rQCC (version 0.19.8.2)

robust.control.chart: Robust statistical control chart

Description

Constructs robust statistical control chart using the median and Hodges-Lehmann (HL1, HL2, HL3) estimators, and the median absolute deviation (MAD) and Shamos estimators. Note that a conventional X-bar chart is also constructed by rcc(x, location="mean", scale="sd").

Usage

rcc (x, location = c("median","HL1","HL2","HL3","mean"), scale = c("mad","shamos","sd"), 
     bias.correction = TRUE, sigma.factor = 3)

Arguments

x

a numeric vector of observations.

location

a character string specifying the location estimator, must be one of "median" (default), "HL1", "HL2" and "HL3."

scale

a character string specifying the scale estimator, must be one of "mad" (default), "shamos" and "sd."

bias.correction

A finite-sample bias correction. TRUE adjusts a finite-sample bias correction using A3.factor function.

sigma.factor

a factor for the standard deviation (\(\sigma\)). 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 provides the center line and the lower and upper control limits.

References

Park, C., H. Kim, and M. Wang (2019). Finite-sample properties of robust location and scale estimators. arXiv:1908.00462.

Examples

# NOT RUN {
# Key in data (10 subgroups with 5 observations each).
x1 = c(4.13, 5.97, 5.54, 5.26, 5.73)
x2 = c(4.11, 6.27, 5.84, 5.17, 5.24)
x3 = c(4.51, 4.83, 5.67, 5.99, 5.85)
x4 = c(3.77, 3.78, 5.69, 4.31, 4.42)
x5 = c(4.83, 5.15, 3.83, 3.48, 2.52)
x6 = c(4.25, 3.66, 5.23, 5.96, 4.75)
x7 = c(4.93, 5.17, 6.44, 4.19, 4.42)
x8 = c(5.28, 4.83, 7.94, 4.89, 3.51)
x9 = c(4.58, 5.60, 5.84, 6.22, 4.54)
x10= c(5.14, 4.31, 3.23, 6.95, 5.35)
data = rbind(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

# Print LCL, CL, UCL.
result = rcc(data)
print(result)

# Plot a control chart
xbar = rowMeans(data)
plot(xbar, type="b", ylim=range(result,xbar) ) 
abline(h=result, lty=2, col="red")
# }