Estimating the cycle time of each job in a wafer fabrication factory is a critical task to every wafer manufacturer. In recent years, a number of hybrid approaches based on job classification (either preclassification or postclassification) for cycle time estimation have been proposed. However, the problem with these methods is that the input variables are not independent. In order to solve this problem, principal component analysis (PCA) is considered useful. In this study, a classifying fuzzy-neural approach, based on the combination of PCA, fuzzy c-means (FCM), and back propagation network (BPN), is proposed to estimate the cycle time of a job in a wafer fabrication factory. Since job classification is an important part of the proposed methodology, a new index is proposed to assess the validity of the classification of jobs. The empirical relationship between the
The competition in the semiconductor industry has been very intense. How to obtain and maintain the competitive edge is an important task for all manufacturers in this industry. Quick response and on-time delivery are obviously pressing needs for any modern enterprise. To this end, accurate estimating and shortening the cycle time (flow time or manufacturing lead time) of each job in the factory is a prerequisite [
Estimating the cycle time of each job in a wafer fabrication factory is very important to the factory because it can signal the manager if the orders are progressed as they were expected. For example, if the estimated cycle time of a job is longer than as it was expected, then this order may not be completed to the customer before its due date. Some production control actions should then immediately be taken to accelerate the progress of the job [
The existing approaches for the job cycle time estimation in a wafer fabrication factory can be classified into six categories: statistical analysis, production simulation (PS), back propagation network (BPN), case-based reasoning (CBR), fuzzy modeling methods, and hybrid approaches [
Considering effectiveness (estimation accuracy) and efficiency (execution time) simultaneously, Chang et al. [
Chiu et al. [
In recent years, a number of hybrid approaches have been proposed, most of which classified jobs before estimating the cycle times. For example, Chen [
In short, the followings have not done before: Some factors used to estimate the cycle time are dependent on each other, which may cause problems in classifying jobs and in fitting the relationship between the job cycle time and these factors. However, this issue has rarely been addressed in previous studies of this field. Job classification has been shown to be conducive to the estimation performance. However, most past studies chose classifiers subjectively and did not evaluate the performance of the classifier. Needless to say optimizing the classifier for the subsequent estimation task.
Principal component analysis (PCA) is a multivariate statistical analysis method. This method constructs a series of linear combinations of the original variables to form a new variable, so that these new variables are unrelated to each other as much as possible, and the relationship among them can be reflected in a better way. In this study, a fuzzy-neural approach, based on the combination of PCA, FCM, and BPN, is proposed to estimate the cycle time of a job in a wafer fabrication factory. The motivation of this study is explained as follows. While in the past some studies combined PCA and FCM, the references on the combination of PCA, FCM, and BPN are still very limited. Chen [ FCM, as a part of the preclassifying approach, cannot be evaluated alone. Its success depends on the performance of the subsequent estimation task. This provides us with a motivation to assess the validity of the classification of jobs from this point of view. The
The contribution compared with some previous works in the literature includes the following. With factors that are dependent on each other, jobs may be misclassified if FCM is used alone. This may be harmful to the estimation accuracy of BPN, because incorrect examples are used to train the BPN. The fuzzy-neural approach replaces the original factors with new independent factors and is expected to be able to generate the correct classification results. The correctness of the classification results must be judged from the estimation performance. In order to measure that, two new indexes are defined. It is anticipated that the new factors found out by PCA have a more explicit relationship with the job cycle time. As a result, the training of BPN may be accelerated. This also means that a more accurate relationship between the factors and the cycle time can also be generated with the same time. A new index is proposed to assess the validity of the classification of jobs. The empirical relationship between the Outliers, that is, jobs that cannot be classified definitely, have not been dealt with properly in the past. However, the overall estimation performance is often affected by the outliers. For this reason, an iterative process is established in this study, which can optimize the overall estimation performance.
The differences between the proposed methodology and the previous methods are summarized in Table
The differences between the proposed methodology and the previous methods.
