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Multivariate Process Capability

Most products have multiple quality characteristics, some of which are correlated. Multivariate process capability analysis incorporates those correlations to penalize the process when the process produces output that doesn't meet the typical relationship between the characteristics.

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This is a useful implementation which Statgraphics has recently implemented.

 

Some very useful tools when two or more process outputs are correlated: 

  • Bivariate Histograms: Implement 3-D histograms for Frequency of X1 and X2 vs Density.  Potentially useful in Graph Builder or as a Standalone Graphing Platform.
  • Multivariate Hypotethesis Test/s for Normality: Roysten's test.  
  • Multivariate Capability Indices:  mCpk.  Multivariate analog of Cpk based on Theta = the probability of a vector of random variables is outside the region defined by the specification limits when calculated from a multivariate normal distribution.
  • Multivariate Statistical Tolerance Limits (aka "Confidence & Reliability" Limits).
    • Eliptical tolerance region-based approach.
    • Bonferroni-based approach (separeate confidence limits/ fitting).
  • Data Transformations for a space of variables, e.g. X1, X2, Xn.... that is not jointly multivariate normal.
    • Box-Cox based approach.