Statistics used in computing and drawing the Hotelling T^2 chart for individual observations data

These functions are used to compute statistics required by the \(T^2\) chart for individual observations.

stats.T2.single(data, center = NULL, cov = NULL)

limits.T2.single(ngroups, size, nvars, conf)

Arguments

data

the observed data values

center

a vector of values to use for center of input variables.

cov

a matrix of values to use for the covariance matrix of input variables.

ngroups

number of groups

size

sample size

nvars

number of variables

conf

confidence level (0 < conf < 1)

Value

The function stats.T2.single returns a list with components:

statistics

a vector of values for the \(T^2\) statistic

means

a matrix of within group means for each variable (which is equal to data since sample are of sizes one)

center

sample/group center statistic

S

covariance matrix

The function limits.T2.single returns a list with components:

control

control limits

prediction

pred.limits

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.

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.

Author

Luca Scrucca

See also

mqcc, stats.T2