Estimating job cycle time in a wafer fabrication factory: A novel and effective approach based on post-classification

Estimating job cycle time is an important task for a semiconductor manufacturer as it helps to strengthen relationships with customers and is also conducive to the sustainable development of the manufacturer. The research trend in this field has moved toward the development of hybrid methods, especially those that are classification-based. Most existing methods use pre-classification; however, such methods have several drawbacks, such as incompatibility with the estimation method and unequal sizes of different job groups. In contrast, a post-classification approach has great potential, and therefore is used as a basis for the new approach in this study. In the proposed methodology, a systematic procedure is established to divide jobs into several groups according to their estimation errors. In this way, the classification and estimation stages can be combined seamlessly because they optimize the same objectives. A real case is used to evaluate the effectiveness of the proposed methodology and the experimental results support its superiority over several existing methods. The shortcomings of the existing methods based on pre-classification are also clearly illustrated.     

Fuzzy-neural approaches with example post-classification for estimating job cycle time in a wafer fab

Estimating the cycle time of a job in a wafer fabrication plant (wafer fab) is a critical task to the wafer fab. Many recent studies have shown that pre-classifying a job before estimating the cycle time was beneficial to the forecasting accuracy. However, most pre-classification approaches applied in this field could not absolutely classify jobs. Besides, whether the pre-classification approach combined with the subsequent forecasting approach was suitable for the data was questionable. For tackling these problems, two hybrid approaches with example post-classification, the equally-divided method and the proportional-to-error method, are proposed in this study in which a job is post-classified by a back propagation network (BPN) instead after the forecasting error is generated. In this novel way, only jobs whose cycle time forecasts are the same accurate will be clustered into the same category, and the classification algorithm becomes tailored to the forecasting approach. For evaluating the effectiveness of the proposed methodology and to make comparison with some existing approaches, production simulation (PS) is applied in this study to generate test data. According to experimental results, the forecasting accuracy (measured with root mean squared error, RMSE) of the proportional-to-error method was significantly better than those of the other approaches in most cases by achieving a 26–56% (and an average of 41%) reduction in RMSE over the comparison basis – multiple-factor linear combination (MFLC). The effect of post-classification was also statistically significant.     

A nonlinearly normalized back propagation network and cloud computing approach for determining cycle time allowance during wafer fabrication

This study investigated the determination of the allowance that must be added to the cycle time estimate, which is a critical concern when assigning internal due dates. Because no method for estimating cycle times is completely accurate, producing such estimates remains problematic but has rarely been addressed in the literature. A large allowance postpones the internal due date, diminishing company appeal when a factory manager negotiates with a customer. Therefore, in this study, a nonlinear approach was proposed to normalize the cycle times. After estimating the cycle time of a job by using a back propagation network, the allowance added to the cycle time can be effectively reduced through the collaboration of several computing clouds. Theoretical properties of the proposed method were validated, and a case from a wafer fabrication factory was used to evaluate the effectiveness of the proposed method in comparison with various existing methods. According to the experimental results, the proposed method facilitated establishing tight upper bounds on the cycle times. The proposed method was proven to be very effective.     

Incorporating the FCM–BPN approach with nonlinear programming for internal due date assignment in a wafer fabrication plant

To enhance the performance of the internal due date assignment in a wafer fab even further, this study incorporated the fuzzy c-means–back propagation network (FCM–BPN) approach with a nonlinear programming model. In the proposed methodology, the jobs are first classified into several categories by fuzzy c-means. Then, an individual back propagation network is constructed for each category to predict the completion time of the jobs. Subsequently, an individual nonlinear programming model is constructed for each back propagation network to adjust the connection weights in the back propagation network, allowing us to determine the internal due dates of the jobs in the category. The nonlinear programming model is finally converted into a goal programming problem that can be solved with existing optimization software. According to the experimental results, the proposed methodology outperforms the baseline multiple linear regression (MLR) approach by 24% in predicting the job completion/cycle times. In addition, the proposed methodology also guarantees that all jobs can be finished before the established internal due dates, without adding too large a fudge factor, and without sacrificing the accuracy of the completion/cycle time forecasts.     

