Developing a Tω (the weakest t-norm) fuzzy GERT for evaluating uncertain process reliability in semiconductor manufacturing

Authors:
Kuo-Ping Lin;Ming-Jia Wu;Kuo-Chen Hung;Yiyo Kuo
Affiliations:
Department of Information Management, Lunghwa University of Science and Technology, Taoyuan 333, Taiwan;Graduate School of Business and Management, Lunghwa University of Science and Technology, Taoyuan 333, Taiwan;Department of Logistics Management, National Defense University, Beitou, Taipei, 112, Taiwan;Department of Marketing and Logistics Management, Hsing Kuo University of Management, Tainan 709, Taiwan
Venue:
Applied Soft Computing
Year:
2011

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Abstract

This paper develops a novel weakest t-norm (T"@w) fuzzy Graphical Evaluation and Review Technique (GERT) simulation technology. This proposal is designed to be useful in a realistic environment and improve upon the traditional fuzzy GERT insofar as it has been developed for analyzing complex systems in uncertain environments; the traditional system usually adopts @a-cut arithmetic operations for its calculations. In this research, the fuzzy support system develops the T"@w fuzzy GERT as a substitute for traditional fuzzy GERT technology. In the examples, the fuzzy support system constructs a model of 300mm manufacturing processes in the context of a lithography area. Moreover, the manufacturing processes model is examined with regard to the fuzzy support system using two types of fuzzy arithmetic: @a-cut arithmetic and the T"@w operator. Notably: (1) both types of fuzzy arithmetic provide a reliable analysis of the fuzzy GERT model with regard to a lithography area; (2) under the traditional fuzzy GERT model, the @a-cut arithmetic provides results such that the fuzziness of the model calculation was fuzzier than that of the T"@w fuzzy arithmetic due to the accumulation of fuzziness of the @a-cut arithmetic; (3) the @a-cut arithmetic cannot effectively preserve the original shape of a membership function; and (4) the T"@w arithmetic gives a justifiable fuzziness/fuzzy spread because it takes only the maximal fuzziness encountered and calculates that into the operation. Our proposed T"@w fuzzy GERT can successfully analyze a 300mm manufacturing process; this has been evidenced in the research. Additionally, the proposed model uses simple arithmetic operations rather than traditional fuzzy GERT with applications in complex manufacturing systems. Moreover, the T"@w arithmetic provides more credible (or conservative) information/results with regard to the amount of fuzziness in the 300mm manufacturing processing model.