230 1.579
## Cp_l 1.490 1.327 1.653
## Cp_u 1.319 1.173 1.465
## Cp_k 1.319 1.145 1.493
## Cpm 1.360 1.187 1.534
##
## Exp<LSL 0% Obs<LSL 0%
## Exp>USL 0% Obs>USL 0%process.capability(q, spec.limits=c(73.95,74.05), target=74.02)
##
## Process Capability Analysis
##
## Call:
## process.capability(object = q, spec.limits = c(73.95, 74.05), target = 74.02)
##
## Number of obs = 125 Target = 74.02
## Center = 74 LSL = 73.95
## StdDev = 0.01187 USL = 74.05
##
## Capability indices:
##
## Value 2.5% 97.5%
## Cp 1.4046 1.2299 1.5790
## Cp_l 1.4902 1.3270 1.6534
## Cp_u 1.3190 1.1727 1.4652
## Cp_k 1.3190 1.1447 1.4932
## Cpm 0.8055 0.6765 0.9341
##
## Exp<LSL 0% Obs<LSL 0%
## Exp>USL 0% Obs>USL 0%process.capability(q, spec.limits=c(73.99,74.01))
##
## Process Capability Analysis
##
## Call:
## process.capability(object = q, spec.limits = c(73.99, 74.01))
##
## Number of obs = 125 Target = 74
## Center = 74 LSL = 73.99
## StdDev = 0.01187 USL = 74.01
##
## Capability indices:
##
## Value 2.5% 97.5%
## Cp 0.2809 0.2460 0.3158
## Cp_l 0.3665 0.3043 0.4288
## Cp_u 0.1953 0.1422 0.2484
## Cp_k 0.1953 0.1320 0.2586
## Cpm 0.2721 0.2374 0.3068
##
## Exp<LSL 14% Obs<LSL 11%
## Exp>USL 28% Obs>USL 24%process.capability(q, spec.limits = c(73.99, 74.1))
##
## Process Capability Analysis
##
## Call:
## process.capability(object = q, spec.limits = c(73.99, 74.1))
##
## Number of obs = 125 Target = 74.05
## Center = 74 LSL = 73.99
## StdDev = 0.01187 USL = 74.1
##
## Capability indices:
##
## Value 2.5% 97.5%
## Cp 1.5450 1.3529 1.7369
## Cp_l 0.3665 0.3043 0.4288
## Cp_u 2.7236 2.4349 3.0122
## Cp_k 0.3665 0.2924 0.4407
## Cpm 0.4205 0.3483 0.4926
##
## Exp<LSL 14% Obs<LSL 11%
## Exp>USL 0% Obs>USL 0%Quality Control Charts
Create an object of class ‘qcc’ to perform statistical quality control. This object may then be used to plot Shewhart charts, drawing OC curves, computes capability indices, and more.
##
## Continuous data
##
data(pistonrings)
attach(pistonrings)## The following object is masked _by_ .GlobalEnv:
##
## diameter## The following objects are masked from pistonrings (pos = 3):
##
## diameter, sample, trialdiameter <- qcc.groups(diameter, sample)
qcc(diameter[1:25,], type="xbar")
## List of 11
## $ call : language qcc(data = diameter[1:25, ], type = "xbar")
## $ type : chr "xbar"
## $ data.name : chr "diameter[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 0.0113
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 74 74
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,])
## List of 15
## $ call : language qcc(data = diameter[1:25, ], type = "xbar", newdata = diameter[26:40, ])
## $ type : chr "xbar"
## $ data.name : chr "diameter[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 0.0113
## $ 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 "diameter[26:40, ]"
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 74 74
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"q <- qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], plot=FALSE)
plot(q, chart.all=FALSE)
qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], nsigmas=2)
## List of 15
## $ call : language qcc(data = diameter[1:25, ], type = "xbar", newdata = diameter[26:40, ], nsigmas = 2)
## $ type : chr "xbar"
## $ data.name : chr "diameter[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 0.0113
## $ 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 "diameter[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(diameter[1:25,], type="xbar", newdata=diameter[26:40,], confidence.level=0.99)
## List of 15
## $ call : language qcc(data = diameter[1:25, ], type = "xbar", newdata = diameter[26:40, ], confidence.level = 0.99)
## $ type : chr "xbar"
## $ data.name : chr "diameter[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 0.0113
## $ 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 "diameter[26:40, ]"
## $ confidence.level: num 0.99
## $ limits : num [1, 1:2] 74 74
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="R")
## List of 11
## $ call : language qcc(data = diameter[1:25, ], type = "R")
## $ type : chr "R"
## $ data.name : chr "diameter[1:25, ]"
## $ data : num [1:25, 1:5] 74 74 74 74 74 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:25] 0.042 0.018 0.031 0.029 0.038 ...
