rQCC (version 2.22.12)

robust.attributes.chart.unbalanced: Robust attributes control charts with balanced/unbalanced samples

Description

Constructs the robust g and h attributes control charts with balanced/unbalanced samples.

Usage

racc (x, gamma, type=c("g","h","t"), parameter, gEstimator=c("cdf", "MM"), 
      tModel=c("E", "W"), location.shift = 0, sigmaFactor=3, nk)

Value

racc returns an object of class "racc". 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.

Arguments

x

a numeric vector of the number of nonconforming units.

gamma

a numeric value for a inlier proportion. gamma should be between 0 and 1 (smaller value means more trimming).

type

a character string specifying the type of control chart.

parameter

a known Bernoulli parameter value for the \(g\) and \(h\) charts. If not known, it is estimated. For more details, refer to vignette("racc", package="rQCC").

gEstimator

a method for estimating the Bernoulli parameter for \(g\) and \(h\) charts. "cdf" is based on the memoryless property and "MM" is based on the truncated geometric distribution.

tModel

Probability model for \(t\) chart. "E" for Exponential and "W" for Weibull.

location.shift

a known location shift parameter value for \(g\) and \(h\) charts.

sigmaFactor

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).

nk

sample size for Phase-II. If nk is missing, the average of the subsample sizes is used.

Author

Chanseok Park

Details

racc constructs the attributes control charts for nonconforming units (\(p\) and \(np\) charts) and for nonconformities per unit (\(c\) and \(u\) charts).

References

Park, C., L. Ouyang, and M. Wang (2021). Robust g-type quality control charts for monitoring nonconformities. Computers and Industrial Engineering, 162, 107765.

Kaminsky, F. C., J. C. Benneyan and R. D. Davis (1992). Statistical Control Charts Based on a Geometric Distribution. Journal of Quality Technology, 24, 63-69.

Examples

# ===============================
# Example 1: g and h charts
# -------------------------------
# Refer to Kaminsky et al. (1992) and Table 2 of Park, et al. (2021).
tmp = c(
11,  2,  8,  2, 4,   1,  1, 11,  2, 1,   1,  7,  1,  1, 9, 
 5,  1,  3,  6, 5,  13,  2,  3,  3, 4,   3,  2,  6,  1, 5,  
 2,  2,  8,  3, 1,   1,  3,  4,  6, 5,   2,  8,  1,  1, 4,  
13, 10, 15,  5, 2,   3,  6,  1,  5, 8,   9,  1, 18,  3, 1,  
 3,  7, 14,  3, 1,   7,  7,  1,  8, 1,   4,  1,  6,  1, 1, 
 1, 14,  2,  3, 7,  19,  9,  7,  1, 8,   5,  1,  1,  6, 1,  
 9,  5,  6,  2, 2,   8, 15,  2,  3, 3,   4,  7, 11,  4, 6,  
 7,  5,  1, 14, 8,   3,  3,  5, 21,10,  11,  1,  6,  1, 2,  
 4,  1,  2, 11, 5,   3,  5,  4, 10, 3,   1,  4,  7,  3, 2, 
 3,  5,  4,  2, 3,   5,  1,  4, 11,17,   1, 13, 13,  2, 1)  
data = matrix(tmp, byrow=TRUE, ncol=5)

# g chart with cdf (trimming) method.
# Print LCL, CL, UCL.
result = racc(data, gamma=0.9, type="g", location=1)
print(result)

# Summary of a control chart
summary(result)

plot(result, cex.text=0.8)

# h chart with MM (truncated geometric) method.
racc(data, gamma=0.9, type="h", location=1, gEstimator="MM")


# ===============================
# Example 2: g and h charts (unbalanced data)
# -------------------------------
x1 = c(11, 2,  8,  2, 4)
x2 = c(1,  1, 11,  2, 1)
x3 = c(1,  7,  1)
x4 = c(5,  1,  3,  6, 5)
x5 = c(13, 2,  3,  3)
x6 = c(3,  2,  6,  1, 5)
x7 = c(2,  2,  8,  3, 1)
x8 = c(1,  3,  4,  6, 5)
x9 = c(2,  8,  1,  1, 4)
data = list(x1, x2, x3, x4, x5, x6, x7, x8, x9)

result = racc(data, gamma=0.9, type="g", location=1, gEstimator="cdf", nk=5)
summary(result)
plot(result)


# ===============================
# Example 3: t charts 
# -------------------------------
x = c(0.35, 0.92, 0.59, 4.28, 0.21, 0.79, 1.75, 0.07, 3.3,
1.7, 0.33, 0.97, 0.96, 2.23, 0.88, 0.37, 1.3, 0.4, 0.19, 1.59)

# Exponential t chart
result = racc(x, type="t", tModel="E")
summary(result)

plot(result, cex.text=0.8)
text(10, 6, labels="Robust exponential t chart" )


# Weibull t chart
result = racc(x, type="t", tModel="W")
summary(result)

plot(result, cex.text=0.8)
text(10, 5.5, labels="Robust Weibull t chart" )