Capability Indices and Nonconforming Proportion in Univariate and Multivariate Processes Articles uri icon

authors

  • GONZALEZ FARIAS, ISABEL MARINA
  • SANCHEZ RODRIGUEZ-MORCILLO, ISMAEL

publication date

  • October 2009

start page

  • 1036

end page

  • 1050

issue

  • 9/10

volume

  • 44

international standard serial number (ISSN)

  • 0268-3768

electronic international standard serial number (EISSN)

  • 1433-3015

abstract

  • The main usefulness of a capability index is to relate the actual variability of the process with the admissible one. This admissible variability is, in turn, related with the nonconforming proportion. Hence, the capability index should be closely related to the nonconforming proportion. In univariate and centered processes, the classical Cp index explicitly admits this interpretation. For instance, if Cp = 0.5, the standarddeviation should be reduced to 50% to attain Cp = 1. However, for noncentered processes and multivariate processes, there is a lack of capability indices that admitsuch an interpretation. This article fills this gap in the literature and proposes univariate and multivariate capability indices that have a direct interpretation of how much the variability of the process should increase or decrease to attain a unitary index. Some numerical examples are used to compare the proposed indiceswith the existing ones, showing the advantages of the proposals.