Applying robust multi-response quality engineering for parameter
selection using a novel neural–genetic algorithm
T.S. Li
a, C.T. Su
b,*, T.L. Chiang
ca
Department of Industrial Engineering and Management, Ming Hsin University of Science and Technology, Hsinchu, Taiwan 304, ROC
b
Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, Taiwan 300, ROC
c
Department of Business Administration, Ming Hsin University of Science and Technology, Hsinchu, Taiwan 304, ROC Received 22 September 2000; accepted 2 September 2002
Abstract
This study presents a neural–genetic algorithm to solve the selection problem of manufacturing process parameters. The proposed algorithm is a combination of artificial neural network (ANN) and genetic algorithms (GAs). In addition, the neural network is used to formulate a fitness function for predicting the value of the response based on the parameter settings. GAs then take the fitness function from the trained neural network to search for the optimal parameter combination. Owing to the most of manufactured products have more than one quality characteristic and the quality characteristics are generally correlated with each other, this study also proposes a desirability function to obtain a compromise, composite solution. A case study of how the silicon manufacturing process parameters are selected offline demonstrates the effectiveness of the proposed approach. # 2002 Elsevier Science B.V. All rights reserved.
Keywords: Artificial neural network; Genetic algorithm; Multi-response optimization; Desirability function; Parameter selection
1. Introduction
A group of responses often characterize the perfor-mance of a manufactured product. These responses are generally correlated and measured by a different measurement scale. Therefore, a decision-maker must resolve the parameter selection problem to optimize each response. This problem is regarded as a multi-response optimization problem, subject to different response requirements. Most of the conventional methods are incomplete in that a response variable
is selected as the primary one and is optimized by adhering to the other constraints set by the criteria[1]. Many heuristic methodologies have been developed to resolve the multi-response problem. Cornell and
Khuri[2]explored the multi-response problem using a
response surface method. Tai et al. [3] assigned a
weight for each response to resolve the problem.
Pignatiello [4] utilized a squared
deviation-from-tar-get and a variance to form an expected loss function
for optimizing a multiple response problem. Layne[5]
presented a procedure capable of simultaneously con-sidering three functions: weighted loss function,
desir-ability function, and distance function. While
providing a multi-response example in which Taguchi
methods are used, Byrne and Taguchi[6]discussed an
example involving a connector and a tube. Logothetis
*Corresponding author. Tel.:þ886-3-5731857;
fax:þ886-3-5722392.
E-mail address: ctsu@cc.nctu.edut.tw (C.T. Su).
0166-3615/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 - 3 6 1 5 ( 0 2 ) 0 0 1 4 0 - 9
and Haigh[7]also discussed a manufacturing process characterized by five responses. In doing so, they selected one of the five response variables as primary and optimized the objective function sequentially while ignoring possible correlations among the responses. Optimizing the process with respect to any single response leads to nonoptimum values for the remaining characteristics.
Optimizing the parameter selection problem
requires developing a model capable of accurately describing the input–output behavior and capturing the range of these input–output parameters. There-fore, this work presents a neural–genetic algorithm that combines the neural network and genetic algo-rithm to identify the nonlinear relationship between input and output parameter and obtain a near-optimal parameter combination. The neural networks have been extensively used to model the engineering pro-cess. Briefly, the neural network maps the input– output observed data and, in doing so, defines the fitness function of the parameter selection. Conse-quently, the genetic algorithm utilizes the fitness function to identify the optimal solution of the pro-blem. In addition, this study proposes a concurrent optimization performance index to obtain a preferable solution by using a desirability function developed by
Derrienger and Suich [8]. Capable of concurrently
optimizing several responses and allowing the user to weigh the responses by their importance, the desir-ability function is easily understood and intuitive[6]. A case study demonstrates the effectiveness of the proposed approach.
The rest of this paper is organized as follows.
Section 2 describes neural networks, genetic
algo-rithms and the hybrid neural–genetic algorithm.
Sec-tion 3 provides details of the multi-response
optimization technique. Section 4 describes a case
study of the silicon manufacturing process in Taiwanto show how the proposed algorithm is implemented.
Concluding remarks are finally drawn inSection 5.
2. Optimization approach 2.1. Neural networks
Describing a manufacturing process precisely is generally too difficult by a mathematical function.
A recent work adopted neural networks to elucidate the ability to learn complex relationships between parameters and responses, usually for process and
quality control[9]. These models are frequently used
to identify optimal process settings. An approximated model can be constructed using a neural network. Although statistical regression methods and neural network method both can effectively correct the dimensional measurements of geometric features on a part profile, Chang et al.[10]indicated that neural network methods will be a very powerful alternative for precision measurement using computer vision system.