## ..- 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 0.0262
## $ std.dev : num 0.0113
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 0 0.0555
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="R", newdata=diameter[26:40,])
## List of 15
## $ call : language qcc(data = diameter[1:25, ], type = "R", newdata = diameter[26:40, ])
## $ type : chr "R"
## $ data.name : chr "diameter[1:25, ]"
## $ data : num [1:25, 1:5] 74 74 74 74 74 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics : Named num [1:25] 0.042 0.018 0.031 0.029 0.038 ...
## ..- 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 0.0262
## $ std.dev : num 0.0113
## $ newstats : Named num [1:15] 0.022 0.043 0.02 0.043 0.014 ...
## ..- 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 "diameter[26:40, ]"
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 0 0.0555
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="S")
## List of 11
## $ call : language qcc(data = diameter[1:25, ], type = "S")
## $ type : chr "S"
## $ data.name : chr "diameter[1:25, ]"
## $ data : num [1:25, 1:5] 74 74 74 74 74 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:25] 0.0164 0.0074 0.0111 0.0115 0.0155 ...
## ..- 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 0.0108
## $ std.dev : num 0.0115
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 0 0.0225
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="S", newdata=diameter[26:40,])
## List of 15
## $ call : language qcc(data = diameter[1:25, ], type = "S", newdata = diameter[26:40, ])
## $ type : chr "S"
## $ data.name : chr "diameter[1:25, ]"
## $ data : num [1:25, 1:5] 74 74 74 74 74 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics : Named num [1:25] 0.0164 0.0074 0.0111 0.0115 0.0155 ...
## ..- 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 0.0108
## $ std.dev : num 0.0115
## $ newstats : Named num [1:15] 0.01033 0.01749 0.00888 0.01613 0.00572 ...
## ..- 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 "diameter[26:40, ]"
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 0 0.0225
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"# add warning limits at 2 std. deviations
q <- qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], plot=FALSE)
(warn.limits <- limits.xbar(q$center, q$std.dev, q$sizes, 2))## LCL UCL
## 73.99273 74.01291plot(q, restore.par = FALSE)
abline(h = warn.limits, lty = 3, col = "chocolate")
# variable control limits
out <- c(9, 10, 30, 35, 45, 64, 65, 74, 75, 85, 99, 100)
diameter <- qcc.groups(pistonrings$diameter[-out], sample[-out])
qcc(diameter[1:25,], type="xbar")
## List of 11
## $ call : language qcc(data = diameter[1:25, ], type = "xbar")
## $ type : chr "xbar"
## $ data.name : chr "diameter[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 3 5 5 5 4 4 5 4 5 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ center : num 74
## $ std.dev : num 0.00986
## $ nsigmas : num 3
## $ limits : num [1:25, 1:2] 74 74 74 74 74 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="R")
## List of 11
## $ call : language qcc(data = diameter[1:25, ], type = "R")
## $ type : chr "R"
## $ data.name : chr "diameter[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 0.009 0.036 0.022 0.026 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ sizes : Named int [1:25] 5 3 5 5 5 4 4 5 4 5 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ center : num 0.0223
## $ std.dev : num 0.00986
## $ nsigmas : num 3
## $ limits : num [1:25, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="S")
## List of 11
## $ call : language qcc(data = diameter[1:25, ], type = "S")
## $ type : chr "S"
## $ data.name : chr "diameter[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 0.00458 0.01475 0.00908 0.01222 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ sizes : Named int [1:25] 5 3 5 5 5 4 4 5 4 5 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ center : num 0.00939
## $ std.dev : num 0.00993
## $ nsigmas : num 3
## $ limits : num [1:25, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,])
## List of 15
## $ call : language qcc(data = diameter[1:25, ], type = "xbar", newdata = diameter[26:40, ])
## $ type : chr "xbar"
## $ data.name : chr "diameter[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 3 5 5 5 4 4 5 4 5 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ center : num 74
## $ std.dev : num 0.00986
## $ 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 "diameter[26:40, ]"
## $ nsigmas : num 3
## $ limits : num [1:40, 1:2] 74 74 74 74 74 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="R", newdata=diameter[26:40,])
## List of 15
## $ call : language qcc(data = diameter[1:25, ], type = "R", newdata = diameter[26:40, ])
## $ type : chr "R"
## $ data.name : chr "diameter[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 0.009 0.036 0.022 0.026 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ sizes : Named int [1:25] 5 3 5 5 5 4 4 5 4 5 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ center : num 0.0223
## $ std.dev : num 0.00986
## $ 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 "diameter[26:40, ]"
## $ nsigmas : num 3
## $ limits : num [1:40, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"qcc(diameter[1:25,], type="S", newdata=diameter[26:40,])
## List of 15
## $ call : language qcc(data = diameter[1:25, ], type = "S", newdata = diameter[26:40, ])
## $ type : chr "S"
## $ data.name : chr "diameter[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 0.00458 0.01475 0.00908 0.01222 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ sizes : Named int [1:25] 5 3 5 5 5 4 4 5 4 5 ...
## ..- attr(*, "names")= chr [1:25] "1" "2" "3" "4" ...
## $ center : num 0.00939
## $ std.dev : num 0.00993
## $ 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 "diameter[26:40, ]"
## $ nsigmas : num 3
## $ limits : num [1:40, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"detach(pistonrings)
##
## Attribute data
##
data(orangejuice)
attach(orangejuice)## The following objects are masked from pistonrings:
##
## sample, trialqcc(D[trial], sizes=size[trial], type="p")
## List of 11
## $ call : language qcc(data = D[trial], type = "p", sizes = size[trial])
## $ type : chr "p"
## $ data.name : chr "D[trial]"
## $ data : int [1:30, 1] 12 15 8 10 4 7 16 9 14 10 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:30] 0.24 0.3 0.16 0.2 0.08 0.14 0.32 0.18 0.28 0.2 ...
## ..- attr(*, "names")= chr [1:30] "1" "2" "3" "4" ...
## $ sizes : int [1:30] 50 50 50 50 50 50 50 50 50 50 ...
## $ center : num 0.231
## $ std.dev : num 0.422
## $ nsigmas : num 3
## $ limits : num [1:30, 1:2] 0.0524 0.0524 0.0524 0.0524 0.0524 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"# remove out-of-control points (see help(orangejuice) for the reasons)
inc <- setdiff(which(trial), c(15,23))
q1 <- qcc(D[inc], sizes=size[inc], type="p")
qcc(D[inc], sizes=size[inc], type="p", newdata=D[!trial], newsizes=size[!trial])
## List of 15
## $ call : language qcc(data = D[inc], type = "p", sizes = size[inc], newdata = D[!trial], newsizes = size[!trial])
## $ type : chr "p"
## $ data.name : chr "D[inc]"
## $ data : int [1:28, 1] 12 15 8 10 4 7 16 9 14 10 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics : Named num [1:28] 0.24 0.3 0.16 0.2 0.08 0.14 0.32 0.18 0.28 0.2 ...
