rcc: Robust quality control chart with balanced/unbalanced samples
In rQCC: Robust Quality Control Chart
robust.chart.unbalanced R Documentation
Robust quality control chart with balanced/unbalanced samples
Description
Constructs the robust control charts with balanced/unbalanced samples.
Usage
rcc (x, location = c("mean", "median", "HL1", "HL2", "HL3"),
scale = c("sd", "range", "mad", "shamos"), type = c("Xbar", "S", "R"),
poolLoc = c("A", "B", "C"), poolScale = c("A", "B", "C"), sigmaFactor=3, nk)
Arguments
x
a numeric matrix or list of vectors. Each row or vector contains a sub-sample.
location
a character string specifying the location estimator, must be
one of "mean" (default), "median", "HL1", "HL2" and "HL3".
scale
a character string specifying the scale estimator, must be
one of "sd" (default), "range", "mad" and "shamos".
type
a character string specifying the type of control chart.
poolLoc
pooling type for location.
poolScale
pooling type for scale.
sigmaFactor
a factor for the standard deviation (σ).
For example, the American Standard uses "3*sigma" limits (0.27% false alarm rate),
while the British Standard uses "3.09*sigma" limits (0.20% false alarm rate).
nk
sample size for Phase-II. If nk is missing, the average sample size is used.
Details
rcc constructs the robust X-bar, S and R control charts.
Using various robust location and scale estimators, one can construct the robust control charts.
For more details on the control charts, refer to vignette("rcc", package="rQCC").
Note that the location and scale estimators used in this fuction are all unbiased.
For more details on how to pool the location and scale estimators, refer to
vignette("pooledEstimator", package="rQCC").
In addition, one can also construct the conventional X-bar chart with S and
X-bar chart with R.
Value
rcc returns an object of class "rcc".
The function summary is used to obtain and print a summary of the results
and the function plot is used to plot the control chart.
Author(s)
Chanseok Park and Min Wang
References
Park, C., L. Ouyang, and M. Wang (2022).
Development of robust X-bar charts with unequal sample sizes.
ArXiv e-prints, 2212.10731.
doi: 10.48550/arXiv.2212.10731
Park, C., H. Kim, and M. Wang (2022).
Investigation of finite-sample properties of robust location and scale estimators.
Communications in Statistics - Simulation and Computation,
51, 2619-2645.
doi: 10.1080/03610918.2019.1699114
ASTM (2010).
Manual on Presentation of Data and Control Chart Analysis (STP 15-D),
8th edition.
American Society for Testing and Materials, West Conshohocken, PA.
Ryan (2000).
Statistical Methods For Quality Improvement, 2nd edition.
John Wiley & Sons, New York, NY.
Montgomery (2013).
Statistical Quality Control: An Modern Introduction, 7th edition.
John Wiley & Sons, New York, NY.
Examples
###############
# X-bar chart #
###############
# ==========
# Example 1a
# ----------
# The conventional X-bar chart with the standard deviation.
# Refer to Example 3 in Section 3.31 of ASTM (2010).
# The data below are from Table 29 in Section 3.31 of ASTM (2010).
# Each subgroup has a sample of size n=6. There are m=10 subgroups.
x1 = c(0.5005, 0.5000, 0.5008, 0.5000, 0.5005, 0.5000)
x2 = c(0.4998, 0.4997, 0.4998, 0.4994, 0.4999, 0.4998)
x3 = c(0.4995, 0.4995, 0.4995, 0.4995, 0.4995, 0.4996)
x4 = c(0.4998, 0.5005, 0.5005, 0.5002, 0.5003, 0.5004)
x5 = c(0.5000, 0.5005, 0.5008, 0.5007, 0.5008, 0.5010)
x6 = c(0.5008, 0.5009, 0.5010, 0.5005, 0.5006, 0.5009)
x7 = c(0.5000, 0.5001, 0.5002, 0.4995, 0.4996, 0.4997)
x8 = c(0.4993, 0.4994, 0.4999, 0.4996, 0.4996, 0.4997)
x9 = c(0.4995, 0.4995, 0.4997, 0.4992, 0.4995, 0.4992)
x10= c(0.4994, 0.4998, 0.5000, 0.4990, 0.5000, 0.5000)
