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A new generation of process capability indices

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  • A. Parchami
  • M. Mashinchi

Abstract

In quality control, we may confront imprecise concepts. One case is a situation in which upper and lower specification limits (SLs) are imprecise. If we introduce vagueness into SLs, we face quite new, reasonable and interesting processes, and the ordinary capability indices are not appropriate for measuring the capability of these processes. In this paper, similar to the traditional process capability indices (PCIs), we develop a fuzzy analogue by a distance defined on a fuzzy limit space and introduce PCIs, where instead of precise SLs we have two membership functions for upper and lower SLs. These indices are necessary when SLs are fuzzy, and they are helpful for comparing manufacturing process with fuzzy SLs. Some interesting relations among these introduced indices are proved. Numerical examples are given to clarify the method.

Suggested Citation

  • A. Parchami & M. Mashinchi, 2010. "A new generation of process capability indices," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 77-89.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:1:p:77-89
    DOI: 10.1080/02664760802695785
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    References listed on IDEAS

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    1. Lee, Hong Tau, 2001. "Cpk index estimation using fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 129(3), pages 683-688, March.
    2. Pearn, W. L. & Wu, Chien-Wei, 2005. "A Bayesian approach for assessing process precision based on multiple samples," European Journal of Operational Research, Elsevier, vol. 165(3), pages 685-695, September.
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    Cited by:

    1. Iván E. Villalón-Turrubiates & Rogelio López-Herrera & Jorge L. García-Alcaraz & José R. Díaz-Reza & Arturo Soto-Cabral & Iván González-Lazalde & Gerardo Grijalva-Avila & José L. Rodríguez-Álvarez, 2022. "A Non-Invasive Method to Evaluate Fuzzy Process Capability Indices via Coupled Applications of Artificial Neural Networks and the Placket–Burman DOE," Mathematics, MDPI, vol. 10(16), pages 1-27, August.
    2. Gholamreza Hesamian & Mohamad Ghasem Akbari, 2021. "A process capability index for normal random variable with intuitionistic fuzzy information," Operational Research, Springer, vol. 21(2), pages 951-964, June.

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