## ..- attr(*, "names")= chr [1:28] "1" "2" "3" "4" ...
## $ sizes : int [1:28] 50 50 50 50 50 50 50 50 50 50 ...
## $ center : num 0.215
## $ std.dev : num 0.411
## $ newstats : Named num [1:24] 0.18 0.12 0.24 0.1 0.12 0.08 0.12 0.06 0.14 0.12 ...
## ..- attr(*, "names")= chr [1:24] "29" "30" "31" "32" ...
## $ newdata : int [1:24, 1] 9 6 12 5 6 4 6 3 7 6 ...
## $ newsizes : int [1:24] 50 50 50 50 50 50 50 50 50 50 ...
## $ newdata.name: chr "D[!trial]"
## $ nsigmas : num 3
## $ limits : num [1:52, 1:2] 0.0407 0.0407 0.0407 0.0407 0.0407 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"detach(orangejuice)
data(orangejuice2)
attach(orangejuice2)## The following objects are masked from pistonrings:
##
## sample, trialnames(D) <- sample
qcc(D[trial], sizes=size[trial], type="p")
## List of 11
## $ call : language qcc(data = D[trial], type = "p", sizes = size[trial])
## $ type : chr "p"
## $ data.name : chr "D[trial]"
## $ data : int [1:24, 1] 9 6 12 5 6 4 6 3 7 6 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:24] 0.18 0.12 0.24 0.1 0.12 0.08 0.12 0.06 0.14 0.12 ...
## ..- attr(*, "names")= chr [1:24] "31" "32" "33" "34" ...
## $ sizes : int [1:24] 50 50 50 50 50 50 50 50 50 50 ...
## $ center : num 0.111
## $ std.dev : num 0.314
## $ nsigmas : num 3
## $ limits : num [1:24, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"q2 <- qcc(D[trial], sizes=size[trial], type="p", newdata=D[!trial], newsizes=size[!trial])
detach(orangejuice2)
# put on the same graph the two orange juice samples
oldpar <- par(no.readonly = TRUE)
par(mfrow=c(1,2), mar=c(5,5,3,0))
plot(q1, title="First samples", ylim=c(0,0.5), add.stats=FALSE, restore.par=FALSE)
par("mar"=c(5,0,3,3), yaxt="n")
plot(q2, title="Second samples", add.stats=FALSE, ylim=c(0,0.5))
par(oldpar)
data(circuit)
attach(circuit)## The following object is masked from pistonrings:
##
## trialqcc(x[trial], sizes=size[trial], type="c")
## List of 11
## $ call : language qcc(data = x[trial], type = "c", sizes = size[trial])
## $ type : chr "c"
## $ data.name : chr "x[trial]"
## $ data : int [1:26, 1] 21 24 16 12 15 5 28 20 31 25 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named int [1:26] 21 24 16 12 15 5 28 20 31 25 ...
## ..- attr(*, "names")= chr [1:26] "1" "2" "3" "4" ...
## $ sizes : int [1:26] 100 100 100 100 100 100 100 100 100 100 ...
## $ center : num 19.8
## $ std.dev : num 4.45
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 6.48 33.21
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"# remove out-of-control points (see help(circuit) for the reasons)
inc <- setdiff(which(trial), c(6,20))
qcc(x[inc], sizes=size[inc], type="c", labels=inc)
## List of 11
## $ call : language qcc(data = x[inc], type = "c", sizes = size[inc], labels = inc)
## $ type : chr "c"
## $ data.name : chr "x[inc]"
## $ data : int [1:24, 1] 21 24 16 12 15 28 20 31 25 20 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named int [1:24] 21 24 16 12 15 28 20 31 25 20 ...
## ..- attr(*, "names")= chr [1:24] "1" "2" "3" "4" ...
## $ sizes : int [1:24] 100 100 100 100 100 100 100 100 100 100 ...
## $ center : num 19.7
## $ std.dev : num 4.43
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 6.36 32.97
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc(x[inc], sizes=size[inc], type="c", labels=inc,
newdata=x[!trial], newsizes=size[!trial], newlabels=which(!trial))
## List of 15
## $ call : language qcc(data = x[inc], type = "c", sizes = size[inc], labels = inc, newdata = x[!trial], newsizes = size[!trial]| __truncated__
## $ type : chr "c"
## $ data.name : chr "x[inc]"
## $ data : int [1:24, 1] 21 24 16 12 15 28 20 31 25 20 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics : Named int [1:24] 21 24 16 12 15 28 20 31 25 20 ...