data1 = rbind(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
# Print LCL, CL, UCL.
# The mean and standard deviation are used.
result = rcc(data1, loc="mean", scale="sd", type="Xbar")
print(result)
# Note: X-bar chart is a default with the mean and sd
# so the below is the same as the above.
rcc(data1)
# Summary of a control chart
summary(result)
RE(n=6, estimator="sd", correction=TRUE)
# The above limits are also calculated as
A3 = factors.cc(n=6, "A3")
xbarbar = mean(data1)
# xbarbar = mean(unlist(data1)) # for list
sbar = mean( apply(data1, 1, sd) )
c(xbarbar-A3*sbar, xbarbar, xbarbar+A3*sbar)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.5005, 0.5005), labels=c("Group 1", "Group 2") )
# ==========
# Example 1b
# ----------
# The conventional X-bar chart with the range.
# Refer to Example 5 in Section 3.31 of ASTM (2010).
# The data are the same as in Example 1a.
# Print LCL, CL, UCL.
# The range is used for the scale estimator.
result = rcc(data1, loc="mean", scale="range")
print(result)
# Summary of a control chart
# Note: the RE is calculated based on the unbiased estimators.
summary(result)
RE(n=6, estimator="range", correction=TRUE)
# The above limits are also calculated as
A2 = factors.cc(n=6, "A2")
xbarbar = mean(data1)
# xbarbar = mean(unlist(data1)) # for list
Rbar = mean( apply(data1, 1, function(x) {diff(range(x))}) )
# Rbar = mean( apply(sapply(data1,range),2,diff) ) # for list
c(xbarbar-A2*Rbar, xbarbar, xbarbar+A2*Rbar)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.5005, 0.5005), labels=c("Group 1", "Group 2") )
# ==========
# Example 1c
# ----------
# The median-MAD chart.
# Refer to Table 4.2 in Section 4.7 of Ryan (2000).
# Data: 20 subgroups with 4 observations each.
tmp = c(
72, 84, 79, 49, 56, 87, 33, 42, 55, 73, 22, 60, 44, 80, 54, 74,
97, 26, 48, 58, 83, 89, 91, 62, 47, 66, 53, 58, 88, 50, 84, 69,
57, 47, 41, 46, 13, 10, 30, 32, 26, 39, 52, 48, 46, 27, 63, 34,
49, 62, 78, 87, 71, 63, 82, 55, 71, 58, 69, 70, 67, 69, 70, 94,
55, 63, 72, 49, 49, 51, 55, 76, 72, 80, 61, 59, 61, 74, 62, 57 )
data2 = matrix(tmp, ncol=4, byrow=TRUE)
# Print LCL, CL, UCL.
# The median (location) and MAD (scale) are used.
rcc(data2, loc="median", scale="mad")
# Note: the RE is calculated based on the unbiased estimators.
RE(n=4, estimator="median", correction=TRUE)
# ==========
# Example 1d
# ----------
# The HL2-Shamos chart.
# The data are the same as in Example 1c.
# Print LCL, CL, UCL.
# The HL2 (location) and Shamos (scale) are used.
rcc(data2, loc="HL2", scale="shamos")
# Note: the RE is calculated based on the unbiased estimators.
RE(n=4, estimator="HL2", correction=TRUE)
############
# S chart #
############
# ==========
# Example 2a
# ----------
# The conventional S chart with the standard deviation.
# Refer to Example 3 in Section 3.31 of ASTM (2010).
# The data are the same as in Example 1a.
# Print LCL, CL, UCL.
# The standard deviaion (default) is used for the scale estimator.
result = rcc(data1, type="S")
print(result)
# The above limits are also calculated as
B3 = factors.cc(n=6, "B3")
B4 = factors.cc(n=6, "B4")
sbar = mean( apply(data1, 1, sd) )
c(B3*sbar, sbar, B4*sbar)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.0005, 0.0005), labels=c("Group 1", "Group 2") )