Method | SOM-WM [ |
BPN-BPN [ |
FCM-FBPN-RBF [ |
The proposed methodology |
---|---|---|---|---|
Job preclassification | Yes | No | Yes | Yes |
Job post/reclassification | No | Yes | Yes | Yes |
Parameter replacement | No | No | No | Yes |
Dealing with outliers | No | No | No | Yes |
Iteration | No | No | No | Yes |
The remainder of this paper is organized as follows. Section
Two characteristics of the proposed methodology are input replacement and job classification. These features not are mathematical skills, but also have implications for the operations of a wafer fabrication factory. First, in the useful information for the estimation of the job cycle time, many factors are in fact mutually dependent. For example, it is well known that the utilization of a factory increases when the work-in-process (WIP) level in the factory rises. Both utilization and the WIP level are important factors considered in some job cycle time estimation approaches. Whether the dependence of the factors will lead to problems in the classification of jobs needs to be checked. Therefore, the replacement of these factors with new independent variables is worth a try.
On the other hand, a number of job cycle time estimation approaches in this field classify jobs. A well-known concept is that the cycle time of a job is proportional to the WIP level of the factory, according to Little’s law; however, that only holds when the factory utilization is 100%. Therefore, it is reasonable to divide jobs into two categories: jobs that are released into the factory when the factory utilization is 100% and jobs released when the factory utilization is less than 100%.
The architecture of the proposed methodology is shown in Figure
The architecture of the proposed methodology.
First, PCA is used to replace the inputs to the FCM-BPN. The combination of PCA and FCM has proven to be a more effective classifier than FCM alone [ Raw data standardization: to eliminate the difference between the dimensions and the impact of large numerical difference in the original variables, The original variables are standardized as the following:
where Establishment of the correlation matrix where Determination of the number of principal components: the variance contribution rate is calculated as:
where where Formation of the following matrixes:
To illustrate the application of the proposed methodology, an example is given in Table
An example.
|
|
|
|
|
|
|
---|---|---|---|---|---|---|
1 | 24 | 1261 | 181 | 781 | 112 | 0.92 |
2 | 24 | 1263 | 181 | 762 | 127 | 0.90 |
3 | 24 | 1220 | 176 | 761 | 127 | 0.89 |
4 | 23 | 1282 | 178 | 802 | 127 | 0.94 |
5 | 23 | 1303 | 180 | 780 | 175 | 0.93 |
6 | 23 | 1281 | 183 | 782 | 175 | 0.93 |
7 | 23 | 1242 | 184 | 741 | 163 | 0.89 |
8 | 24 | 1262 | 182 | 681 | 139 | 0.86 |
9 | 22 | 1260 | 182 | 701 | 98 | 0.86 |
10 | 22 | 1260 | 179 | 700 | 257 | 0.87 |
11 | 24 | 1301 | 163 | 722 | 99 | 0.84 |
12 | 22 | 1221 | 184 | 641 | 131 | 0.82 |
13 | 23 | 1323 | 159 | 740 | 247 | 0.87 |
14 | 24 | 1362 | 181 | 782 | 191 | 0.95 |
15 | 24 | 1261 | 181 | 762 | 219 | 0.91 |
16 | 23 | 1321 | 177 | 801 | 219 | 0.96 |
17 | 22 | 1343 | 180 | 822 | 219 | 0.97 |
18 | 24 | 1321 | 177 | 762 | 54 | 0.93 |
19 | 25 | 1343 | 179 | 781 | 54 | 0.96 |
20 | 25 | 1300 | 180 | 740 | 54 | 0.92 |
21 | 22 | 1320 | 181 | 721 | 54 | 0.91 |
22 | 24 | 1321 | 182 | 742 | 49 | 0.92 |
23 | 23 | 1262 | 165 | 680 | 201 | 0.80 |
24 | 22 | 1240 | 161 | 722 | 103 | 0.82 |
25 | 23 | 1183 | 183 | 661 | 53 | 0.82 |
26 | 23 | 1282 | 184 | 701 | 53 | 0.88 |
27 | 22 | 1202 | 177 | 680 | 248 | 0.84 |
28 | 23 | 1202 | 178 | 681 | 248 | 0.85 |
29 | 24 | 1202 | 185 | 701 | 82 | 0.86 |
30 | 23 | 1202 | 158 | 721 | 98 | 0.81 |
31 | 24 | 1343 | 181 | 760 | 67 | 0.94 |
32 | 24 | 1381 | 185 | 801 | 67 | 0.97 |
33 | 22 | 1362 | 156 | 780 | 67 | 0.91 |
34 | 23 | 1282 | 179 | 782 | 223 | 0.92 |
35 | 23 | 1320 | 180 | 782 | 176 | 0.93 |
36 | 25 | 1340 | 176 | 801 | 462 | 0.97 |
37 | 23 | 1320 | 182 | 781 | 168 | 0.95 |
38 | 22 | 1361 | 181 | 781 | 141 | 0.94 |
39 | 22 | 1381 | 179 | 781 | 95 | 0.97 |
40 | 23 | 1363 | 178 | 802 | 179 | 0.97 |
The box plot.
