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 (T-omega) 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 alpha-cut arithmetic operations for its calculations. In this research, the fuzzy support system develops the T-omega 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: alpha-cut arithmetic and the T-omega 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 alpha-cut arithmetic provides results such that the fuzziness of the model calculation was fuzzier than that of the T-omega fuzzy arithmetic due to the accumulation of fuzziness of the alpha-cut arithmetic; (3) the alpha-cut arithmetic cannot effectively preserve the original shape of a membership function; and (4) the T-omega arithmetic gives a justifiable fuzziness/fuzzy spread because it takes only the maximal fuzziness encountered and calculates that into the operation. Our proposed T-omega 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 T-omega arithmetic provides more credible (or conservative) information/results with regard to the amount of fuzziness in the 300 mm manufacturing processing model. (C) 2011 Elsevier B. V. All rights reserved.