Measuring process capability index Cpmk with fuzzy data and compare it with other fuzzy process capability indices

Authors:
Mohammad Abdolshah;Rosnah Mohd. Yusuff;Tang Sai Hong;Md. Yusof B. Ismail;Aghdas Naimi Sadigh
Affiliations:
Engineering Faculty, Islamic Azad University, Semnan Branch, P.O. Box 35136-93688, Semnan, Iran;Engineering Faculty, Department of Mechanical and Manufacturing Engineering, Universiti Putra Malaysia, Malaysia;Engineering Faculty, Department of Mechanical and Manufacturing Engineering, Universiti Putra Malaysia, Malaysia;Faculty of Manufacturing Engineering, University Malaysia Pahang, Malaysia;Engineering Faculty, Islamic Azad University, Semnan Branch, P.O. Box 35136-93688, Semnan, Iran
Venue:
Expert Systems with Applications: An International Journal
Year:
2011

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Abstract

The index C"p"m"k is a well-known loss-based process capability index. It can reveal more information about the location of the process mean compared with other classic process capability indices. This index is also more sensitive than other capability indices to any deviations from process mean. When there are some uncertainties in observations, fuzzy logic can be employed to manage these uncertainties. There is some research on different fuzzy process capability indices and this paper is an extension of Tsai and Chen (2006), Chen, Lin, and Chen (2003) for the process capability index C"p"m"k of fuzzy numbers. In order to find the membership function of process capability index C"p"m"k, the @a-cuts of the fuzzy observation were employed. An example of fuzzy process capability C"p"m"k calculator was illustrated and compared with other classic fuzzy process capability indices C~"p,C~"p"l,C~"p"u,C~"p"k and C~"p"m . Results showed that fuzzy C~"p"m"k has the advantages of both C~"p"k and C~"p"m . Since the index C"p"m"k is a more sensitive index compared with other classic indices, the fuzzy process capability index C~"p"m"k can be a more sensitive fuzzy index compared with C~"p,C~"p"l,C~"p"u,C~"p"k and C~"p"m.