Subsequently, we standardize the data (see Table
The standardized data.
|
|
|
|
|
|
|
---|---|---|---|---|---|---|
1 | 0.88 | −0.53 | 0.40 | 0.74 | −0.40 | 0.37 |
2 | 0.88 | −0.49 | 0.48 | 0.30 | −0.22 | −0.05 |
3 | 0.88 | −1.27 | −0.17 | 0.29 | −0.22 | −0.31 |
4 | −0.22 | −0.15 | 0.07 | 1.18 | −0.22 | 0.65 |
5 | −0.22 | 0.24 | 0.37 | 0.71 | 0.35 | 0.58 |
6 | −0.22 | −0.17 | 0.78 | 0.74 | 0.35 | 0.45 |
7 | −0.22 | −0.87 | 0.90 | −0.14 | 0.21 | −0.19 |
8 | 0.88 | −0.51 | 0.53 | −1.45 | −0.08 | −0.87 |
9 | −1.32 | −0.55 | 0.60 | −1.01 | −0.56 | −0.81 |
10 | −1.32 | −0.54 | 0.23 | −1.03 | 1.34 | −0.55 |
11 | 0.88 | 0.20 | −1.87 | −0.57 | −0.56 | −1.19 |
12 | −1.32 | −1.25 | 0.80 | −2.33 | −0.18 | −1.64 |
13 | −0.22 | 0.60 | −2.40 | −0.16 | 1.22 | −0.60 |
14 | 0.88 | 1.31 | 0.47 | 0.75 | 0.55 | 0.94 |
15 | 0.88 | −0.53 | 0.40 | 0.31 | 0.88 | 0.19 |
16 | −0.22 | 0.57 | −0.05 | 1.17 | 0.88 | 1.13 |
17 | −1.32 | 0.97 | 0.33 | 1.62 | 0.88 | 1.38 |
18 | 0.88 | 0.56 | −0.01 | 0.31 | −1.09 | 0.62 |
19 | 1.97 | 0.96 | 0.15 | 0.74 | −1.09 | 1.06 |
20 | 1.97 | 0.19 | 0.38 | −0.16 | −1.09 | 0.36 |
21 | −1.32 | 0.55 | 0.51 | −0.57 | −1.09 | 0.10 |
22 | 0.88 | 0.55 | 0.54 | −0.13 | −1.16 | 0.32 |
23 | −0.22 | −0.52 | −1.59 | −1.47 | 0.67 | −2.00 |
24 | −1.32 | −0.91 | −2.11 | −0.57 | −0.51 | −1.54 |
25 | −0.22 | −1.95 | 0.72 | −1.89 | −1.11 | −1.64 |
26 | −0.22 | −0.15 | 0.89 | −1.01 | −1.11 | −0.36 |
27 | −1.32 | −1.59 | −0.07 | −1.47 | 1.23 | −1.26 |
28 | −0.22 | −1.60 | 0.07 | −1.47 | 1.23 | −1.11 |
29 | 0.88 | −1.60 | 0.93 | −1.03 | −0.76 | −0.87 |
30 | −0.22 | −1.59 | −2.57 | −0.58 | −0.56 | −1.86 |
31 | 0.88 | 0.97 | 0.41 | 0.27 | −0.94 | 0.70 |
32 | 0.88 | 1.65 | 1.00 | 1.16 | −0.94 | 1.27 |
33 | −1.32 | 1.30 | −2.73 | 0.71 | −0.94 | 0.10 |
34 | −0.22 | −0.14 | 0.16 | 0.74 | 0.92 | 0.33 |
35 | −0.22 | 0.55 | 0.34 | 0.75 | 0.36 | 0.54 |