# ==========
# Example 2b
# ----------
# The S-type chart with the MAD.
# The data are the same as in Example 2a.
# Print LCL, CL, UCL.
# The mad (scale) are used.
result = rcc(data1, scale="mad", type="S")
print(result)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.00045, 0.00045), labels=c("Group 1", "Group 2") )
############
# R chart #
############
# ==========
# Example 3a
# ----------
# The conventional R chart with the range.
# Refer to Example 5 in Section 3.31 of ASTM (2010).
# The data are the same as in Example 1a.
# Print LCL, CL, UCL.
# The range is used for the scale estimator.
# Unlike the S chart, scale="range" is not a default.
# Thus, for the conventional R chart, use the option (scale="range") as below.
result = rcc(data1, scale="range", type="R")
print(result)
# The above limits are also calculated as
D3 = factors.cc(n=6, "D3")
D4 = factors.cc(n=6, "D4")
Rbar = mean( apply(data1, 1, function(x) {diff(range(x))}) )
# Rbar = mean( apply(sapply(data1,range),2,diff) ) # for list
c(D3*Rbar, Rbar, D4*Rbar)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.00135, 0.00135), labels=c("Group 1", "Group 2") )
# ==========
# Example 3b
# ----------
# The R-type chart with the Shamos.
# Refer to Example 5 in Section 3.31 of ASTM (2010).
# The data are the same as in Example 3a.
# Print LCL, CL, UCL.
# The mad (scale) are used.
result = rcc(data1, scale="shamos", type="R")
print(result)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.00135, 0.00135), labels=c("Group 1", "Group 2") )
###################
# Unbalanced Data #
###################
# ==========
# Example 4
# ----------
# Refer to Example 4 in Section 3.31 of ASTM (2010).
# Data set is from Table 30 in Section 3.31 of ASTM (2010).
x1 = c( 73, 73, 73, 75, 75)
x2 = c( 70, 71, 71, 71, 72)
x3 = c( 74, 74, 74, 74, 75)
x4 = c( 70, 70, 70, 72, 73)
x5 = c( 70, 70, 70, 70, 70)
x6 = c( 65, 65, 66, 69, 70)
x7 = c( 72, 72, 74, 76)
x8 = c( 69, 70, 71, 73, 73)
x9 = c( 71, 71, 71, 71, 72)
x10 = c( 71, 71, 71, 71, 72)
x11 = c( 71, 71, 72, 72, 72)
x12 = c( 70, 71, 71, 72, 72)
x13 = c( 73, 74, 74, 75, 75)
x14 = c( 74, 74, 75, 75, 75)
x15 = c( 72, 72, 72, 73, 73)
x16 = c( 75, 75, 75, 76)
x17 = c( 68, 69, 69, 69, 70)
x18 = c( 71, 71, 72, 72, 73)
x19 = c( 72, 73, 73, 73, 73)
x20 = c( 68, 69, 70, 71, 71)
x21 = c( 69, 69, 69, 69, 69)
# For unbalanced data set, use list.
data = list(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10,
x11,x12,x13,x14, x15, x16, x17, x18, x19, x20, x21)
# Xbar chart (witn nk=5)
rcc(data, nk=5)
# S chart (witn nk=4)
rcc(data, type="S", nk=4)
# ==========
# Example 5a
# ----------
# Data set is from Example 6.4 of Montgomery (2013)
# Statistical Quality Control (7th ed), Wiley.
# Data set for Phase I
x1 = c(74.030, 74.002, 74.019, 73.992, 74.008)
x2 = c(73.995, 73.992, 74.001)
x3 = c(73.988, 74.024, 74.021, 74.005, 74.002)
x4 = c(74.002, 73.996, 73.993, 74.015, 74.009)
x5 = c(73.992, 74.007, 74.015, 73.989, 74.014)
x6 = c(74.009, 73.994, 73.997, 73.985)
x7 = c(73.995, 74.006, 73.994, 74.000)
x8 = c(73.985, 74.003, 73.993, 74.015, 73.988)
x9 = c(74.008, 73.995, 74.009, 74.005)
x10 = c(73.998, 74.000, 73.990, 74.007, 73.995)
x11 = c(73.994, 73.998, 73.994, 73.995, 73.990)
x12 = c(74.004, 74.000, 74.007, 74.000, 73.996)
x13 = c(73.983, 74.002, 73.998)
x14 = c(74.006, 73.967, 73.994, 74.000, 73.984)
x15 = c(74.012, 74.014, 73.998)
x16 = c(74.000, 73.984, 74.005, 73.998, 73.996)
x17 = c(73.994, 74.012, 73.986, 74.005)
x18 = c(74.006, 74.010, 74.018, 74.003, 74.000)
x19 = c(73.984, 74.002, 74.003, 74.005, 73.997)
x20 = c(74.000, 74.010, 74.013)
x21 = c(73.982, 74.001, 74.015, 74.005, 73.996)
x22 = c(74.004, 73.999, 73.990, 74.006, 74.009)
x23 = c(74.010, 73.989, 73.990, 74.009, 74.014)
x24 = c(74.015, 74.008, 73.993, 74.000, 74.010)
x25 = c(73.982, 73.984, 73.995, 74.017, 74.013)
