Title page for ETD etd-06062008-155730


Type of Document Dissertation
Author Kapatou, Alexandra
URN etd-06062008-155730
Title Multivariate nonparametric control charts using small samples
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Reynolds, Marion R. Jr. Committee Chair
Arnold, Jesse C. Committee Member
Hinkelmann, Klaus H. Committee Member
Palettas, Panickos N. Committee Member
Terrell, George R. Committee Member
Keywords
  • normal distribution
Date of Defense 1996-02-05
Availability restricted
Abstract
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.

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