A transformation technique to estimate the process capability index for non-normal processes

  • S. Z. Hosseinifard
  • Babak AbbasiEmail author
  • S. Ahmad
  • M. Abdollahian


Estimating the process capability index (PCI) for non-normal processes has been discussed by many researches. There are two basic approaches to estimating the PCI for non-normal processes. The first commonly used approach is to transform the non-normal data into normal data using transformation techniques and then use a conventional normal method to estimate the PCI for transformed data. This is a straightforward approach and is easy to deploy. The alternate approach is to use non-normal percentiles to calculate the PCI. The latter approach is not easy to implement and a deviation in estimating the distribution of the process may affect the efficacy of the estimated PCI. The aim of this paper is to estimate the PCI for non-normal processes using a transformation technique called root transformation. The efficacy of the proposed technique is assessed by conducting a simulation study using gamma, Weibull, and beta distributions. The root transformation technique is used to estimate the PCI for each set of simulated data. These results are then compared with the PCI obtained using exact percentiles and the Box-Cox method. Finally, a case study based on real-world data is presented.


Process capability index Non-normal process Root transformation Box-Cox transformation and quintile-based capability indices 


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Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  • S. Z. Hosseinifard
    • 1
  • Babak Abbasi
    • 2
    • 4
    Email author
  • S. Ahmad
    • 3
  • M. Abdollahian
    • 3
  1. 1.Department of Industrial EngineeringIran University of Science and TechnologyTehranIran
  2. 2.Department of Industrial EngineeringSharif University of TechnologyTehranIran
  3. 3.Department of Statistics and Operations ResearchRMIT UniversityMelbourneAustralia
  4. 4.TehranIran

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