36 | 1.97 | 0.91 | −0.23 | 1.17 | 3.79 | 1.28 |
37 | −0.22 | 0.55 | 0.61 | 0.73 | 0.27 | 0.91 |
38 | −1.32 | 1.28 | 0.42 | 0.72 | −0.05 | 0.81 |
39 | −1.32 | 1.66 | 0.14 | 0.72 | −0.60 | 1.36 |
40 | −0.22 | 1.33 | 0.13 | 1.18 | 0.40 | 1.42 |
The eigenvalues and eigenvectors of
The Pareto analysis chart.
Subsequently, the component scores are computed (see Table
New inputs to the FCM-BPN.
|
|
|
---|---|---|
−0.56 | 0.91 | −0.19 |
−0.13 | 0.87 | −0.34 |
0.51 | 0.57 | −0.37 |
−0.97 | −0.10 | 0.20 |
−0.87 | −0.20 | −0.26 |
−0.75 | 0.14 | −0.51 |
0.57 | 0.56 | −0.66 |
1.30 | 1.18 | −0.55 |
1.55 | 0.31 | 0.47 |
1.37 | −0.87 | −1.04 |
1.11 | −0.59 | 0.91 |
3.04 | 0.63 | −0.20 |
0.51 | −2.44 | −0.02 |
−1.94 | 0.12 | −0.43 |
−0.30 | 0.35 | −1.29 |
−1.62 | −0.84 | −0.48 |
−2.04 | −1.24 | −0.17 |
−0.87 | 0.77 | 0.89 |
−1.92 | 1.34 | 0.64 |
−0.58 | 1.70 | 0.34 |
0.22 | 0.23 | 1.29 |
−0.62 | 1.31 | 0.73 |
2.54 | −1.26 | −0.16 |
2.39 | −1.64 | 1.20 |
3.02 | 1.57 | 0.14 |
0.89 | 1.21 | 0.66 |
2.56 | −0.74 | −1.19 |
2.19 | −0.13 | −1.54 |
1.61 | 1.90 | −0.42 |
2.72 | −1.23 | 0.87 |
−1.27 | 0.99 | 0.71 |
−2.56 | 1.07 | 0.78 |
−0.37 | −2.44 | 2.47 |
−0.60 | −0.51 | −0.82 |
−1.06 | −0.27 | −0.17 |
−2.54 | −1.36 | −3.41 |
−1.31 | −0.02 | −0.18 |
−1.32 | −0.63 | 0.67 |
−1.77 | −0.58 | 1.32 |
−2.13 | −0.66 | 0.12 |
The component scores.
After employing PCA, examples are then classified using FCM. If a crisp clustering method is applied instead, then it is very likely that some clusters will have very few examples. In contrast, an example belongs to multiple clusters to different degrees in FCM, which provides a solution to this problem. Similarly, in probability theory, the naïve Bayes method provides the probability that the item belongs to each class. However, the application of FCM can consider subjective factors in classifying the jobs.
