Multivariate nonparametric control charts using small samples

The problem under consideration is simultaneous monitoring of the means of two or more correlated variables of a process, by collecting a small fixed random sample at fixed time intervals. The target values are considered known, whereas the variance covariance matrix of the data must be estimated. A typical parametric chart to monitor this process would involve the assumption that the data follow a multivariate normal distribution. If this assumption is not reasonable or if it is difficult to verify, for example in a short production run, a multivariate control chart based on classical nonparametric statistics could be used. Control charts based on the sign and signed rank statistics are explored. Past sample information for each variable is retained through an exponentially weighted moving average statistic (EWMA) in order to increase the sensitivity of the charts to detect small shifts from the target. The properties of the charts are evaluated using simulation. Such charts are not distribution-free in the nonparametric sense, but they are more robust than the parametric equivalent chart because, among other reasons, they require only covariance estimates. Nonparametric charts are less efficient than the parametric equivalent chart if the measurements follow a normal distribution, but they improve significantly if the measurements follow a distribution with heavier tails.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1996

Author dc:creator

• Kapatou, Alexandra

Chair dc:contributor.committeechair

• Reynolds, Marion R. Jr.

Committee members dc:contributor.committeemember

• Arnold, Jesse C.
• Hinkelmann, Klaus H.
• Palettas, Panickos N.
• Terrell, George R.

• normal distribution

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-06062008-155730

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/38138