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Making decision to evaluate process capability index C p with fuzzy numbers

Abstract

The process capability index C p has wide applications in the manufacturing industry. This paper extends those applications to a fuzzy environment, with a methodology for testing the index C p of fuzzy numbers. A pair of nonlinear functions is formulated to find the α-cut of index \(\widetilde{C}_{p} \). From various values of α, the membership function of index \(\widetilde{C}_{p} \) is constructed, and the probability of rejecting the null hypothesis is calculated based on this membership function. Different from classical tests, the statistical decision proposed in this paper shows a grade of acceptability of the null hypothesis and the alternative hypothesis, respectively. With crisp values, the developed approach not only can boil down to the classical formula for calculating Ĉ p , but also lead to a binary decision: to reject or to accept the null hypothesis. An example is used to illustrate the performance of the proposed approach.

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Correspondence to Cheng-Che Chen.

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Tsai, CC., Chen, CC. Making decision to evaluate process capability index C p with fuzzy numbers. Int J Adv Manuf Technol 30, 334–339 (2006). https://doi.org/10.1007/s00170-005-0052-7

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Keywords

  • Decision making
  • Fuzzy number
  • Hypothesis testing
  • Process capability indices