An intelligent hybrid system for wafer lot output time prediction

Lot output time prediction is a critical task to a wafer fab (fabrication plant). To further enhance the accuracy of wafer lot output time prediction, an intelligent hybrid system is constructed in this study. Firstly, the concept of input classification is applied to Chen’s fuzzy back propagation network (FBPN) approach in this study by pre-classifying wafer lots with the k-means (kM) classifier before predicting the output times with FBPN. Examples belonging to different categories are then learned with different FBPNs but with the same topology. Secondly, the future release plan of the fab, which is influential but has been ignored in traditional approaches, is also incorporated in the intelligent hybrid system. To evaluate the effectiveness of the proposed methodology, production simulation has been applied in this study to generate test examples. According to experimental results, the prediction accuracy of the intelligent hybrid system was significantly better than those of six approaches: BPN, case-based reasoning (CBR), FBPN, look-ahead FBPN, evolving fuzzy rules (EFR), and kM-FBPN without look-ahead in most cases by achieving a 17-47% (and an average of 34%) reduction in the root-mean-squared-error (RMSE) over the comparison basis - BPN.     

Fuzzy forecasting based on fuzzy time series

This article presents an improved method of fuzzy time series to forecast university enrollments. The historical enrollment data of the University of Alabama were first adopted by Song and Chissom (Song, Q. and Chissom, B. S. (1993). Forecasting enrollment with fuzzy time series-part I, Fuzzy Sets and Systems, 54, 1–9; Song, Q. and Chissom, B. S. (1994). Forecasting enrollment with fuzzy time series-part II, Fuzzy Sets and Systems, 54, 267–277) to illustrate the forecasting process of the fuzzy time series. Later, Chen proposed a simpler method. In this article, we show that our method is as simple as Chen's method but more accurate. In forecasting the enrollment of the University of Alabama, the root mean square percentage error (RMSPE) of our method is 3.1113% while the RMSPE of Chen's method is 4.0516%, which shows that our method is doing much better.     

A slack-diversifying nonlinear fluctuation smoothing rule for job dispatching in a wafer fabrication factory

This study proposes a slack-diversifying nonlinear fluctuation smoothing rule to reduce the average cycle time in a wafer fabrication factory. The slack-diversifying nonlinear fluctuation smoothing rule is derived from the one-factor tailored nonlinear fluctuation smoothing rule for cycle time variation (1f-TNFSVCT) by dynamically maximizing the standard deviation of the slack, which has been shown to improve scheduling performance in several previous studies. The effectiveness of the proposed rule has been validated via using it with a simulated data set. Based on the findings in this research we also derived several directions that can be exploited in the future.     

A distance-based fuzzy time series model for exchange rates forecasting

Fuzzy time series model has been successfully employed in predicting stock prices and foreign exchange rates. In this paper, we propose a new fuzzy time series model termed as distance-based fuzzy time series (DBFTS) to predict the exchange rate. Unlike the existing fuzzy time series models which require exact match of the fuzzy logic relationships (FLRs), the distance-based fuzzy time series model uses the distance between two FLRs in selecting prediction rules. To predict the exchange rate, a two factors distance-based fuzzy time series model is constructed. The first factor of the model is the exchange rate itself and the second factor comprises many candidate variables affecting the fluctuation of exchange rates. Using the exchange rate data released by the Central Bank of Taiwan, we conducted several experiments on exchange rate forecasting. The experiment results showed that the distance-based fuzzy time series outperformed the random walk model and the artificial neural network model in terms of mean square error.     

Linguistic time series forecasting using fuzzy recurrent neural network

It is known that one of the most spread forecasting methods is the time series analysis. A weakness of traditional crisp time series forecasting methods is that they process only measurement based numerical information and cannot deal with the perception-based historical data represented by linguistic values. Application of a new class of time series, a fuzzy time series whose values are linguistic values, can overcome the mentioned weakness of traditional forecasting methods. In this paper we propose a fuzzy recurrent neural network (FRNN) based time series forecasting method for solving forecasting problems in which the data can be presented as perceptions and described by fuzzy numbers. The FRNN allows effectively handle fuzzy time series to apply human expertise throughout the forecasting procedure and demonstrates more adequate forecasting results. Recurrent links in FRNN also allow for simplification of the overall network structure (size) and forecasting procedure. Genetic algorithm-based procedure is used for training the FRNN. The effectiveness of the proposed fuzzy time series forecasting method is tested on the benchmark examples.     

Deterministic fuzzy time series model for forecasting enrollments

The fuzzy time series has recently received increasing attention because of its capability of dealing with vague and incomplete data. There have been a variety of models developed to either improve forecasting accuracy or reduce computation overhead. However, the issues of controlling uncertainty in forecasting, effectively partitioning intervals, and consistently achieving forecasting accuracy with different interval lengths have been rarely investigated. This paper proposes a novel deterministic forecasting model to manage these crucial issues. In addition, an important parameter, the maximum length of subsequence in a fuzzy time series resulting in a certain state, is deterministically quantified. Experimental results using the University of Alabama’s enrollment data demonstrate that the proposed forecasting model outperforms the existing models in terms of accuracy, robustness, and reliability. Moreover, the forecasting model adheres to the consistency principle that a shorter interval length leads to more accurate results.     

