Multivariate process capability via Löwner ordering
Anderson's theorem, Bootstrap, Eigenvalues, Union-intersection test, Wishart distribution
Linear Algebra and Its Applications
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.
Original Publication Date
DOI of published version
Kirmani, S. N.U.A. and Polansky, Alan M., "Multivariate process capability via Löwner ordering" (2009). Faculty Publications. 2257.