## ..- attr(*, "names")= chr [1:24] "1" "2" "3" "4" ...
## $ sizes : int [1:24] 100 100 100 100 100 100 100 100 100 100 ...
## $ center : num 19.7
## $ std.dev : num 4.43
## $ newstats : Named int [1:20] 16 18 12 15 24 21 28 20 25 19 ...
## ..- attr(*, "names")= chr [1:20] "27" "28" "29" "30" ...
## $ newdata : int [1:20, 1] 16 18 12 15 24 21 28 20 25 19 ...
## $ newsizes : int [1:20] 100 100 100 100 100 100 100 100 100 100 ...
## $ newdata.name: chr "x[!trial]"
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 6.36 32.97
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"qcc(x[inc], sizes=size[inc], type="u", labels=inc,
newdata=x[!trial], newsizes=size[!trial], newlabels=which(!trial))
## List of 15
## $ call : language qcc(data = x[inc], type = "u", sizes = size[inc], labels = inc, newdata = x[!trial], newsizes = size[!trial]| __truncated__
## $ type : chr "u"
## $ data.name : chr "x[inc]"
## $ data : int [1:24, 1] 21 24 16 12 15 28 20 31 25 20 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics : Named num [1:24] 0.21 0.24 0.16 0.12 0.15 0.28 0.2 0.31 0.25 0.2 ...
## ..- attr(*, "names")= chr [1:24] "1" "2" "3" "4" ...
## $ sizes : int [1:24] 100 100 100 100 100 100 100 100 100 100 ...
## $ center : num 0.197
## $ std.dev : num 0.443
## $ newstats : Named num [1:20] 0.16 0.18 0.12 0.15 0.24 0.21 0.28 0.2 0.25 0.19 ...
## ..- attr(*, "names")= chr [1:20] "27" "28" "29" "30" ...
## $ newdata : int [1:20, 1] 16 18 12 15 24 21 28 20 25 19 ...
## $ newsizes : int [1:20] 100 100 100 100 100 100 100 100 100 100 ...
## $ newdata.name: chr "x[!trial]"
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 0.0636 0.3297
## ..- attr(*, "dimnames")=List of 2
## $ violations :List of 2
## - attr(*, "class")= chr "qcc"detach(circuit)
data(pcmanufact)
attach(pcmanufact)
qcc(x, sizes=size, type="u")
## List of 11
## $ call : language qcc(data = x, type = "u", sizes = size)
## $ type : chr "u"
## $ data.name : chr "x"
## $ data : int [1:20, 1] 10 12 8 14 10 16 11 7 10 15 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:20] 2 2.4 1.6 2.8 2 3.2 2.2 1.4 2 3 ...
## ..- attr(*, "names")= chr [1:20] "1" "2" "3" "4" ...
## $ sizes : int [1:20] 5 5 5 5 5 5 5 5 5 5 ...
## $ center : num 1.93
## $ std.dev : num 1.39
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 0.0661 3.7939
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"detach(pcmanufact)
data(dyedcloth)
attach(dyedcloth)
qcc(x, sizes=size, type="u")
## List of 11
## $ call : language qcc(data = x, type = "u", sizes = size)
## $ type : chr "u"
## $ data.name : chr "x"
## $ data : int [1:10, 1] 14 12 20 11 7 10 21 16 19 23
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:10] 1.4 1.5 1.538 1.1 0.737 ...