An efficient time series forecasting model based on fuzzy time series

In this paper, we present a new model to handle four major issues of fuzzy time series forecasting, viz., determination of effective length of intervals, handling of fuzzy logical relationships (FLRs), determination of weight for each FLR, and defuzzification of fuzzified time series values. To resolve the problem associated with the determination of length of intervals, this study suggests a new time series data discretization technique. After generating the intervals, the historical time series data set is fuzzified based on fuzzy time series theory. Each fuzzified time series values are then used to create the FLRs. Most of the existing fuzzy time series models simply ignore the repeated FLRs without any proper justification. Since FLRs represent the patterns of historical events as well as reflect the possibility of appearances of these types of patterns in the future. If we simply discard the repeated FLRs, then there may be a chance of information lost. Therefore, in this model, it is recommended to consider the repeated FLRs during forecasting. It is also suggested to assign weights on the FLRs based on their severity rather than their patterns of occurrences. For this purpose, a new technique is incorporated in the model. This technique determines the weight for each FLR based on the index of the fuzzy set associated with the current state of the FLR. To handle these weighted FLRs and to obtain the forecasted results, this study proposes a new defuzzification technique. The proposed model is verified and validated with three different time series data sets. Empirical analyses signify that the proposed model have the robustness to handle one-factor time series data set very efficiently than the conventional fuzzy time series models. Experimental results show that the proposed model also outperforms over the conventional statistical models.     

A FCM-based deterministic forecasting model for fuzzy time series

The study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling uncertainty and vagueness inherent in the data collected. A variety of forecasting models including high-order models have been devoted to improving forecasting accuracy. However, the high-order forecasting approach is accompanied by the crucial problem of determining an appropriate order number. Consequently, such a deficiency was recently solved by Li and Cheng [S.-T. Li, Y.-C. Cheng, Deterministic Fuzzy time series model for forecasting enrollments, Computers and Mathematics with Applications 53 (2007) 1904–1920] using a deterministic forecasting method. In this paper, we propose a novel forecasting model to enhance forecasting functionality and allow processing of two-factor forecasting problems. In addition, this model applies fuzzy c-means (FCM) clustering to deal with interval partitioning, which takes the nature of data points into account and produces unequal-sized intervals. Furthermore, in order to cope with the randomness of initially assigned membership degrees of FCM clustering, Monte Carlo simulations are used to justify the reliability of the proposed model. The superior accuracy of the proposed model is demonstrated by experiments comparing it to other existing models using real-world empirical data.     

A collaborative and artificial intelligence approach for semiconductor cost forecasting

Forecasting the unit cost of a semiconductor product is an important task to the manufacturer. However, it is not easy to deal with the uncertainty in the unit cost. In order to effectively forecast the semiconductor unit cost, a collaborative and artificial intelligence approach is proposed in this study. In the proposed methodology, a group of domain experts is formed. These domain experts are asked to configure their own fuzzy neural networks to forecast the semiconductor unit cost based on their viewpoints. A collaboration mechanism is therefore established. To facilitate the collaboration process and to derive a single representative value from these forecasts, a radial basis function (RBF) network is used. The effectiveness of the proposed methodology is shown with a case study.     

A hybrid modular neural network architecture with fuzzy Sugeno integration for time series forecasting

We describe in this paper the application of a modular neural network architecture to the problem of simulating and predicting the dynamic behavior of complex economic time series. We use several neural network models and training algorithms to compare the results and decide at the end, which one is best for this application. We also compare the simulation results with the traditional approach of using a statistical model. In this case, we use real time series of prices of consumer goods to test our models. Real prices of tomato in the U.S. show complex fluctuations in time and are very complicated to predict with traditional statistical approaches. For this reason, we have chosen a neural network approach to simulate and predict the evolution of these prices in the U.S. market.     

A new linguistic out-sample approach of fuzzy time series for daily forecasting of Malaysian electricity load demand

The fuzzy logical relationships and the midpoints of interval have been used to determine the numerical in-out-samples forecast in the fuzzy time series modeling. However, the absolute percentage error is still yet significantly improved. This can be done where the linguistics time series values should be forecasted in the beginning before the numerical forecasted values obtained. This paper introduces the new approach in determining the linguistic out-sample forecast by using the index numbers of linguistics approach. Moreover, the weights of fuzzy logical relationships are also suggested to compensate the presence of bias in the forecasting. The daily load data from National Electricity Board (TNB) of Malaysia is used as an empirical study and the reliability of the proposed approach is compared with the approach proposed by Yu. The result indicates that the mean absolute percentage error (MAPE) of the proposed approach is smaller than that as proposed by Yu. By using this approach the linguistics time series forecasting and the numerical time series forecasting can be resolved.     