Neural networks have been successfully applied to diverse areas such as speech synthesis and pattern
recognition[11]. Once trained, a neural network can
be evaluated very quickly, particularly during the optimization phase. Recent review of neural network
applications in manufacturing, Zhang and Huang[12]
cited such diverse venues as milling, metal cutting, injection modeling, arc welding and spray painting. Details regarding further applications can be found in
[13–17].
Neural networks are formed by processing parallel units called neurons, which closely resemble the structure of a human neurological system. The ele-mentary processors are interconnected so that knowl-edge pertaining to the relationship between input and output parameters are stored in the weights of the connections between them. Each neuron except the first layer contains the weighted sum of previous input neuron by an exponential function. This function allows neural networks to be generalized with a wide range of application.
Neural networks can be categorized into network structures such as multilayer perceptron, the feedback
model of Hopfield[18]and Hopfield and Tank[19],
the adaptive resonance technique (ART) networks and Kohonen network etc., and the learning methods such as back-probagation. The ability to learn is one of the main advantages that makes the neural networks so attractive. They also have the capability of performing parallel processing and possess significant fault tol-erance. Since the BP neural network can be used to
approximately realize continuous mapping[20], this
work adopts the BP neural network owing to its ability to map the complex relationship between input data and corresponding outputs.
2.2. Genetic algorithms
Genetic algorithms (GAs), an optimization metho-dology based on a direct analogy to Darwinian natural selection and genetics in biological systems, is a promising alternative to conventional heuristic
meth-ods[21]. GAs differ from conventional search
tech-niques that conduct a point-to-point search in the solution space. GAs work with a set of candidate solutions called population and, based on the Darwi-nian principle of ‘‘survival of the fittest’’, obtain the optimal solution after a series of iterative computa-tions. This characteristic, associated with their sto-chastic nature, enables GAs to deal with large search spaces randomly and efficiently.
Genetic algorithms (GAs) have been extensively used to optimize complicated production systems. GAs are known for their robustness and effective
overall search capabilities [22]. Hung and Adeli
[23], and Hsu et al.[24]demonstrated the superiority of GAs over other networks capability in terms of its optimum search. Highly promising for obtaining near optimal solutions to complex problems, GAs have been extensively applied to diverse areas such as
scheduling and sequencing [25–28], cellular
manu-facturing [29], PCB layout design[30], and process
control strategies[31].
GA, a local search technique, can find solutions for a wide range of application. To achieve the desired response, GAs generate a successive population of alternate solutions which are represented by a chro-mosome, i.e. a solution to the problem, until accep-table results are obtained. In this manner, a GA can quickly yield a successful outcome without examining all possible solutions to the problem. The procedure using the fitness function is to assess the performance of the solution. The reproduction, crossover, and mutation are the main operators that randomly impact the fitness value. Chromosomes are selected for repro-duction by evaluating the fitness value. The fittest chromosomes are then saved and copied into the next generation. Crossover, the critical genetic operator that allows new solution regions in the search space to be explored, is a random mechanism for exchanging genes between two chromosomes. The probability of crossover is generally set between 0.5 and 0.9. Muta-tion, in which the genes may occasionally be altered, i.e. a ‘‘0’’ becomes an ‘‘1’’ or vice versa. During the
search, the mutation must avoid the premature loss important information although they are typically set at an extremely low value, 0.01 to 0.05.
2.3. A hybrid neural–genetic algorithm
This study proposes a novel hybrid neural–genetic algorithm to determine the parameter settings in a manufacturing process. The proposed approach com-bines the neural network and GA to the problem. The proposed approach consists of two stages. The first stage in a hybrid procedure involves identifying the desirability function deriving from the multiple responses. A BP network is trained to derive the relationship between input parameters and output responses. Notably, the trained network can accurately predict the behavior of possible parameter combina-tions. Thus, tuning the input parameters in the trained network allow us to obtain the corresponding response. The trained network is used as the fitness function in the GA. During the second stage, GA is directly used to solve the problem. Herein, the chro-mosome is used to represent the possible solution. Each gene in the chromosome represents the value of the input parameter. For example, a manufacturing process has three input parameters P, Q, and R. A chromosome can represent the value of the three parameters (P, Q, R), respectively. The essential genetic operators during the iterative procedure can be found in the previous section. These operations are conducted to obtain the optimal response, which is evaluated by the fitness function. Therefore, the
opti-mal parameter of the problem can be obtained.Fig. 1
schematically depicts the proposed hybrid procedure. The detailed procedure is summarized as given further.
Step 1. Collect the input parameters and
correspond-ing responses.
