A novel quality prediction method based on feature selection considering high dimensional product quality data

Junying Hu; Xiaofei Qian; Jun Pei; Changchun Tan; Panos M. Pardalos; Xinbao Liu

doi:10.3934/jimo.2021099

Article Contents

2022, Volume 18, Issue 4: 2977-3000. Doi: 10.3934/jimo.2021099

This issue Previous Article A three echelon supply chain model with stochastic demand dependent on price, quality and energy reduction Next Article Managing piracy: Dual-channel strategy for digital contents

A novel quality prediction method based on feature selection considering high dimensional product quality data

1.
School of Management, Hefei University of Technology, Hefei 230009, China
2.
Center for Applied Optimization, Department of Industrial and Systems, Engineering University of Florida, Gainesville, FL 32611, USA
3.
Key Laboratory of Process Optimization and Intelligent Decision-making, of the Ministry of Education, Hefei 230009, China
4.
School of Economics, Hefei University of Technology, Hefei 230009, China
5.
Ministry of Education Engineering Research Center for Intelligent Decision-Making & Information System Technologies, Hefei 230009, China

^* Corresponding author: Xiaofei Qian, Xinbao Liu
^* Corresponding author: Xiaofei Qian, Xinbao Liu

Received: December 2019

Revised: January 2021

Published: July 2022

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Abstract

Product quality is the lifeline of enterprise survival and development. With the rapid development of information technology, the semiconductor manufacturing process produces multitude of quality features. Due to the increasing quality features, the requirement on the training time and classification accuracy of quality prediction methods becomes increasingly higher. Aiming at realizing the quality prediction for semiconductor manufacturing process, this paper proposes a modified support vector machine (SVM) model based on feature selection, considering the high dimensional and nonlinear characteristics of data. The model first improves the Radial Basis Function (RBF) in SVM, and then combines the Duelist algorithm (DA) and variable neighborhood search algorithm (VNS) for feature selection and parameters optimization. Compared with some other SVM models that are based on DA, genetic algorithm (GA), and Information Gain algorithm (IG), the experiment results show that our DA-VNS-SVM can obtain higher classification accuracy rate with a smaller feature subset. In addition, we compare the DA-VNS-SVM with some common machine learning algorithms such as logistic regression, naive Bayes, decision tree, random forest, and artificial neural network. The results indicate that our model outperform these machine learning algorithms for the quality prediction of semiconductor.

Keywords:

Mathematics Subject Classification: Primary: 62C99, 62P30; Secondary: 68T20.

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Figure 1. Stages of semiconductor manufacturing

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Figure 2. Flowchart of proposed method

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Figure 3. Flowchart of DA-VNS algorithm

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Figure 4. Encoding of DA-VNS algorithm

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Figure 5. Running results after 500 iterations of GA, DA and DA-VNS algorithms respectively (The blue points indicate the projection of the solutions on $ (q(\theta),R(\theta)) $.)

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Figure 6. The evolution of the best $ q(\theta) $ and $ R(\theta) $ for GA, DA and DA-VNS respectively over 500 iterations

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Figure 7. Performance improvement between DA-VNS-SVM and other algorithms

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Table 1. Quality prediction problems in semiconductor manufacturing processes in recent years

Publications	Problems	Methods	Data Driven
Fridgeirsdottir [73]	Fault diagnosis	Data mining	√
Kim [37]	Prediction of plasma etch processes	PNN	√
Bae [9]	Modeling and rule extraction of the ingot fabrication	DPNN	√
Su [59]	Quality prognostics for plasma sputtering	NN	√
Chou [16]	Prediction of dynamic wafer quality	SVM	√
Purwins [55]	Prediction of Silicon Nitride layer thickness	Collinearity regression	√
Melhem [49]	Prediction of batch scrap	Regularized regression	√
Alagic [5]	Prediction of the damage intensity	Image processing and statistical modeling	√
Al-Kharaz [4]	Prediction of quality state	ANN	√
Kim [36]	Prediction of wafers errors	Ordinary least squares regression and ridge regression	√

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Table 2. Common Kernel Function

Kernel function name	Kernel function representation
Radial basis function	$ \kappa(x_i,x_j)=\exp(-\gamma \|\|x_i-x_j\|\|) $
Linear kernel function	$ \kappa(x_i,x_j)=x_i\cdot x_j $
Polynomial kernel function	$ \kappa(x_i,x_j)=(x_i\cdot x_j+1)^d $
Sigmoid kernel function	$ \kappa(x_i,x_j)=\tanh[n <x_i\cdot x_j >+\theta] $

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Table 3. List of preset parameters in DA-VNS

