Statistics used in computing and drawing a Shewhart xbar chart for one-at-time data

Description

These functions are used to compute statistics required by the xbar chart for one-at-time data.

Usage

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stats.xbar.one(data, sizes)
sd.xbar.one(data, sizes, std.dev = c("MR", "SD"), k=2)
limits.xbar.one(center, std.dev, sizes, conf)

Arguments

data

the observed data values

center

sample/group center statistic.

sizes

samples sizes. Not needed, size=1 is used.

k

number of successive pairs of observations for computing the standard deviation based on moving ranges of k points.

std.dev

within group standard deviation. Optional for sd.xbar.one function, required for limits.xbar.one. See details.

conf

a numeric value used to compute control limits, specifying the number of standard deviations (if conf > 1) or the confidence level (if 0 < conf < 1).

Details

Methods available for estimating the process standard deviation:

Method Description
"MR" moving range: this is estimate is based on the scaled mean of moving ranges
"SD" sample standard deviation: this estimate is defined as as(x)/cd(n), where n = number of observations x.

Value

The function stats.xbar.one returns a list with components statistics and center.

The function sd.xbar.one returns std.dev the standard deviation of the statistic charted.

The function limits.xbar.one returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca luca@stat.unipg.it

References

Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Ryan T.P. (2000) Statistical Methods for Quality Improvement, New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

Examples

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# Water content of antifreeze data (Wetherill and Brown, 1991, p. 120)
x <- c(2.23, 2.53, 2.62, 2.63, 2.58, 2.44, 2.49, 2.34, 2.95, 2.54, 2.60, 2.45,
       2.17, 2.58, 2.57, 2.44, 2.38, 2.23, 2.23, 2.54, 2.66, 2.84, 2.81, 2.39,
       2.56, 2.70, 3.00, 2.81, 2.77, 2.89, 2.54, 2.98, 2.35, 2.53)
# the Shewhart control chart for one-at-time data
# 1) using MR (default)
qcc(x, type="xbar.one", data.name="Water content (in ppm) of batches of antifreeze")
# 2) using SD
qcc(x, type="xbar.one", std.dev = "SD", data.name="Water content (in ppm) of batches of antifreeze")

# "as the size inceases further, we would expect sigma-hat to settle down
#  at a value close to the overall sigma-hat" (Wetherill and Brown, 1991,
# p. 121)
sigma <- NA
k <- 2:24
for (j in k)
    sigma[j] <- sd.xbar.one(x, k=j)
plot(k, sigma[k], type="b")     # plot estimates of sigma for 
abline(h=sd(x), col=2, lty=2)   # different values of k

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