Step 2. Develop a BP network model to obtain the
relationship between the input parameters and output responses. The trained network is referred to as a fitness function.
Step 3. Set the GA operating condition (e.g.
popula-tion size, maximum number of generapopula-tion, parameter number, crossover rate, and mutation rate).
Step 4. Create an initial population by randomly selecting the value of the input parameters.
Step 5. Repeat steps 6–10 until the stopping condition
is reached.
Step 6. Calculate the responses, by inputting the
parameter values to the fitness function (responses are taken from Step 2).
Step 7. Select the parameter values according to the
computed response.
Step 8. Crossover the fitness parameter values.
Step 9. Mutate the parameter values to yield the next
generation.
Step 10. Obtain the current optimal parameter values.
Step 11. Obtain the optimal parameter settings and
responses.
3. Multi-response problem 3.1. General scheme
Optimization of the multi-response problem is an attempt to optimize all output responses simulta-neously. Among the concurrent optimization methods, most of the authors used the approaches that combine all the different response requirements into one
com-posite requirement[1]. Hence, the compromise
solu-tion is obtained in a much simpler way. A simple
weighting method was found in Ilhan et al. [32], as applied in an electrochemical grinding (ECG) process.
Zadeh[33]normalized each response and then gave a
simple weight for each response. The discussion regarding the assignments of weights can be found in[34].
3.2. Desirability function
The desirability function transforms each response
to a corresponding desirability value dið0 2 d 2 1Þ.
All the desirabilities are combined to form a compo-site desirability function:
D¼ f ðd1; d2; d3; . . . dnÞ (1)
where n is number of responses. The value of D may
be defined as the geometric mean of the di’s and
thus D lies between 0 and 1. Consequently, the desirability approach can convert a multi-response problem into a single-response one. The plant man-ager can easily determine the optimal parameters among a group of solutions. However, the user spe-cifies the parameters ‘‘p’’ ofEqs. (2) and (3)based on technical, economical and other considerations. For two-sided specification limits with a target value T
for the response Y, Derringer[33]used the following
transformations di¼ Yi LSLi Ti LSLi p LSLi Yi Ti Yi USLi Ti USLi p Ti Yi USLi 0 Yi< LSL or Yi> USL otherwise 8 > > > > > > > < > > > > > > > : (2)
where LSLiis ith lower specification of limit; USLithe ith upper specification of limit; Tithe ith target of the response; and Yi is the ith response.
For a one-sided specification limit (higher-the bet-ter-type response), Derringer[8]suggested the follow-ing transformations: di¼ 0 Yi LSLi Yi LSLi Yimax LSLi p LSLi< Yi< Yimax 1 Yi Yimax otherwise 8 > > < > > : (3)
where Yimax is the highest value which is practically attainable.
3.3. The proposed approach
This study proposes a desirability function to solve multi-response optimization problems. When the multi-response problem is transformed into a single-response problem, the single-single-response problem is divided into two problems: how to specify the weights and how to transform each response into a more ‘‘desirable’’ response. This work proposes a compo-site approach by using the desirability function[8,35]
to determine the overall value of scalar function. The scalar function ranges between 0 and 1, and the larger the value implies a more stringent user requirement. This value can also be used as a performance index for the multiple responses.
Herein, the hybrid neural–genetic algorithm and the desirability function are combined. The neural net-work is first trained by using the process production data. The desirability function is then used to trans-form the multiple responses into a single response. Finally, GA is applied to obtain the best desirability value (i.e. fitness value). Consequently, the optimal parameter settings of the manufacturing process can be determined.
4. Illustrative example 4.1. Problem description
The silicon compound of RC50 is a critical part that is used in the computer peripheral and medical
appli-ance assemblies.Fig. 2 shows a flow chart of RC50
silicon compound manufacturing process. The process starts by mixing two silicon raw materials: silicon filler and catalyst under a high temperature. The materials are then polymerized in a chemical chamber under parameter settings, which were originally assigned by an equipment provider in Japan. The process of polymerization in the chamber is the most complicated and critical process that strongly depends
on parameter settings (e.g. N2 flow, release agent,
conductivity, and oil absorption). Filtering, water cleaning and purification are then applied to remove small amounts of contamination and improve the
product’s characteristics. Table 1 lists the operating ranges with respect to process parameters. To satisfy customer’s requirements, QA takes a certain amount of finished goods to conduct a 2-day functional test after forming and cutting processes. The entire pro-duct is sent back to line for reworking if it fails the QA test. Consequently, it interferes with the regular pro-duction schedules, resulting in late deliveries.
