
Research Article


Employing Artificial Neural Networks into Achieving Parameter Optimization of MultiResponse Problem with Different Importance Degree Consideration 

KunLin Hsieh



ABSTRACT

This study proposed a procedure based on Artificial Neural Networks (ANNs) technique with different importance degree consideration to address parameter optimization of a multiple responses problem. No matter what type of the experimental designs being employed, the proposed approach can be directly employed. Besides, the consistency and difference between those multiple responses can be also studied via the aggregation weight values in our proposed procedure. An illustrative example owing to the lead frame manufacturer in Taiwan is also employed to demonstrate the effectiveness and rationality of the proposed procedure.







INTRODUCTION
Design of Experiment (DOE) can be viewed as a well known technique to be used to address the process improvement or parameter optimization. The philosophy is to study the relationship between the design parameter (or the noise parameters) and the response. Herein, the design parameters and noise parameters will affect the quality of products or operational processes. The design parameters are factors that can be controlled by the designers and the noise parameters, e.g., the environmental factors, are factors that can not be controlled by designers. As for the issue of parameter optimization, how to obtain the parameter setting to achieve the response optimization is the primary consideration. That is, setting status of the design parameters will be expected in such a way that the response can attain the desired target with the minimum variation.
After reviewing the related studies (Fowlkes and Creveling,
1995; Montgomery, 1991; Myers and
Montgomery, 1995), many studies only address a single evaluation response
of the manufactured product or process. The complexity and relationship among
the multiple responses will let it be a difficult problem to be addressed. However,
the customer or the process frequently considers more than one quality response
in practice in the recent years. For a multiresponse problem, the conventional
MANOVA (Johnson and Wichern, 1992) and the Response Surface
Method (RSM) (Myers and Montgomery, 1995) are two techniques
frequently applied in the experimental designs domain. But, both theories were
hard to be understood for most practitioners. Besides, Taguchi method (Fowlkes
and Creveling, 1995; Peace, 1993; Phadke,
1989) is another approach which had frequently used to achieve robust experiment
in quality engineering. However, most successful applications of Taguchi method
still keep to addressing a single response problem. For addressing the multiple
responses problem, Taguchi method need to separately optimize the single evaluation
response and the optimum setting of parameter can be then determined via engineering
judgment. Until now, several approaches (Ames et al.,
1997; Castillo et al., 1996; Chapman,
1995; Leon, 1996; Phadke, 1989;
Su and Tong, 1997; Tong et al.,
1997; Su and Heish, 1998; Lan,
2009; Lan and Wang, 2009) were proposed to perform
the optimization of multiple responses. However, most proposed approaches almost
intend to make an integrated index under final decisionmaking for parameter
optimization. However, the information inhibited behind the system might be
lost under making the integration action.
Artificial Neural Networks (ANNs) had mentioned to be applied into process
modeling problem (Rumelhart et al., 1986; Barletta
et al., 2007; Hsieh and Lu, 2008; Krishnaiah
et al., 2006; Ozel et al., 2007; Lan
and Wang, 2009; KunLin, 2009). Tong
and Hsieh (2001) had proposed a novel means of applying artificial neural
network to solve the multiresponse optimization combining the quantitative
and qualitative response. Although, the parameter optimization can be obtained,
the different importance among those multiple responses still can not be included
well into the process analysis. In lieu of above circumstances, we will propose
a procedure based on ANNs to perform optimization of the multiresponses problem
with different importance consideration in arbitrary experimental design. No
matter that the control factors owing to the level form or the real value, this
proposed procedure could be utilized.
PARAMETER OPTIMIZATION DURING MULTIRESPONSE PROBLEM
Derringer and Suich (1980) applied the desirability
function to optimize the multiresponses problems in a static experiment. Castillo
et al. (1996) demonstrated the modified desirability functions for
optimizing the multiresponse. However, their method may lead to an inaccurate
result for some inexperienced users and may increase the uncertainty in determining
the optimal parameter setting and is difficult for the practitioners who have
only limited statistical training. Layne (1995) presented
a procedure, which considers simultaneously three methods: weighted loss function,
desirability function and a distance function, to determine the optimum parameter
combination. The controversies may be generated by simultaneously comparing
three methods to determine the optimum setting. Khuri and
Conlon (1981) proposed a procedure, based on a polynomial regression model,
to simultaneously optimize several responses. Logothetis