## ..- attr(*, "names")= chr [1:10] "1" "2" "3" "4" ...
## $ sizes : num [1:10] 10 8 13 10 9.5 10 12 10.5 12 12.5
## $ center : num 1.42
## $ std.dev : num 1.19
## $ nsigmas : num 3
## $ limits : num [1:10, 1:2] 0.291 0.158 0.431 0.291 0.262 ...
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"# standardized control chart
q <- qcc(x, sizes=size, type="u", plot=FALSE)
z <- (q$statistics - q$center)/sqrt(q$center/q$size)
plot(z, type="o", ylim=range(z,3,-3), pch=16)
abline(h=0, lty=2)
abline(h=c(-3,3), lty=2)
detach(dyedcloth)
##
## Continuous one-at-time data
##
# viscosity data (Montgomery, pag. 242)
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)
qcc(x, type="xbar.one")
## List of 11
## $ call : language qcc(data = x, type = "xbar.one")
## $ 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 0.426
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 32.2 34.8
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"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"Grouping data based on a sample indicator
data(pistonrings)
attach(pistonrings)## The following object is masked _by_ .GlobalEnv:
##
## diameter## The following objects are masked from pistonrings (pos = 3):
##
## diameter, sample, trial# 40 sample of 5 obs each
qcc.groups(diameter, sample)## [,1] [,2] [,3] [,4] [,5]
## 1 74.030 73.995 73.988 74.002 73.992
## 2 74.009 73.995 73.985 74.008 73.998
## 3 73.994 74.004 73.983 74.006 74.012
## 4 74.000 73.994 74.006 73.984 74.000
## 5 73.988 74.004 74.010 74.015 73.982
## 6 74.012 73.995 73.987 74.008 74.003
## 7 73.994 74.008 74.001 74.015 74.030
## 8 74.001 74.015 74.035 74.017 74.010
## 9 74.002 73.992 74.024 73.996 74.007
## 10 73.994 74.006 74.003 73.995 74.000
## 11 73.998 74.000 74.002 73.967 74.014
## 12 73.984 74.012 74.010 74.002 74.010
## 13 74.001 73.999 73.989 74.008 73.984
## 14 74.015 74.010 73.999 74.010 74.000
## 15 74.003 74.002 74.004 74.000 74.005
## 16 73.990 74.020 74.010 74.013 74.005
## 17 74.019 74.001 74.021 73.993 74.015
## 18 73.997 73.994 73.993 74.009 73.990
## 19 73.994 74.007 73.998 73.994 73.998
## 20 74.005 73.986 74.018 74.003 74.013
## 21 74.009 73.990 73.990 73.993 73.995
## 22 74.030 73.990 73.985 74.003 74.001
## 23 74.015 74.018 73.990 74.016 74.000
## 24 73.995 74.024 74.012 74.036 74.029
## 25 73.992 NA 74.005 74.015 73.989
## 26 73.985 74.000 74.015 74.005 74.007
## 27 73.995 74.000 NA 74.000 NA
## 28 73.998 74.005 74.003 74.005 NA
## 29 74.005 74.006 74.009 74.000 74.017
## 30 73.986 74.015 74.000 73.991 73.986
## 31 74.020 73.995 73.996 74.025 74.016
## 32 74.010 74.005 74.015 74.025 74.000
## 33 74.008 NA 74.002 74.009 74.014
## 34 NA NA 73.988 NA 73.995
## 35 73.990 73.996 NA 73.984 NA
## 36 73.996 NA 74.000 73.997 NA
## 37 73.996 74.009 74.014 74.010 74.013
## 38 74.000 74.001 73.990 74.006 73.997
## 39 74.004 74.005 73.998 74.000 74.012
## 40 74.024 74.019 74.026 74.026 74.020# some obs are removed, the result is still a 40x5 matrix but with NAs added
qcc.groups(diameter[-c(1,2,50,52, 199)], sample[-c(1,2,50,52, 199)])## [,1] [,2] [,3] [,4] [,5]