FCM classifies jobs by minimizing the following objective function:
Normalize the input data. Produce a preliminary clustering result. (Iterations) Calculate the centroid of each category as the following:
where Remeasure the distance from each job to the centroid of each category and then recalculate the corresponding membership. Stop if the following condition is met. Otherwise, return to step where
The performance of FCM is highly affected by the settings for the initial values, and therefore can be repeated multiple times in order to find the optimal solution. Finally, the separate distance test (
The Fuzzy Logic Toolbox of MATLAB can be used to implement the FCM approach. A sample code is shown in Algorithm
In the illustrative example, the data have been standardized and therefore are not normalized again. The results of the
The results of the
Number of categories ( |
|
|
|
---|---|---|---|
2 | 1.96 | 0.14 | 0.34 |
3 | 1.21 | 0.09 | 0.34 |
4 | 0.86 | 0.07 | 0.30 |
5 | 0.67 | 0.06 | 0.26 |
6 | 0.53 | 0.03 | 0.43 |
The classifying results (
Category | Jobs |
---|---|
1 | 1, 2, 18, 19, 20, 22, 31, 32 |
2 | 3, 7, 8, 9, 12, 25, 26, 29 |
3 | 4, 5, 6, 14, 16, 17, 34, 35, 37, 38, 39, 40 |
4 | 10, 11, 23, 24, 27, 30 |
The classifying results (
Category | Jobs |
---|---|
1 | 1, 2, 18, 19, 20, 21, 22, 31, 32 |
2 | 2, 3, 7, 8, 9, 12, 25, 26, 28, 29 |
3 | 4, 5, 6, 14, 15, 16, 17, 33, 34, 35, 36, 37, 38, 39, 40 |
4 | 10, 11, 13, 23, 24, 27, 28, 30, 33 |
We also note that the classification results are very different according to the new variables, compared with the results based on the original variables. In other words, the results of FCM and PCA-FCM are not the same. The optimal number of categories in FCM is 6, while that in PCA-FCM is 5. If jobs are divided into four categories in these two methods, then the results are compared in Figure
Comparison of the classification results by PCA-FCM and FCM.
In Figure
Finally, the jobs/examples of a category are learned with the same BPN. Artificial neural networks have been proposed to solve a wide variety of problems usually characterized by sets of different equations. Although there have been some more advanced artificial neural networks, such as compositional pattern-producing network, cascading neural network, and dynamic neural network, a well-trained BPN with an optimized structure can still produce very good results. The configuration of the BPN is established as follows. Inputs: the new factors determined by PCA associated with the Single hidden layer: generally one or two hidden layers are more beneficial for the convergence property of the BPN. For simplicity, the number of neurons in the hidden layer is twice that in the input layer. An increase in the number of hidden-layer nodes lessens the output errors for the training examples, but increases the errors for novel examples. Such a phenomena is often called “over-fitting.” There has been some research considering the relation among the complexity of a BPN, the performance for the training data and the number of examples, for example using Akaike’s information criterion (AIC) or the minimum description length (MDL). Output: the (normalized) cycle time estimate of the example.
The procedure for determining the parameter values is now described. After preclassification, a portion of the adopted examples in each category is fed as “training examples” into the BPN to determine the parameter values for the category. Two phases are involved at the training stage. At first, in the forward phase, inputs are multiplied with weights, summated, and transferred to the hidden layer. Then activated signals
The network parameters are placed in vector
The Levenberg-Marquardt algorithm is an iterative procedure. In the beginning, the user should specify the initial values of the network parameters
In the illustrative example, 3/4 of the examples in each category are used as the training example. The remaining 1/4 is left for testing. A three-layer BPN is then used to estimate the cycle time of jobs in each category according to the new variables with the following setting. Single hidden layer. The number of neurons in the hidden layer: Convergence criterion:
For an outlier, the BPNs of all categories are applied to estimate the cycle time
The estimation performances.
Category | MAE (hrs) | MAPE | RMSE (hrs) |
---|---|---|---|
1 | 18 | 1.6% | 42 |
2 | 1 | 0.1% | 3 |
3 | 6 | 0.4% | 12 |
4 | 23 | 1.8% | 53 |
Outliers | 149 | 11.9% | 152 |
Total | 42 | 3.5% | 85 |
Obviously, the overall estimation performance is affected by the outliers. If the outliers can be dealt with properly, the overall estimation will be improved. To this end, an iterative feedback control procedure is established in the next subsection (see Figure
Comparing the performances of two training algorithms (group 4, convergence criterion: SSE < 10−6).
