robust.attributes.chart.unbalanced {rQCC}

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)

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.

Details

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

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.

Author(s)

Chanseok Park

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" )