Decision-making in testing process performance with fuzzy data
Over the years, numerous process capability indices (PCIs) have been proposed to the manufacturing industry to provide numerical measures of process performance. Most research efforts have focused on developing and investigating PCIs that assess process capability by precise measurements of output quality. However, real observations of continuous quantities are not precise numbers; in practice, they are more or less imprecise. Since observations of continuous random variables are imprecise the values of related test statistics become imprecise. Therefore, decision rules for statistical tests have to be adapted to this situation. This article presents a set of confidence intervals that produces triangular fuzzy numbers for the estimation of Cpk index using Buckley's approach with some modification. Additionally, a three-decision testing rule and step-by-step procedure are developed to assess process performance based on fuzzy critical values and fuzzy p-values. This concept is also illustrated with an example for testing process performance.
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- Lee, Hong Tau, 2001. "Cpk index estimation using fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 129(3), pages 683-688, March.
- Hong, Dug Hun, 2004. "A note on Cpk index estimation using fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 158(2), pages 529-532, October.
- 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.
- P. Filzmoser & R. Viertl, 2004. "Testing hypotheses with fuzzy data: The fuzzy p-value," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 21-29, 02.
- Wu, Chien-Wei, 2008. "Assessing process capability based on Bayesian approach with subsamples," European Journal of Operational Research, Elsevier, vol. 184(1), pages 207-228, January.
- Bernhard Arnold, 1996. "An approach to fuzzy hypothesis testing," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 119-126, December.
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