# For unbalanced data set, use list.
data = list(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
x16, x17, x18, x19, x20, x21, x22, x23, x24, x25)
# Xbar chart (witn nk=5)
rcc(data, nk=5)
# Xbar chart (witn nk=5) with different pooling methods
rcc(data, nk=5, poolLoc="C", poolScale="C")
# S chart (witn nk=5)
rcc(data, type="S", nk=5)
# S chart (witn nk=5) with plling method C.
rcc(data, type="S", nk=5, poolScale="C")
# ==========
# Example 5b
# ----------
# With contaminated data set.
# Two contaminated observations are added
# in the first subgroup (70.5, 77.0) of Example 5a.
datan = data
datan[[1]] = c(data[[1]], 70.5, 77.0)
# Xbar chart with non-robust estimators
rcc(datan, nk=5)
# robust Xbar chart (median and mad estimates)
rcc(datan, loc="median", sc="mad", nk=5)
# robust Xbar chart (median and mad estimates) with different pooling methods
rcc(datan, loc="median", sc="mad", nk=5, poolLoc="C", poolScale="C")
# robust S chart (mad estimate) with different pooling methods
rcc(datan, type="S", sc="mad", nk=5, poolScale="B")
rcc(datan, type="S", sc="mad", nk=5, poolScale="C")
rQCC documentation built on Dec. 28, 2022, 1:49 a.m.
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| robust.chart.unbalanced | R Documentation |
Robust quality control chart with balanced/unbalanced samples
Description
Constructs the robust control charts with balanced/unbalanced samples.
Usage
rcc (x, location = c("mean", "median", "HL1", "HL2", "HL3"),
scale = c("sd", "range", "mad", "shamos"), type = c("Xbar", "S", "R"),
poolLoc = c("A", "B", "C"), poolScale = c("A", "B", "C"), sigmaFactor=3, nk)
Arguments
x |
a numeric matrix or list of vectors. Each row or vector contains a sub-sample. |
location |
a character string specifying the location estimator, must be
one of |
scale |
a character string specifying the scale estimator, must be
one of |
type |
a character string specifying the type of control chart. |
poolLoc |
pooling type for location. |
poolScale |
pooling type for scale. |
sigmaFactor |
a factor for the standard deviation (σ). For example, the American Standard uses "3*sigma" limits (0.27% false alarm rate), while the British Standard uses "3.09*sigma" limits (0.20% false alarm rate). |
nk |
sample size for Phase-II. If |
Details
rcc constructs the robust X-bar, S and R control charts.
Using various robust location and scale estimators, one can construct the robust control charts.
For more details on the control charts, refer to vignette("rcc", package="rQCC").
Note that the location and scale estimators used in this fuction are all unbiased.
For more details on how to pool the location and scale estimators, refer to
vignette("pooledEstimator", package="rQCC").
In addition, one can also construct the conventional X-bar chart with S and X-bar chart with R.
Value
rcc returns an object of class "rcc".
The function summary is used to obtain and print a summary of the results
and the function plot is used to plot the control chart.
Author(s)
Chanseok Park and Min Wang
References
Park, C., L. Ouyang, and M. Wang (2022).
Development of robust X-bar charts with unequal sample sizes.
ArXiv e-prints, 2212.10731.
doi: 10.48550/arXiv.2212.10731
Park, C., H. Kim, and M. Wang (2022).
