stats.xbar.one | R Documentation |
These functions are used to compute statistics required by the xbar chart for one-at-time data.
stats.xbar.one(data, sizes) sd.xbar.one(data, sizes, std.dev = c("MR", "SD"), r = 2, ...) limits.xbar.one(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
data |
the observed data values |
center |
sample/group center statistic. |
sizes |
samples sizes. Not needed, |
r |
number of successive pairs of observations for computing the standard deviation based on moving ranges of r points. |
std.dev |
within group standard deviation. Optional for |
nsigmas |
a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the |
conf |
a numeric value in (0,1) specifying the confidence level to use for computing control limits. |
... |
catches further ignored arguments. |
Methods available for estimating the process standard deviation:
"MR"
= moving range: this is estimate is based on the scaled mean of moving ranges
"SD"
= sample standard deviation: this estimate is defined as sd(x)/cd(n)
, where n
is the number of individual measurements of x
.
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.
Luca Scrucca
Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.
Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd ed. New York: John Wiley & Sons, Inc.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.
qcc
# 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 increases 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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