The manufacturer had difficulty in achieving effi-cient process control due to insuffieffi-cient knowledge of the relationship between process parameters and
cor-responding responses. Table 2 lists the process
cap-ability indices for the seven responses; the
performance is obviously improved in terms of pro-cess capability. However, conducting experimental design to improve the quality would be infeasible
since the factory employs a continuous process with an enormous amount of material and long production time. Hence, this study adopts the historical process data to obtain the required model, thereby optimizing the product’s responses.
The problem considered herein is the multi-response optimization problem as the process para-meter selection applied in a silicon manufacturing company. The problem dealing with the multi-input and multi-output is common in practice. The silicon factory must determine the levels of 14 parameters for seven quality characteristics to satisfy different cus-tomer’s requirements.
4.2. Training of neural networks
The relationship model between parameters and responses is developed by using BP neural network, in which historical production data of four hundred lots are employed for training as well as 100 lots are used for testing. The convergence criterion employed
in the network training is the RMSE. Table 3 lists
Fig. 2. Manufacturing process of silicon compound of RC50.
Table 1
Input parameters and their operation ranges
Parameter Code Range Water content P1 80–90 pH value P2 10–20 Conductivity P3 0.0017–0.002 Release agent Z1 2.26–3.2 Specific area W1 1.2–3.1 Oil content W2 0.1–0.2 Whiteness W3 1.0–1.1 Particle size W4 3.3–3.7 Al2O3content W5 0.15–0.3 Fe2O3content F1 0.5–1.0 Residue sieve F2 10–15 Volatile material F3 7.5–17.5 Temperature C1 17.1–25 Nitrogen flow C2 50–60 Table 2
Specifications and process capability indices of seven responses Responses (code, dimension) Specification Cp Cpk
Density (Y1, g/cc) 1.140–1.15 0.71 0.67 Plasticity (Y2, point) 210–250 1.00 0.98 Hardness (Y3, durometer) 51–55 0.52 0.49 Tensile strength (Y4, kg/cm2) 6.2 0.80 0.80 Elongation (Y5, %) 250 0.79 0.79 Shrinkage ( Y6, %) 3.7–3.9 0.39 0.34 Rebound (Y7, %) 66 0.34 0.34
several options of the neural network architecture, in which the structure 14-7-7 is selected to obtain a better performance. The trained network 14-7-7 is used as the fitness function of the GA, as further explored in the next section.
4.3. Determination of the fitness function
Once a BP neural network was well trained, the weights connected between layers in the neural net-work structure illustrated the relationship between input parameters and output responses. The value of each response was calculated by weighted sum con-nected to output node and transferred by an acti-vation function (e.g. sigmoid function). Hence, the weights obtained from a trained BP neural network and activation functions of each node formed the fitness function adopted in GA optimization proce-dure. In this case, responses Y1, Y2, Y3, and Y6have the corresponding target values and Y4, Y5, and Y7 have lower specifications. After training the BP neural network, the value of (Y1–Y7) will be the near-optimal
solution in this case. Then, using theEqs. (2) and (3)
will transfer the value of Yiinto di. Herein, a geometric mean of seven responses is employed as a desirability function to solve the multi-response problem. We have
D¼ f ðd1; d2; d3; d4; d5; d6; d7Þ (4)
where di is calculated from Eqs. (2) and (3). For
computational convenience, p is equal to 1 in this case. While a diis approaching to 1, it means that diis approaching the target. While the D is approaching to 1, it is noted that each response in the process is simultaneously approaching to 1 (say the target). The value of D demonstrates the performance metric of the proposed method.
4.4. Optimization using genetic algorithm
Each input parameter in a silicon factory is normal-ized to the value between 0 and 1 and they are combined into one string. For example, the input
parameters listed in Table 1, are transformed into
the chromosome representation (P1, P2, P3, Z1,. . ., C2) in a string. Strings are randomly generated to form the initial population. When GA is applied to optimize
Table 3
Options for neural networks Architecture RMSE Training Testing 14-5-7 0.10121 0.11912 14-6-7 0.09963 0.09632 14-7-7 0.08521 0.09541 14-8-7 0.08754 0.09674 14-9-7 0.08737 0.09724 Note: Learning rate: 0.2, momentum: 0.9, and number of epochs: 10,000.