Parameters	$ DA-VNS_{RBF} $	$ DA-VNS_{\kappa_{1}} $	$ DA-VNS_{\kappa_{2}} $
Population size	100	100	100
Iteration times	500	500	500
Nearest neighbor number	/	5	5
Learning probability	0.8	0.8	0.8
Innovation probability	0.1	0.1	0.1
Mutation probability	0.1	0.1	0.1
Search range of penalty parameter $ C $	$ [10^{-3},10^{3}] $	$ [10^{-3},10^3] $	$ [10^{-3},10^3] $
Search range of kernel width $ \gamma $	$ [2^{-6},2^6] $	$ [2^{-6},2^6] $	$ [2^{-6},2^6] $
Search range of amplitude regulating parameter $ t_1 $	/	/	$ [-10,10] $
Search range of displacement regulating parameter $ t_2 $	/	/	$ [-10,10] $
Luck coefficient	{0, 0.01, 0.1, 0.2, 0.5}	{0, 0.01, 0.1, 0.2, 0.5}	{0, 0.01, 0.1, 0.2, 0.5}
$ w_c $, $ w_f $, $ c_{f1} $, $ c_{f2} $	0.8, 0.2, 0.8, 0.2	0.8, 0.2, 0.8, 0.2	0.8, 0.2, 0.8, 0.2

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Table 4. Comparison of performance between DA-VNS and other algorithms

Algorithm	Optimal parameters				$ q(\theta) $	$ R(\theta) $	Selected features
Algorithm	$ C $	$ \gamma $	$ t_1 $	$ t_2 $	$ q(\theta) $	$ R(\theta) $	Selected features
$ GA_{RBF} $	78.54	3.36	/	/	0.6136	0.725	60
$ GA_{\kappa_1} $	73.11	0.80	/	/	0.6217	0.7333	47
$ GA_{\kappa_2} $	11.21	0.94	1.53	4.41	0.6262	0.7416	56
$ GA_{RBF} $	96.10	0.52	/	/	0.6329	0.75	64
$ DA_{\kappa_{1}} $	62.34	0.49	/	/	0.6559	0.775	43
$ DA_{\kappa_{1}} $	42.04	0.49	9.81	9.96	0.6695	0.7917	41
IG	/	/	/	/	0.6957	0.8105	24
$ GA-VNS_{RBF} $	21.32	1.31	/	/	0.6882	0.8033	48
$ DA-VNS{\kappa_{1}} $	60.82	1.60	/	/	0.7038	0.8333	36
$ DA-VNS{\kappa_{2}} $	96	0.91	-2.69	8.77	0.7221	0.8583	49

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Table 5. Performance improvement of $ q(\theta) $ between DA-VNS and other algorithms. $ Improvement = \frac{q(\theta)-q^{\prime}(\theta)}{q(\theta)}*100\% $

Improvement	$ GA_{RBF} $	$ GA_{\kappa_{1}} $	$ GA_{\kappa_{2}} $	$ DA_{RBF} $	$ DA_{\kappa_{1}} $	$ DA_{\kappa_{2}} $	IG	$ DA-VNS_{RBF} $	$ DA-VNS_{\kappa_{1}} $
$ DA-VNS{\kappa_{1}} $	12.82	11.66	11.02	10.07	6.81	4.87	1.15	2.22	/
$ DA-VNS{\kappa_{2}} $	15.03	13.90	13.28	12.35	9.17	7.28	3.66	4.69	2.53

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Table 6. Performance improvement of $ R(\theta) $ between DA-VNS and other algorithms. $ Improvement = \frac{R(\theta)-R^{\prime}(\theta)}{R(\theta)}*100\% $

Improvement	$ GA_{RBF} $	$ GA_{\kappa_{1}} $	$ GA_{\kappa_{2}} $	$ DA_{RBF} $	$ DA_{\kappa_{1}} $	$ DA_{\kappa_{2}} $	IG	$ DA-VNS_{RBF} $	$ DA-VNS_{\kappa_{1}} $
$ DA-VNS{\kappa_{1}} $	13.00	12.00	11.00	10.00	7.00	4.99	2.74	3.60	/
$ DA-VNS{\kappa_{2}} $	15.53	14.56	13.60	12.62	9.70	7.76	5.57	6.41	2.91

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Table 7. Comparison of performance between DA-VNS-SVM and common machine learning algorithms

Algorithm	Accuracy
Logistic Regression (LR)	0.4917
Naive Bayes (NB)	0.6167
Artificial Neural Network (ANN)	0.6417
Decision Tree (DT)	0.658
Random Forest (RF)	0.667
DA-VNS$ _{\kappa_1} $-SVM	0.7038
DA-VNS$ _{\kappa_2} $-SVM	0.7221

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