Statistics used in computing and drawing a Shewhart xbar chart

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

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.

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.

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