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

This paper develops a novel weakest t-norm (Tω) 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 α-cut arithmetic operations for its calculations. In this research, the fuzzy support system develops the Tω fuzzy GERT as a substitute for traditional fuzzy GERT technology. In the examples, the fuzzy support system constructs a model of 300 mm 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: α-cut arithmetic and the Tω 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 α-cut arithmetic provides results such that the fuzziness of the model calculation was fuzzier than that of the Tω fuzzy arithmetic due to the accumulation of fuzziness of the α-cut arithmetic; (3) the α-cut arithmetic cannot effectively preserve the original shape of a membership function; and (4) the Tω arithmetic gives a justifiable fuzziness/fuzzy spread because it takes only the maximal fuzziness encountered and calculates that into the operation. Our proposed Tω fuzzy GERT can successfully analyze a 300 mm 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 Tω arithmetic provides more credible (or conservative) information/results with regard to the amount of fuzziness in the 300 mm manufacturing processing model.

► We develop a novel weakest t-norm (Tω) fuzzy Graphical Evaluation and Review Technique (GERT) simulation technology. ► A model of 300 mm manufacturing processes of a lithography area is examined by using the Tω fuzzy GERT. ► Our proposed Tω fuzzy GERT can successfully analyze a 300 mm manufacturing process. ► The proposed model uses simple arithmetic operations rather than traditional fuzzy GERT with applications in complex manufacturing systems. ► Moreover, the Tω arithmetic provides more credible (or conservative) information/results with regard to the amount of fuzziness in the 300 mm manufacturing processing model.