## 1 73.988 74.002 73.992 NA NA
## 2 74.009 73.995 73.985 74.008 73.998
## 3 73.994 74.004 73.983 74.006 74.012
## 4 74.000 73.994 74.006 73.984 74.000
## 5 73.988 74.004 74.010 74.015 73.982
## 6 74.012 73.995 73.987 74.008 74.003
## 7 73.994 74.008 74.001 74.015 74.030
## 8 74.001 74.015 74.035 74.017 74.010
## 9 74.002 73.992 74.024 73.996 74.007
## 10 73.994 74.006 74.003 73.995 NA
## 11 73.998 74.002 73.967 74.014 NA
## 12 73.984 74.012 74.010 74.002 74.010
## 13 74.001 73.999 73.989 74.008 73.984
## 14 74.015 74.010 73.999 74.010 74.000
## 15 74.003 74.002 74.004 74.000 74.005
## 16 73.990 74.020 74.010 74.013 74.005
## 17 74.019 74.001 74.021 73.993 74.015
## 18 73.997 73.994 73.993 74.009 73.990
## 19 73.994 74.007 73.998 73.994 73.998
## 20 74.005 73.986 74.018 74.003 74.013
## 21 74.009 73.990 73.990 73.993 73.995
## 22 74.030 73.990 73.985 74.003 74.001
## 23 74.015 74.018 73.990 74.016 74.000
## 24 73.995 74.024 74.012 74.036 74.029
## 25 73.992 NA 74.005 74.015 73.989
## 26 73.985 74.000 74.015 74.005 74.007
## 27 73.995 74.000 NA 74.000 NA
## 28 73.998 74.005 74.003 74.005 NA
## 29 74.005 74.006 74.009 74.000 74.017
## 30 73.986 74.015 74.000 73.991 73.986
## 31 74.020 73.995 73.996 74.025 74.016
## 32 74.010 74.005 74.015 74.025 74.000
## 33 74.008 NA 74.002 74.009 74.014
## 34 NA NA 73.988 NA 73.995
## 35 73.990 73.996 NA 73.984 NA
## 36 73.996 NA 74.000 73.997 NA
## 37 73.996 74.009 74.014 74.010 74.013
## 38 74.000 74.001 73.990 74.006 73.997
## 39 74.004 74.005 73.998 74.000 74.012
## 40 74.024 74.019 74.026 74.020 NASet or return options for the ‘qcc’ package.
This function can be used to control the behavior of the ‘qcc’ library such as the background color, out-of-control points appearance, and many others.
old <- qcc.options() # save defaults
qcc.options("cex.stats") # get a single parameter## [1] 0.9qcc.options("cex.stats"=1.2) # change parameters
qcc.options(bg.margin="azure2")
qcc.options("violating.runs" = list(pch = 15, col = "purple"))
qcc.options("beyond.limits" = list(pch = 15, col = "orangered"))
qcc(rnorm(100), type = "xbar.one", std.dev = 0.7) # see the results
## List of 11
## $ call : language qcc(data = rnorm(100), type = "xbar.one", std.dev = 0.7)
## $ type : chr "xbar.one"
## $ data.name : chr "rnorm(100)"
## $ data : num [1:100, 1] -1.063 -0.281 -0.922 0.555 1.014 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:100] -1.063 -0.281 -0.922 0.555 1.014 ...
## ..- attr(*, "names")= chr [1:100] "1" "2" "3" "4" ...
## $ sizes : int [1:100] 1 1 1 1 1 1 1 1 1 1 ...
## $ center : num 0.0929
## $ std.dev : num 0.7
## $ nsigmas : num 3
## $ limits : num [1, 1:2] -2.01 2.19
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc.options(old) # restore old defaultsOverdispersion test for binomial and poisson data
# data from Wetherill and Brown (1991) pp. 212--213, 216--218:
x <- c(12,11,18,11,10,16,9,11,14,15,11,9,10,13,12,
8,12,13,10,12,13,16,12,18,16,10,16,10,12,14)
size <- rep(50, length(x))
qcc.overdispersion.test(x,size)##
## Overdispersion test Obs.Var/Theor.Var Statistic p-value
## binomial data 0.7644566 22.16924 0.81311x <- c(11,8,13,11,13,17,25,23,11,16,9,15,10,16,12,
8,9,15,4,12,12,12,15,17,14,17,12,12,7,16)
qcc.overdispersion.test(x)##
## Overdispersion test Obs.Var/Theor.Var Statistic p-value
## poisson data 1.472203 42.69388 0.048579Functions specifying rules for Shewhart charts
shewhart.rules
Functions to plot Shewhart c chart
stats.c
Statistics used in computing and drawing a Shewhart g chart
stats.g
success <- rbinom(1000, 1, 0.01)
num.noevent <- diff(which(c(1,success)==1))-1
qcc(success, type = "np", sizes = 1)
## List of 11
## $ call : language qcc(data = success, type = "np", sizes = 1)
## $ type : chr "np"
## $ data.name : chr "success"
## $ data : int [1:1000, 1] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named int [1:1000] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
## $ sizes : num [1:1000] 1 1 1 1 1 1 1 1 1 1 ...
## $ center : num 0.01
## $ std.dev : num 0.0995
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 0 0.308
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"qcc(num.noevent, type = "g")## Warning in limits.g(center = 94.6, std.dev = 94.0986716165537, sizes =