Table 4
Implementation results of GA
Item Data
The largest D value in 20 runs 0.7212 The smallest D value in 20 runs 0.5724 Average D value 0.6602
S.E. 0.0413
Table 5
A comparison of responses
Method Parameter values Predicted responses Initial state P1¼ 85.0, Z1¼ 2.96, W3¼ 1.00, F1¼ 1.00, C1¼ 18.1, P2¼ 15.00, W1¼ 1.70, W4¼ 3.30, F2¼ 10.00, C2¼ 60.00, P3¼ 0.0019, W2¼ 0.10, W5¼ 0.15, F3¼ 15.00, Y1¼ 1.142, Y4¼ 7.00, Y7¼ 67.00, Y2¼ 224.00, Y5¼ 270.00, Y3¼ 53.4, Y6¼ 3.85, Proposed approach (optimal condition) P1¼ 84.3, Z1¼ 2.76, W3¼ 1.06, F1¼ 0.64, C1¼ 28.76, P2¼ 10.54, W1¼ 1.75, W4¼ 3.53, F2¼ 13.06, C2¼ 50.18, P3¼ 0.0019, W2¼ 0.16, W5¼ 0.24, F3¼ 14.43, Y1¼ 1.145, Y4¼ 8.4178, Y7¼ 74.88, Y2¼ 229.94, Y5¼ 298.22, Y3¼ 52.37, Y6¼ 3.81,
the silicon parameter selection, the essential operators, including reproduction, crossover and mutation, should be determined in advance. Herein, a roulette wheel approach is adopted as the selection procedure. The crossover rate and mutation rate are set as 0.5 and 0.01, respectively. Fifty strings are randomly gener-ated to establish the initial population. Notably, 5000 generations were processed. In this case, the optimal target, a geometric mean of seven responses will be set to 1. The fitness function is formed by the BP learning algorithm and desirability function. The specification of each response will be the constraints in the GA optimization procedure.
4.5. Results
The above information is used and the GA is
executed 20 runs.Table 4summarizes the
implemen-tation results. The higher the D value implies a much better compromised solution. The largest D value is 0.7212 and its optimum chromosome is (84.3, 10.54, 0.0019, 2.76, 1.75, 0.16, 1.06, 3.53, 0.24, 0.64, 13.06, 14.43, 28.76, 50.18). These settings are the optimal condition for our 14 process parameters. The pre-dicted responses under the optimal condition are
Y1 ¼ 1:145, Y2¼ 229:94, Y3¼ 52:37, Y4¼ 84:178,
Y5 ¼ 298:22, Y6¼ 3:81, Y7¼ 74:88. Table 5
com-pares the responses between the initial condition and the proposed one (optimal condition).
Table 6also compares the initial process capability and the process capability based on the proposed approach. According to this table, the proposed approach outperforms the original state. Correspond-ingly, the feasibility of the proposed approach is established.
5. Conclusion
This study proposes an integrated method using neural network, genetic algorithm, and desirability function to optimize the manufacturing process with multiple responses. The neural network is used to
explore the nonlinear multivariate relationship
between the parameters and responses and then GA is performed to obtain the optimal parameter settings. During the implementation of GA, the fit-ness function is defined in terms of a desirability function, which is utilized to transform multiple responses into a single response. The proposed approach can easily and efficiently achieve the opti-mization of the complex process with multiple responses. These settings facilitate the process engi-neers in achieving acceptable process control during the production. In addition, all of the experiments are conducted under computerized simulations with his-torical production data without any manufacturing interruption. The improvement in process capability allows the factory to more easily fabricate products with superior quality.
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Te-Sheng Lireceived the BS degree in industrial management from National Chen-Kung University, Tainan, Taiwan, ROC and the MS degree in engineering management from University of Missouri-Rolla, USA in 1985 and 1990, respec-tively. He holds the PhD degree in indus-trial engineering and management from the National Chiao-Tung University, Hsinchu, Taiwan, ROC in 2002. Dr. Li is currently an associate professor in the Department of Industrial Engineering and Management at Ming Shin University of Science and Technology, Taiwan. His research interests include quality engineering, neural networks application and data mining in semiconductor manufacturing industry.
Chao-Ton Sureceived the PhD degree in Industrial Engineering from University of Missouri-Columbia, USA, in 1993. He is a Professor in the Department of Indus-trial Engineering and Management at National Chiao Tung University, Taiwan. His current research activities include quality engineering and management, operation management and data mining in industrial applications. He has pub-lished over 50 referred international jour-nal papers. Dr. Su obtained the 2000–2001 Outstanding Research Award of the National Science Council of the Republic of China. In 2001, Dr. Su also obtained the Individual Award of the National Quality Awards of the Republic of China.
Tai-Lin Chiangis currently an associate professor in the Department of Business Administration at Ming Shin University of Science and Technology, Taiwan. He
holds a PhD in Industrial Engineering and Management from National Chiao-Tung University, Taiwan. His research interests include Six Sigma, quality engineering, neural networks applica-tions, and semiconductor manufacturing engineering.
