stats.xbar: Statistics used in computing and drawing a Shewhart xbar...

In luca-scr/qcc: Quality Control Charts

Statistics used in computing and drawing a Shewhart xbar chart

Description

These functions are used to compute statistics required by the xbar chart.

Usage

stats.xbar(data, sizes)
sd.xbar(data, sizes, 
        std.dev = c("UWAVE-R", "UWAVE-SD", "MVLUE-R", "MVLUE-SD", "RMSDF"), 
        ...)
limits.xbar(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

data	the observed data values
center	sample/group center statistic
sizes	samples sizes. Optional
std.dev	within group standard deviation. Optional for sd.xbar function, required for limits.xbar. See details.
nsigmas	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the conf argument is provided.
conf	a numeric value in (0,1) specifying the confidence level to use for computing control limits.
...	catches further ignored arguments.

Details

The following methods are available for estimating the process standard deviation:

"UWAVE-R"

UnWeighted AVErage of within-group estimates based on within-group Ranges

"UWAVE-SD"

UnWeighted AVErage of within-group estimates based on within-group Standard Deviations

"MVLUE-R"

Minimum Variance Linear Unbiased Estimator computed as a weighted average of within-group estimates based on within-group Ranges

"MVLUE-SD"

Minimum Variance Linear Unbiased Estimator computed as a weighted average of within-group estimates based on within-group Standard Deviations

"RMSDF"

Root-Mean-Square estimator computed as a weighted average of within-group estimates based on within-group Standard Deviations

Depending on the chart, a method may be available or not, or set as the default according to the following table:

Detailed definitions of formulae implemented are available in the SAS/QC User's Guide.

Value

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

The function sd.xbar returns std.dev the standard deviation of the statistic charted. This is based on results from Burr (1969).

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

Author(s)

Luca Scrucca

References

Burr, I.W. (1969) Control charts for measurements with varying sample sizes. Journal of Quality Technology, 1(3), 163-167.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

luca-scr/qcc documentation built on Feb. 25, 2023, 3:33 p.m.