## c(1L, : The Geometric distribution is quite skewed, it is better to set
## conf at the required confidence level (0 < conf < 1) instead of as a
## multiplier of sigma.
## List of 11
## $ call : language qcc(data = num.noevent, type = "g")
## $ type : chr "g"
## $ data.name : chr "num.noevent"
## $ data : num [1:10, 1] 72 157 69 190 11 49 90 53 173 82
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:10] 72 157 69 190 11 49 90 53 173 82
## ..- attr(*, "names")= chr [1:10] "1" "2" "3" "4" ...
## $ sizes : int [1:10] 1 1 1 1 1 1 1 1 1 1
## $ center : num 94.6
## $ std.dev : num 94.1
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 0 377
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"Statistics used in computing and drawing a Shewhart np chart
stats.np
Statistics used in computing and drawing a Shewhart p chart
stats.p
Statistics used in computing and drawing a Shewhart R chart
stats.R
Functions to plot Shewhart S chart
stats.S
Statistics used in computing and drawing the Hotelling T^2 chart for subgrouped data
stats.T2
Statistics used in computing and drawing the Hotelling T^2 chart for individual observations data
stats.T2.single
Statistics used in computing and drawing a Shewhart u chart
stats.u
Statistics used in computing and drawing a Shewhart xbar chart
stats.xbar
Statistics used in computing and drawing a Shewhart xbar chart for one-at-time data
stats.xbar.one
# Water content of antifreeze data (Wetherill and Brown, 1991, p. 120)
x <- c(2.23, 2.53, 2.62, 2.63, 2.58, 2.44, 2.49, 2.34, 2.95, 2.54, 2.60, 2.45,
2.17, 2.58, 2.57, 2.44, 2.38, 2.23, 2.23, 2.54, 2.66, 2.84, 2.81, 2.39,
2.56, 2.70, 3.00, 2.81, 2.77, 2.89, 2.54, 2.98, 2.35, 2.53)
# the Shewhart control chart for one-at-time data
# 1) using MR (default)
qcc(x, type="xbar.one", data.name="Water content (in ppm) of batches of antifreeze")
## List of 11
## $ call : language qcc(data = x, type = "xbar.one", data.name = "Water content (in ppm) of batches of antifreeze")
## $ type : chr "xbar.one"
## $ data.name : chr "Water content (in ppm) of batches of antifreeze"
## $ data : num [1:34, 1] 2.23 2.53 2.62 2.63 2.58 2.44 2.49 2.34 2.95 2.54 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:34] 2.23 2.53 2.62 2.63 2.58 2.44 2.49 2.34 2.95 2.54 ...
## ..- attr(*, "names")= chr [1:34] "1" "2" "3" "4" ...
## $ sizes : int [1:34] 1 1 1 1 1 1 1 1 1 1 ...
## $ center : num 2.57
## $ std.dev : num 0.179
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 2.03 3.11
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"# 2) using SD
qcc(x, type="xbar.one", std.dev = "SD", data.name="Water content (in ppm) of batches of antifreeze")
## List of 11
## $ call : language qcc(data = x, type = "xbar.one", std.dev = "SD", data.name = "Water content (in ppm) of batches of antifreeze")
## $ type : chr "xbar.one"
## $ data.name : chr "Water content (in ppm) of batches of antifreeze"
## $ data : num [1:34, 1] 2.23 2.53 2.62 2.63 2.58 2.44 2.49 2.34 2.95 2.54 ...
## ..- attr(*, "dimnames")=List of 2
## $ statistics: Named num [1:34] 2.23 2.53 2.62 2.63 2.58 2.44 2.49 2.34 2.95 2.54 ...
## ..- attr(*, "names")= chr [1:34] "1" "2" "3" "4" ...
## $ sizes : int [1:34] 1 1 1 1 1 1 1 1 1 1 ...
## $ center : num 2.57
## $ std.dev : num 0.222
## $ nsigmas : num 3
## $ limits : num [1, 1:2] 1.9 3.23
## ..- attr(*, "dimnames")=List of 2
## $ violations:List of 2
## - attr(*, "class")= chr "qcc"# "as the size increases further, we would expect sigma-hat to settle down
# at a value close to the overall sigma-hat" (Wetherill and Brown, 1991,
# p. 121)
sigma <- NA
k <- 2:24
for (j in k)
sigma[j] <- sd.xbar.one(x, k=j)
plot(k, sigma[k], type="b") # plot estimates of sigma for
abline(h=sd(x), col=2, lty=2) # different values of k