Title page for ETD etd-06062008-155730
|Type of Document
||Multivariate nonparametric control charts using small samples
|Reynolds, Marion R. Jr.
|Arnold, Jesse C.
|Hinkelmann, Klaus H.
|Palettas, Panickos N.
|Terrell, George R.
|Date of Defense
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
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.
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