Algorithm | Number of epochs | MAE | MAPE | RMSE |
---|---|---|---|---|
Gradient descent | 10000 | 79 | 6.7% | 98 |
Levenberg-Marquardt | <100 | 23 | 1.8% | 53 |
The iterative process of dealing with outliers.
Job classification in the proposed methodology is based on the combination of FCM (or PCA-FCM) and the
The relationship between the
There are absolute rules for the classification of jobs in a wafer fabrication factory. It usually depends on the purpose of job classification, apparently to enhance the estimation accuracy in the proposed methodology. Therefore, a job is correctly classified if its cycle time is accurately estimated after classification. Otherwise, the job is misclassified.
Assuming the cycle time of job
The degree that job
The correctness/correct percentage of the classification results by classifier
The correctness of the classification results.
|
|
---|---|
1 | 1.00 |
2 | 1.00 |
3 | 1.00 |
4 | 1.00 |
5 | 1.00 |
6 | 1.00 |
7 | 1.00 |
8 | 1.00 |
9 | 1.00 |
10 | 1.00 |
11 | 1.00 |
12 | 1.00 |
13 | 1.00 |
14 | 1.00 |
15 | 1.00 |
16 | 1.00 |
17 | 1.00 |
18 | 1.00 |
19 | 1.00 |
20 | 1.00 |
21 | 1.00 |
22 | 1.00 |
23 | 1.00 |
24 | 1.00 |
25 | 1.00 |
26 | 0.63 |
27 | 1.00 |
28 | 0.58 |
29 | 1.00 |
30 | 1.00 |
31 | 1.00 |
32 | 1.00 |
33 | 1.00 |
34 | 1.00 |
35 | 1.00 |
36 | 1.00 |
37 | 1.00 |
38 | 0.55 |
39 | 0.00 |
40 | 1.00 |
Subsequently, the estimation error is fed back to the FCM classifier to adjust the classification results. The difference with Chen and Wang’s method [
The estimation performances.
Category | MAE (hrs) | MAPE | RMSE (hrs) |
---|---|---|---|
1 | 1 | 0.0% | 1 |
2 | 1 | 0.1% | 2 |
3 | 1 | 0.1% | 2 |
4 | 2 | 0.2% | 5 |
Outliers | 56 | 4.5% | 80 |
Total | 15 | 1.2% | 36 |
Comparison of the classification results.
To further evaluate the advantages and/or disadvantages of the proposed methodology, eight existing approaches, statistical analysis, CBR [
The proposed methodology was implemented on a PC with an Intel Dual CPU E2200 2.2 GHz and 2.0 G RAM. FCM was implemented with the Fuzzy toolbox of MATLAB 2006a. In addition, BPN was implemented with the Neural Network Toolbox under the following conditions. Number of epochs per replication: 10000. Number of initial conditions/replications: 10. Stop training if MSE < 10−6 is satisfied or 10000 epochs have been run.
Among the steps, PCA and FCM can be done instantaneously. The training of BPN usually takes less than 1 minute per replication.
The performances with the nine approaches are compared and summarized in Table
Comparisons of the performances of various approaches.
