ENBIS-11 in Coimbra

4 – 8 September 2011 Abstract submission: 1 January – 25 June 2011

Multivariate Process Capability Indices—A New Principal Component Analysis Approach

6 September 2011, 15:45 – 16:05

Abstract

Submitted by
Ingrid Tano
Authors
Ingrid Tano and Kerstin Vännman
Affiliation
University West and Luleå University of Technology, Sweden
Abstract
Often the quality of a process is determined by several correlated quality characteristics. In such cases the quality characteristic should be treated as a vector and a number of different multivariate process capability indices (MPCI:s) have been developed for such a situation. One of the existing MPCIs described in the literature is based on principal component analysis (PCA). The idea behind this MPCI is to do a PCA and consider only the first few principle components that explain the main part of the variability. Then one of the well-known univariate process capability indices is applied to each selected principle component and thereafter the univariate process capability indices for the selected principle components are combined to one MPCI. In order define this MPCI the tolerance region for the quality characteristic vector is transformed to a separate specification interval for each principal component. Recently it was shown that this transformation of the tolerance region into separate specification intervals is done in an improper way. And it is far from obvious how to obtain the individual specification limits for each selected principal component when the transformation is properly made. This problem gets complicated for 2 principal components and even worse for more than 2 principal components. We propose a new method based on PCA that circumvent these difficulties for the case when the tolerance region is a hyper-rectangular. This method first transforms the original data in a suitable way. Then PCA is done on the transformed data and it is shown that only the first principal component is needed to deem a process as capable or not at a stated significance level. Hence, a multivariate situation is transferred into a univariate situation and well-known theory for univariate process capability indices can be used to draw conclusions about the process capability. The properties of this method are investigated through a simulation study.

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