Faculty Publications

Multivariate Process Capability Via Löwner Ordering

Document Type

Article

Keywords

Anderson's theorem, Bootstrap, Eigenvalues, Union-intersection test, Wishart distribution

Journal/Book/Conference Title

Linear Algebra and Its Applications

Volume

430

Issue

10

First Page

2681

Last Page

2689

Abstract

Probability bounds can be derived for distributions whose covariance matrices are ordered with respect to Löwner partial ordering, a relation that is based on whether the difference between two matrices is positive definite. One example is Anderson's Theorem. This paper develops a probability bound that follows from Anderson's Theorem that is useful in the assessment of multivariate process capability. A statistical hypothesis test is also derived that allows one to test the null hypothesis that a given process is capable versus the alternative hypothesis that it is not capable on the basis of a sample of observed quality characteristic vectors from the process. It is argued that the proposed methodology is viable outside the multivariate normal model, where the p-value for the test can be computed using the bootstrap. The methods are demonstrated using example data, and the performance of the bootstrap approach is studied empirically using computer simulations. © 2008 Elsevier Inc. All rights reserved.

Department

Department of Biology

Original Publication Date

5-1-2009

DOI of published version

10.1016/j.laa.2008.11.032

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