qcc (version 1.2)

stats.xbar.one: Functions to plot 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

stats.xbar.one(data, sizes)
sd.xbar.one(data, sizes, std.dev, 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

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).

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.

References

Montgomery, D.C. (2000) Introduction to Statistical Quality Control, 4th ed. New York: John Wiley & Sons. Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

Examples

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

# the Shewhart control chart for one-at-time data
qcc(x, type="xbar.one", data.name="Water content (in ppm) of batches of antifreeze")