Investigation of finite-sample properties of robust location and scale estimators.
Communications in Statistics - Simulation and Computation,
51, 2619-2645.
doi: 10.1080/03610918.2019.1699114
ASTM (2010). Manual on Presentation of Data and Control Chart Analysis (STP 15-D), 8th edition. American Society for Testing and Materials, West Conshohocken, PA.
Ryan (2000). Statistical Methods For Quality Improvement, 2nd edition. John Wiley & Sons, New York, NY.
Montgomery (2013). Statistical Quality Control: An Modern Introduction, 7th edition. John Wiley & Sons, New York, NY.
Examples
###############
# X-bar chart #
###############
# ==========
# Example 1a
# ----------
# The conventional X-bar chart with the standard deviation.
# Refer to Example 3 in Section 3.31 of ASTM (2010).
# The data below are from Table 29 in Section 3.31 of ASTM (2010).
# Each subgroup has a sample of size n=6. There are m=10 subgroups.
x1 = c(0.5005, 0.5000, 0.5008, 0.5000, 0.5005, 0.5000)
x2 = c(0.4998, 0.4997, 0.4998, 0.4994, 0.4999, 0.4998)
x3 = c(0.4995, 0.4995, 0.4995, 0.4995, 0.4995, 0.4996)
x4 = c(0.4998, 0.5005, 0.5005, 0.5002, 0.5003, 0.5004)
x5 = c(0.5000, 0.5005, 0.5008, 0.5007, 0.5008, 0.5010)
x6 = c(0.5008, 0.5009, 0.5010, 0.5005, 0.5006, 0.5009)
x7 = c(0.5000, 0.5001, 0.5002, 0.4995, 0.4996, 0.4997)
x8 = c(0.4993, 0.4994, 0.4999, 0.4996, 0.4996, 0.4997)
x9 = c(0.4995, 0.4995, 0.4997, 0.4992, 0.4995, 0.4992)
x10= c(0.4994, 0.4998, 0.5000, 0.4990, 0.5000, 0.5000)
data1 = rbind(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
# Print LCL, CL, UCL.
# The mean and standard deviation are used.
result = rcc(data1, loc="mean", scale="sd", type="Xbar")
print(result)
# Note: X-bar chart is a default with the mean and sd
# so the below is the same as the above.
rcc(data1)
# Summary of a control chart
summary(result)
RE(n=6, estimator="sd", correction=TRUE)
# The above limits are also calculated as
A3 = factors.cc(n=6, "A3")
xbarbar = mean(data1)
# xbarbar = mean(unlist(data1)) # for list
sbar = mean( apply(data1, 1, sd) )
c(xbarbar-A3*sbar, xbarbar, xbarbar+A3*sbar)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.5005, 0.5005), labels=c("Group 1", "Group 2") )
# ==========
# Example 1b
# ----------
# The conventional X-bar chart with the range.
# Refer to Example 5 in Section 3.31 of ASTM (2010).
# The data are the same as in Example 1a.
# Print LCL, CL, UCL.
# The range is used for the scale estimator.
result = rcc(data1, loc="mean", scale="range")
print(result)
# Summary of a control chart
# Note: the RE is calculated based on the unbiased estimators.
summary(result)
RE(n=6, estimator="range", correction=TRUE)
# The above limits are also calculated as
A2 = factors.cc(n=6, "A2")
xbarbar = mean(data1)
# xbarbar = mean(unlist(data1)) # for list
Rbar = mean( apply(data1, 1, function(x) {diff(range(x))}) )
# Rbar = mean( apply(sapply(data1,range),2,diff) ) # for list
c(xbarbar-A2*Rbar, xbarbar, xbarbar+A2*Rbar)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.5005, 0.5005), labels=c("Group 1", "Group 2") )