A hybrid multi-order fuzzy time series for forecasting stock markets

This paper proposes a hybrid model based on multi-order fuzzy time series, which employs rough sets theory to mine fuzzy logical relationship from time series and an adaptive expectation model to adjust forecasting results, to improve forecasting accuracy. Two empirical stock markets (TAIEX and NASDAQ) are used as empirical databases to verify the forecasting performance of the proposed model, and two other methodologies, proposed earlier by Chen and Yu, are employed as comparison models. Besides, to compare with conventional statistic method, the partial autocorrelation function and autoregressive models are utilized to estimate the time lags periods within the databases. Based on comparison results, the proposed model can effectively improve the forecasting performance and outperforms the listing models. From the empirical study, the conventional statistic method and the proposed model both have revealed that the estimated time lags for the two empirical databases are one lagged period.     

Applying the hybrid fuzzy c-means-back propagation network approach to forecast the effective cost per die of a semiconductor product

Forecasting the unit cost of every product type in a factory is an important task to the factory. After the unit cost of every product type in a factory is accurately forecasted, several managerial goals (including pricing, cost down projecting, capacity planning, ordering decision support, and guiding subsequent operations) can be simultaneously achieved. However, it is not easy to deal with the uncertainty in the unit cost. In addition, most references in this field were focused on costing and seldom investigated the forecasting of the unit cost. To tackle these problems, the hybrid fuzzy linear regression (FLR) and back propagation network (BPN) approach is applied to forecast the unit cost of every product type in a wafer fabrication plant, which is usually referred to as the determination of the effective cost per die. In practical situations the long-term effective cost per die of a product type is usually approximated with a linear regression (LR) equation, according to the “continuous cost down” philosophy, which is prone to error. Conversely, the proposed FLR–BPN approach is more accurate and be able to deal with the uncertainty in the unit cost in a simple and intuitive way. For evaluating the effectiveness of the proposed methodology, a demonstrative case was used. Experimental results showed that the hybrid FLR–BPN approach was superior to some existing approaches in forecasting accuracy and precision.     

A high-order fuzzy time series forecasting model for internet stock trading

Recently, many fuzzy time series models have already been used to solve nonlinear and complexity issues. However, first-order fuzzy time series models have proven to be insufficient for solving these problems. For this reason, many researchers proposed high-order fuzzy time series models and focused on three main issues: fuzzification, fuzzy logical relationships, and defuzzification. This paper presents a novel high-order fuzzy time series model which overcomes the drawback mentioned above. First, it uses entropy-based partitioning to more accurately define the linguistic intervals in the fuzzification procedure. Second, it applies an artificial neural network to compute the complicated fuzzy logical relationships. Third, it uses the adaptive expectation model to adjust the forecasting during the defuzzification procedure. To evaluate the proposed model, we used datasets from both the Taiwanese stock index from 2000 to 2003 and from the student enrollment records of the University of Alabama. The results of our study show that the proposed model is able to obtain an accurate forecast without encountering conventional fuzzy time series issues.     

基于序列分解的复杂系统的时序预测方法

现实中的时序数据，往往取自于复杂系统，表现出长记忆效应与短时不规则波动同时并存。传统的时序数据的分析和预测方法一般对不同层次的影响不加以区分，而是为其建立一个统一的模型，这使得在对复杂系统建模时需要用大量的参数予以表征，影响预测效率与精度。为此采用新的方法，将序列数据本身进行多平滑因子分解，对分解后的序列进行多尺度的采样并分别建模、预测，最后将结果整合。该方法应用于股票的实验表明，即使对起伏波动很大的时间序列，也能够得到较好的预测结果。     

Fuzzy Delphi and back-propagation model for sales forecasting in PCB industry

Reliable prediction of sales can improve the quality of business strategy. In this research, fuzzy logic and artificial neural network are integrated into the fuzzy back-propagation network (FBPN) for sales forecasting in Printed Circuit Board (PCB) industry. The fuzzy back propagation network is constructed to incorporate production-control expert judgments in enhancing the model's performance. Parameters chosen as inputs to the FBPN are no longer considered as of equal importance, but some sales managers and production control experts are requested to express their opinions about the importance of each input parameter in predicting the sales with linguistic terms, which can be converted into pre-specified fuzzy numbers. The proposed system is evaluated through the real world data provided by a printed circuit board company and experimental results indicate that the Fuzzy back-propagation approach outperforms other three different forecasting models in MAPE measures.