MAE (hours) | MAPE | RMSE (hours) | |
---|---|---|---|
Statistical analysis | 73 | 6.1% | 99 |
CBR | 81 | 6.5% | 104 |
BPN | 33 | 2.8% | 71 |
SOM-WM | 30 | 2.5% | 64 |
EFR | 30 | 2.6% | 65 |
SOM-FBPN | 22 | 2.0% | 38 |
Postclassifying FBPN | 40 | 2.7% | 88 |
Bidirectional classifying BPN | 19 | 1.9% | 37 |
The proposed methodology | 15 | 1.2% | 36 |
In statistical analysis, a linear regression equation is used to estimate the job cycle time. In the CBR approach, the weights of factors (the cycle times of the previous cases) are proportional to the similarities of the new job with the previous cases. The optimal value of parameter
Statistical analysis was adopted as a comparison basis. According to experimental results, the following points are made. The combination of BPN and PCA could reduce about 50% of space for storing the input variables in the modeling of the wafer fabrication system. From the effectiveness viewpoint, the estimation accuracy (measured with the MAPE) of the proposed methodology was significantly better than those of the other approaches. The average advantage over statistical analysis is 80%. The standard deviation of the cycle time for this case is 100 hours. Compared with this, the accuracy of the proposed methodology is good. The estimation performance of the proposed methodology was also better than the existing classifying methods, such as SOM-WM, SOM-FBN, EFR, SOM-FBPN, the postclassifying FBPN, and the bidirectional classifying BPN approach. The advantage of the proposed methodology was reasonable due to the replacement of the variables and the iterative process of dealing with the outliers. In general, the performances with the preclassifying approaches are better than that with the post-classifying approach. The proposed methodology was also applied to other cases. The results are summarized in Table : When estimating the job cycle time the estimating performance of the proposed methodology is the same as that of the existing approach being compared. : When estimating the job cycle time, the estimating performance of the proposed methodology is better than that of the existing approach being compared.
Performances in other cases.
RMSE | Case I | Case II | Case III | Case IV |
---|---|---|---|---|
Statistical analysis | 77 | 83 | 104 | 78 |
CBR | 74 | 78 | 96 | 72 |
BPN | 53 | 68 | 84 | 63 |
SOM-WM | 49 | 71 | 86 | 66 |
EFR | 50 | 50 | 62 | 47 |
SOM-FBPN | 38 | 53 | 66 | 50 |
Postclassifying FBPN | 62 | 93 | 113 | 86 |
Bidirectional classifying BPN | 24 | 31 | 38 | 28 |
The proposed methodology | 23 | 23 | 28 | 22 |
The results are summarized in Table To ascertain the effect of each treatment taken in the proposed methodology, the performances of BPN, FCM-BPN, PCA-BPN, and PCA-FCM-BPN (the proposed methodology) are compared in Table
Results of the Wilcoxon sign-rank test.
| |
---|---|
Statistical analysis |
|
CBR | 1.83* |
BPN | 1.83* |
SOM-WM | 1.83* |
EFR | 1.64 |
SOM-FBPN | 1.83* |
Postclassifying FBPN | 1.83* |
Bidirectional classifying BPN | 1.83* |
The effects of the treatments taken in the proposed methodology.
RMSE (hrs) | BPN | FCM-BPN | PCA-BPN | PCA-FCM-BPN |
---|---|---|---|---|
Training data | 73 | 58 | 71 | 36 |
Estimating the cycle time of each job in a wafer fabrication factory is a critical task to the wafer fabrication factory and has been widely studied in recent years. In order to further enhance the accuracy of the job cycle time estimation, PCA is applied to the FCM-BPN approach in this study, which is an innovative treatment in this field. Through replacing the variables, job classification can be more accurate. In addition, the relationship between the factors and the cycle time can be clearly specified.
On the other hand, since job classification is the core for the proposed methodology, a new index is used to validate the classification of jobs. The empirical relationship between the
An example is used to illustrate the proposed methodology. According to the experimental results, the estimation accuracy (measured with MAE, MAPE, and RMSE) using the proposed methodology was significantly better than those with the existing approaches; the advantage of PCA is for improving the correctness of job classification. The simple combination of PCA and BPN does not show much advantage; after combining with PCA, the estimation accuracy of FCM-BPN was significantly improved; the overall estimation performance is often affected by the outliers. The iterative procedure tries to remove the outliers and gradually improves the overall estimation performance.
Some other issues for this topic can be further investigated. Most of the existing methods are based on the job clustering. The aim of this study is to provide positive impacts on certain measures for these methods. However, if there are the other variable replacement techniques that can be as effective is also worth exploring in future studies. In addition, the iterative procedure used to optimize the results of job classification is quite time consuming especially for a large-scale problem, and therefore a more efficient way should be found.
This work was supported by the National Science Council of Taiwan.