# ==========
# Example 1c
# ----------
# The median-MAD chart.
# Refer to Table 4.2 in Section 4.7 of Ryan (2000).
# Data: 20 subgroups with 4 observations each.
tmp = c(
72, 84, 79, 49, 56, 87, 33, 42, 55, 73, 22, 60, 44, 80, 54, 74,
97, 26, 48, 58, 83, 89, 91, 62, 47, 66, 53, 58, 88, 50, 84, 69,
57, 47, 41, 46, 13, 10, 30, 32, 26, 39, 52, 48, 46, 27, 63, 34,
49, 62, 78, 87, 71, 63, 82, 55, 71, 58, 69, 70, 67, 69, 70, 94,
55, 63, 72, 49, 49, 51, 55, 76, 72, 80, 61, 59, 61, 74, 62, 57 )
data2 = matrix(tmp, ncol=4, byrow=TRUE)
# Print LCL, CL, UCL.
# The median (location) and MAD (scale) are used.
rcc(data2, loc="median", scale="mad")
# Note: the RE is calculated based on the unbiased estimators.
RE(n=4, estimator="median", correction=TRUE)
# ==========
# Example 1d
# ----------
# The HL2-Shamos chart.
# The data are the same as in Example 1c.
# Print LCL, CL, UCL.
# The HL2 (location) and Shamos (scale) are used.
rcc(data2, loc="HL2", scale="shamos")
# Note: the RE is calculated based on the unbiased estimators.
RE(n=4, estimator="HL2", correction=TRUE)
############
# S chart #
############
# ==========
# Example 2a
# ----------
# The conventional S chart with the standard deviation.
# Refer to Example 3 in Section 3.31 of ASTM (2010).
# The data are the same as in Example 1a.
# Print LCL, CL, UCL.
# The standard deviaion (default) is used for the scale estimator.
result = rcc(data1, type="S")
print(result)
# The above limits are also calculated as
B3 = factors.cc(n=6, "B3")
B4 = factors.cc(n=6, "B4")
sbar = mean( apply(data1, 1, sd) )
c(B3*sbar, sbar, B4*sbar)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.0005, 0.0005), labels=c("Group 1", "Group 2") )
# ==========
# Example 2b
# ----------
# The S-type chart with the MAD.
# The data are the same as in Example 2a.
# Print LCL, CL, UCL.
# The mad (scale) are used.
result = rcc(data1, scale="mad", type="S")
print(result)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.00045, 0.00045), labels=c("Group 1", "Group 2") )
############
# R chart #
############
# ==========
# Example 3a
# ----------
# The conventional R chart with the range.
# Refer to Example 5 in Section 3.31 of ASTM (2010).
# The data are the same as in Example 1a.
# Print LCL, CL, UCL.
# The range is used for the scale estimator.
# Unlike the S chart, scale="range" is not a default.
# Thus, for the conventional R chart, use the option (scale="range") as below.
result = rcc(data1, scale="range", type="R")
print(result)
# The above limits are also calculated as
D3 = factors.cc(n=6, "D3")
D4 = factors.cc(n=6, "D4")
Rbar = mean( apply(data1, 1, function(x) {diff(range(x))}) )
# Rbar = mean( apply(sapply(data1,range),2,diff) ) # for list
c(D3*Rbar, Rbar, D4*Rbar)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.00135, 0.00135), labels=c("Group 1", "Group 2") )
# ==========
# Example 3b
# ----------
# The R-type chart with the Shamos.
# Refer to Example 5 in Section 3.31 of ASTM (2010).
# The data are the same as in Example 3a.
# Print LCL, CL, UCL.
# The mad (scale) are used.
result = rcc(data1, scale="shamos", type="R")
print(result)
# Plot a control chart
plot(result, cex.text=0.8)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.00135, 0.00135), labels=c("Group 1", "Group 2") )
