Process Capability Indices as Fuzzy Numbers
DOI:
https://doi.org/10.17713/ajs.v34i4.425Abstract
Most of the traditional methods for assessing the capability of manufacturing processes are dealing with crisp quality. In this paper we discuss the fuzzy quality and introduce fuzzy process capability indices, where instead of precise quality we have two membership functions for specification limits. These indices are necessary when the specification limits are fuzzy and they are helpful for comparing manufacturing processes with fuzzy specification limits. Some interesting relations among the introduced indices are obtained. Numerical examples are given to clarify the method.
References
Boyles, R. A. (1994). Process capability with asymmetric tolerances. Communications in Statistics - Simulation and Computation, 23, 613-643.
Hsiang, T. C., and Taguchi, G. (1985). Tutorial on quality control and assurance - The Taguchi methods. Joint Meetings of the American Statistical Association.
Juran, J. M. (1974). Juran’s Quality Control Handbook (3rd ed.). New York: McGraw-Hill.
Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18, 41-52.
Kaufmann, A., and Gupta, M. M. (1988). Fuzzy Mathematical Models in Engineering and Management Science. Amsterdam: North-Holland.
Kotz, S. (1993). Process Capability Indices. New York: Chapman and Hall.
Kotz, S., and Johnson, N. (2002). Process capability indices - a review, 1992-2000. Journal of Quality Technology, 34, 2-19.
Lee, H. T. (2001). cpk index estimation using fuzzy numbers. European Journal of Operational Research, 129, 683-688.
Montgomery, D. C. (2001). Introduction to statistical quality control. New York: Wiley.
Nguyen, H. T., and Walker, E. A. (2000). A First Course in Fuzzy Logic (2nd ed.). London: Chapman and Hall/CRC.
Pearn, W. L., Kotz, S., and Johnson, N. L. (1992). Distribution and inferential properties of capability indices. Journal of Quality Technology, 24, 41-52.
Sadeghpour-Gildeh, B. (2003). Comparison of cp, cpk and ~cp process capability indices in the case of measurement error occurrence. In IFSA world congress (p. 563-567).
Istanbul, Turkey.
Taheri, S. M. (2003). Trends in fuzzy statistics. Austrian Journal of Statistics, 32, 239-257.
Vannman, K. (1995). A unified approach to the capability indices. Statistica Sinica, 5, 805-820.
Vannman, K. (1997). A general class of capability indices in the case of tolerances. Communications in Statistics - Theory and Methods, 26, 2049-2072.
Vannman, K. (1998). Families of capability indices for one-side specification limits. Statistics, 31, 43-66.
Viertl, R. (1996). Statistical Methods for Non-Precise Data. Boca Raton: CRC Press.
Wang, X. (2001). Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Sets and Systems, 118, 387-405.
Yongting, C. (1996). Fuzzy quality and analysis on fuzzy probability. Fuzzy Sets and Systems, 83, 283-290.
Yuan, Y. (1991). Criteria for evaluating fuzzy ranking methods. Fuzzy Sets and Systems, 43, 139-157.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-359.
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