Title: Measuring process capability index C″_p(u, v) for fuzzy data and fuzzy requirements

Authors: Daniel Grau

Addresses: Laboratory of Applied Mathematics, CNRS UMR 5142, IUT de Bayonne, Université de Pau et des Pays de l'Adour, 17 Place Paul Bert, 64100 Bayonne, France

Abstract: Process capability indices are quantitative measures on process performance. The C″_p(u, v) indices family depending on two parameters allows to generalise the common indices used in industry. Ordinarily the process data and process requirements are assumed to be precise numbers. In practical situations, however, it is more realistic to assume that they are more or less imprecise. Such observations are called fuzzy. This paper presents a family of fuzzy indices for processes where the observations, the specification limits and the target are fuzzy. The membership function of fuzzy capability indices is constructed on the basis of the α-cuts of fuzzy data. A three-decision testing rule is developed to assess process performance based on p-values or critical values. With precise values the suggested approach boils down to the usual binary decision. A real example with a linguistic variable illustrates the setting up of the said method.

Keywords: process capability indices; fuzzy data; fuzzy requirements; fuzzy hypothesis testing; fuzzy logic; three-decision testing rule; process performance; p-values; critical values; precise values.

DOI: 10.1504/IJQET.2013.055873

International Journal of Quality Engineering and Technology, 2013 Vol.3 No.4, pp.273 - 288

Received: 12 Dec 2012
Accepted: 21 Dec 2012
Published online: 19 Jul 2014 *

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