###################
# Unbalanced Data #
###################
# ==========
# Example 4
# ----------
# Refer to Example 4 in Section 3.31 of ASTM (2010).
# Data set is from Table 30 in Section 3.31 of ASTM (2010).
x1 = c( 73, 73, 73, 75, 75)
x2 = c( 70, 71, 71, 71, 72)
x3 = c( 74, 74, 74, 74, 75)
x4 = c( 70, 70, 70, 72, 73)
x5 = c( 70, 70, 70, 70, 70)
x6 = c( 65, 65, 66, 69, 70)
x7 = c( 72, 72, 74, 76)
x8 = c( 69, 70, 71, 73, 73)
x9 = c( 71, 71, 71, 71, 72)
x10 = c( 71, 71, 71, 71, 72)
x11 = c( 71, 71, 72, 72, 72)
x12 = c( 70, 71, 71, 72, 72)
x13 = c( 73, 74, 74, 75, 75)
x14 = c( 74, 74, 75, 75, 75)
x15 = c( 72, 72, 72, 73, 73)
x16 = c( 75, 75, 75, 76)
x17 = c( 68, 69, 69, 69, 70)
x18 = c( 71, 71, 72, 72, 73)
x19 = c( 72, 73, 73, 73, 73)
x20 = c( 68, 69, 70, 71, 71)
x21 = c( 69, 69, 69, 69, 69)
# For unbalanced data set, use list.
data = list(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10,
x11,x12,x13,x14, x15, x16, x17, x18, x19, x20, x21)
# Xbar chart (witn nk=5)
rcc(data, nk=5)
# S chart (witn nk=4)
rcc(data, type="S", nk=4)
# ==========
# Example 5a
# ----------
# Data set is from Example 6.4 of Montgomery (2013)
# Statistical Quality Control (7th ed), Wiley.
# Data set for Phase I
x1 = c(74.030, 74.002, 74.019, 73.992, 74.008)
x2 = c(73.995, 73.992, 74.001)
x3 = c(73.988, 74.024, 74.021, 74.005, 74.002)
x4 = c(74.002, 73.996, 73.993, 74.015, 74.009)
x5 = c(73.992, 74.007, 74.015, 73.989, 74.014)
x6 = c(74.009, 73.994, 73.997, 73.985)
x7 = c(73.995, 74.006, 73.994, 74.000)
x8 = c(73.985, 74.003, 73.993, 74.015, 73.988)
x9 = c(74.008, 73.995, 74.009, 74.005)
x10 = c(73.998, 74.000, 73.990, 74.007, 73.995)
x11 = c(73.994, 73.998, 73.994, 73.995, 73.990)
x12 = c(74.004, 74.000, 74.007, 74.000, 73.996)
x13 = c(73.983, 74.002, 73.998)
x14 = c(74.006, 73.967, 73.994, 74.000, 73.984)
x15 = c(74.012, 74.014, 73.998)
x16 = c(74.000, 73.984, 74.005, 73.998, 73.996)
x17 = c(73.994, 74.012, 73.986, 74.005)
x18 = c(74.006, 74.010, 74.018, 74.003, 74.000)
x19 = c(73.984, 74.002, 74.003, 74.005, 73.997)
x20 = c(74.000, 74.010, 74.013)
x21 = c(73.982, 74.001, 74.015, 74.005, 73.996)
x22 = c(74.004, 73.999, 73.990, 74.006, 74.009)
x23 = c(74.010, 73.989, 73.990, 74.009, 74.014)
x24 = c(74.015, 74.008, 73.993, 74.000, 74.010)
x25 = c(73.982, 73.984, 73.995, 74.017, 74.013)
# For unbalanced data set, use list.
data = list(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
x16, x17, x18, x19, x20, x21, x22, x23, x24, x25)
# Xbar chart (witn nk=5)
rcc(data, nk=5)
# Xbar chart (witn nk=5) with different pooling methods
rcc(data, nk=5, poolLoc="C", poolScale="C")
# S chart (witn nk=5)
rcc(data, type="S", nk=5)
# S chart (witn nk=5) with plling method C.
rcc(data, type="S", nk=5, poolScale="C")
# ==========
# Example 5b
# ----------
# With contaminated data set.
# Two contaminated observations are added
# in the first subgroup (70.5, 77.0) of Example 5a.
datan = data
datan[[1]] = c(data[[1]], 70.5, 77.0)
# Xbar chart with non-robust estimators
rcc(datan, nk=5)
# robust Xbar chart (median and mad estimates)
rcc(datan, loc="median", sc="mad", nk=5)
# robust Xbar chart (median and mad estimates) with different pooling methods
rcc(datan, loc="median", sc="mad", nk=5, poolLoc="C", poolScale="C")
# robust S chart (mad estimate) with different pooling methods
rcc(datan, type="S", sc="mad", nk=5, poolScale="B")
rcc(datan, type="S", sc="mad", nk=5, poolScale="C")
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