robust.control.chart: Robust quality control chart

Description

Constructs a robust control chart.

Usage

rcc (x, location = c("mean","median","HL1","HL2","HL3"), 
     scale = c("sd", "range","mad","shamos"), type = c("Xbar","S","R"), sigma.factor = 3)

Arguments

a numeric vector of observations.

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.

sigma.factor

a factor for the standard deviation (\(\sigma\)). 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).

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.

Details

rcc constructs a robust X-bar control chart. Using various robust location and scale estimates, one can construct a robust X-bar chart. The location and scale estimates used in this fuction are all unbiased. In addition, one can also construct the conventional \(\bar{X}\) chart with \(S\) and \(\bar{X}\) chart with \(R\). For more details, see the vignette.

References

Park, C., H. Kim, and M. Wang (2020). Investigation of finite-sample properties of robust location and scale estimators. Communications in Statistics - Simulation and Computation, To appear. https://doi.org/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.

Examples

Run this code

# NOT RUN {
##############
# 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). 
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, method="sd", correction=TRUE)

# The above limits are also calculated as 
A3 = factors.cc(n=6, "A3")
xbarbar = mean(data1)
sbar = mean( apply(data1, 1, sd) )
c(xbarbar-A3*sbar, xbarbar, xbarbar+A3*sbar)

# Plot a control chart
plot(result, cex.text=0.8, x.text=4.1)
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 estimate.
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, method="range", correction=TRUE)

# The above limits are also calculated as 
A2 = factors.cc(n=6, "A2")
xbarbar = mean(data1)
Rbar = mean( apply(data1, 1, function(x) {diff(range(x))}) )
c(xbarbar-A2*Rbar, xbarbar, xbarbar+A2*Rbar)

# Plot a control chart
plot(result, cex.text=0.8, x.text=4.2)
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.
result = rcc(data2, loc="median", scale="mad")
print(result)

# Summary of a control chart
summary(result)
# Note: the RE is calculated based on the unbiased estimators.
RE(n=4, method="median", correction=TRUE)
RE(n=4, method="mad", correction=TRUE)

# Plot a control chart
plot(result)

# ==========
# 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.
result = rcc(data2, loc="HL2", scale="shamos")
print(result)

# Summary of a control chart
summary(result)
# Note: the RE is calculated based on the unbiased estimators.
RE(n=4, method="HL2", correction=TRUE)
RE(n=4, method="shamos", correction=TRUE)

# Plot a control chart
plot(result)


############
# 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 estimate.
result = rcc(data1, type="S")
print(result)

# Summary of a control chart
# Note: the RE is calculated based on the unbiased estimators.
summary(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, x.text=4.1)
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)

# Summary of a control chart
# Note: the RE is calculated based on the unbiased estimators.
summary(result)

# Plot a control chart
plot(result, cex.text=0.8, x.text=4.1)
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 estimate.
# 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)

# Summary of a control chart
# Note: the RE is calculated based on the unbiased estimators.
summary(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))}) )
c(D3*Rbar, Rbar, D4*Rbar)

# Plot a control chart
plot(result, cex.text=0.8, x.text=4.1)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.0014, 0.0014), 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)

# Summary of a control chart
# Note: the RE is calculated based on the unbiased estimators.
summary(result)

# Plot a control chart
plot(result, cex.text=0.8, x.text=4.1)
abline(v=5.5, lty=1, lwd=2, col="gold")
text( c(3,8), c(0.0014, 0.0014), labels=c("Group 1", "Group 2") )


############
# vignette #
############
if (interactive()) vignette("rcc", package="rQCC")

# }

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