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Capability indices and nonconforming proportion in univariate and multivariate processes

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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 C p index explicitly admits this interpretation. For instance, if C p  = 0.5, the standard deviation should be reduced to 50% to attain C p  = 1. However, for noncentered processes and multivariate processes, there is a lack of capability indices that admit such 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 indices with the existing ones, showing the advantages of the proposals.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avd. de la Universidad 30, 28911, Leganés, Madrid, Spain

    Isabel González

  2. Department of Statistics, Universidad Carlos III de Madrid, Avd. de la Universidad 30, 28911, Leganés, Madrid, Spain

    Ismael Sánchez

Authors
  1. Isabel González
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  2. Ismael Sánchez
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Correspondence to Isabel González.

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González, I., Sánchez, I. Capability indices and nonconforming proportion in univariate and multivariate processes. Int J Adv Manuf Technol 44, 1036–1050 (2009). https://doi.org/10.1007/s00170-008-1907-5

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  • DOI: https://doi.org/10.1007/s00170-008-1907-5

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