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3.2.2 Measurement Control for Heart Valve Manufacturer
Keith R. Eberhardt Statistical Engineering Division, CAML
James J. Filliben Statistical Engineering Division, CAML
Howard Harary Manufacturing Engineering Laboratory, NIST
Tom Waits Medical Carbon Research, Inc., Austin, Texas During the process of manufacturing artificial heart valves, Medical Carbon Research, Inc., makes a very large number of measurements using a coordinate measurement machine (CMM). The company contacted NIST because they were experiencing difficulty in establishing control charts to monitor all 146 dimensions of their multivariate measurements on a check standard artifact. In particular, there were too many out-of-control signals being generated when they used 146 univariate control charts and required that all dimensions be inside the control limits for each complete set of measurements.
To address the practical problem, we transformed the raw data matrix,
consisting of 24 replications of a 146-dimensional vector, into principal
components. The eigenvalues of the first 10 principal components are shown in
the figure, which also shows the expected result that a very large proportion
of the variation is captured in the first one to three principal components.
This result was transmitted to MCRI, along with a copy of Dataplot software
and an example program to compute the principal components and construct a
control chart for them. The figure shows the quite satisfactory behavior of
the first principal component for the MCRI data in control chart form. At
last report, our contact at MCRI had installed Dataplot and had successfully
reproduced the calculation of the principal components and the control chart.
Figure 14: Reduced data from 146-dimensional measurements on an artificial heart valve check standard. The top plot shows a Pareto chart of the first ten eigenvalues from a principal components analysis. The bottom plot shows a control chart based on the first principal component.
Date created: 7/20/2001 |