Applied Soft Computing 11 (2011) 5165–5180 Contents lists available at ScienceDirect Applied Soft Computing j ourna l ho mepage: www.elsevier.com/locate/asoc Developing a T ω (the weakest t-norm) fuzzy GERT for evaluating uncertain process reliability in semiconductor manufacturing Kuo-Ping Lin a,∗ , Ming-Jia Wu b , Kuo-Chen Hung c , Yiyo Kuo d a Department of Information Management, Lunghwa University of Science and Technology, Taoyuan 333, Taiwan b Graduate School of Business and Management, Lunghwa University of Science and Technology, Taoyuan 333, Taiwan c Department of Logistics Management, National Defense University, Beitou, Taipei, 112, Taiwan d Department of Marketing and Logistics Management, Hsing Kuo University of Management, Tainan 709, Taiwan a r t i c l e i n f o Article history: Received 26 October 2010 Received in revised form 7 April 2011 Accepted 20 May 2011 Available online 13 June 2011 Keywords: Graphical Evaluation and Review Technique (GERT) Fuzzy GERT The weakest t-norm arithmetic operations Lithography area a b s t r a c t This paper develops a novel weakest t-norm (T ω ) 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 ˛-cut arithmetic operations for its calculations. In this research, the fuzzy support system develops the T ω fuzzy GERT as a substitute for traditional fuzzy GERT technology. In the examples, the fuzzy support system constructs a model of 300 mm manufac- turing 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: ˛-cut arithmetic and the T ω 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 ˛-cut arithmetic provides results such that the fuzziness of the model calculation was fuzzier than that of the T ω fuzzy arithmetic due to the accumulation of fuzziness of the ˛-cut arithmetic; (3) the ˛-cut arith- metic cannot effectively preserve the original shape of a membership function; and (4) the T ω arithmetic gives a justifiable fuzziness/fuzzy spread because it takes only the maximal fuzziness encountered and calculates that into the operation. Our proposed T ω fuzzy GERT can successfully analyze a 300 mm manu- facturing 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 ω arithmetic provides more credible (or conservative) information/results with regard to the amount of fuzziness in the 300 mm manufacturing processing model. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Semiconductor manufacturing involves many complex pro- cesses in order to produce a high quality wafer. Semiconductor manufacturing has specific manufacturing characteristics, for instance: long cycle times, re-entry processes, reworking, mechan- ical breakdowns, queue time limits, random yields, and dependent setup times. In semiconductor manufacturing, photolithography manufacturing technology is crucial and the reliability of the pho- tolithography process can influence the overall quality of a wafer. Hence, evaluation of the process qua the reliability of the pho- tolithography process is a very important issue for those wishing to remain competitive in the semiconductor industry. Most of the process reliability of photolithography in the literature hereto- fore has been modeled and analyzed using standard simulation ∗ Corresponding author. Tel.: +886 2 82093211x6329; fax: +886 4 82094650. E-mail address: kplin@mail.lhu.edu.tw (K.-P. Lin). techniques; i.e., structured modeling (see [1,16,27]). Moreover, the manufacture of lithography is somewhat unique in that the process generates reentry phenomena due to the reparability of the wafer. Owing to the influences of large numbers of product reworking and the frequent changes in product and manufacturing flow design, decisions are often made with relative uncertainty. Following cur- rent research methods, GERT can effectively solve certain problems stemming from reentry phenomena in manufacturing, while fuzzy sets can objectively handle uncertainty with regard to other spe- cific problems. Therefore, in this study, the process reliability of the lithographic production area is paired with fuzzy GERT in order to simulate scenarios. Based on fuzzy GERT, this study develops a novel T ω fuzzy GERT aimed at industry leading decision-makers. Our proposed T ω fuzzy GERT adopts fuzzy GERT simulations in order to model/analyze the reliability of specific manufactur- ing processes. The Graphical Evaluation and Review Technique is a useful graphical tool for modeling as well for concurrent analysis of complex systems due to the fact that GERT is able to analyze stochastic networks with logical nodes and directed branches. The 1568-4946/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2011.05.043