and Haigh (1988) also optimized a fiveresponse process by utilizing the
multiple regression technique and the linear programming approach. These two
methods are also computationally complex and, therefore, are difficult to be
utilized on the shop floor. Pignatiello (1993) utilized
a variance component and a squared deviationfromtarget to form an expected
loss function to optimize a multiple response problem. This method is hard to
implement for that a cost matrix must be obtained, in addition, the amount of
the experimental observations are required. Chapman (1995)
proposed a cooptimization approach, which composites all response by using
a composite response. This approach might confuse some inexperienced practitioners
in determining which ranges of the constraint’s can be safely expanded.
Leon (1996) presented a method, which is based on the
notions of a standardized loss function with the specification limits, to optimize
a multiresponse problem. However, only the NominalTheBest (NTB) characteristic
is suitable to employ this approach, which may limit the capability for this
approach. Ames et al. (1997) presented a quality
loss function approach in the response surface models to deal with a multiresponse
problem. The basic strategy is to describe the response surfaces with experimentally
derived polynomials, which can be combined into a single loss function by using
known or desired targets. Next, minimizing the loss function with respect to
process inputs locates the best operating conditions. Lai
and Chang (1994) proposed a fuzzy multiresponse optimization procedure
to search for an appropriate combination or process parameter settings. A strategy
of optimizing the most possible response values and minimizing the deviation
from the most possible values is used which considers not only the most possible
value, but also the imprecision of the predicted responses. Tong
and Su (1997) developed a MultiResponse Signal to Noise (MRSN) ratio, which
integrates the quality loss for all responses, to solve the multiresponse problem.
Conventional Taguchi method can be applied based on MSRN. The optimum factor/level
combination can be obtained. Su and Tong (1997) also
proposed a principle component analysis approach to perform the optimization
of the multiresponse problem. Initially, standardizing the quality loss of
each response; the principle component analysis is then applied to transform
the primary quality responses into fewer quality responses. Finally, the optimum
parameter combination can be obtained by maximizing the summation standardized
quality loss. Hsieh (2006) had proposed an AI technique,
i.e., the Backpropoagation Neural Network (BPNN), to address the multiresponse
problem. The nonlinear relationship between the process parameter and process
response can be modeled well by using BPNN. Besides, the continuous parameter
settings can be obtained by their proposed approach. However, the different
importance among multiresponses can not be included in Hsieh’s approach
and it will limit his real application.
WEIGHT VALUE CONSIDERATION DURING MULTIRESPONSE PROBLEM
The choice and the summation for the weight values of several criterions and
the difference comparison among several performances with weighted consideration
will be the problem for the issue of Multiple Criterions DecisionMaking (MDCM)
(Zeleny, 1982, 1992). As for the
choice of weight value, it will be more difficult to be determined during the
multiple criterions consideration for those practitioners. Hence, AHP (Saaty,
1994, 1996, 2001;Lai
et al., 1999; Rammanathan and Ganesh, 1995;
Ngai, 2003) was developed to overcome such issue by
dividing those criterions into the primary and secondary criterions with hierarchy.
However, the test of consistency frequently limited its real applications (Nishizawa,
1995). As for the summation of the weight value, the practitioners will
face the problem of how to summarize the weight effect of each criterion with
the case of several experts. The average concept was the method frequently been
used to compute the weight value of each criterion. However, the variation between
different experts will be omitted by using the average concept to compute the
weight value. Restated, it can be viewed as meeting the problem of common consensus
during those experts. Generally, the larger degree of importance of criterion
will denote the corresponding weight value to be set a larger value. Tong
and Su (1997) proposed a procedure, which applied fuzzy set theory to Multiple
Attribute Decision Making (MADM) for optimizing a multiresponses problem. Although,
their method can reduce the uncertainty in determining each response’s
weight, it is still computational complicated to be practically used. Shen
and Hsieh (2006) had proposed a fuzzy weight aggregator to address the decisionmaking
about the weight values with different experts. The consistency and difference
between several experts can be included in their proposed approach. Hence, it
will be included into this study.
PROPOSED APPROACH
Generally, a particular relationship may exist between input and output for
a system. From mathematical viewpoint, the logical relationship can be modeled
by constructing the model for system. System’s output can be viewed as
a function of system’s input. Due to the logical analysis, the reverse
inference can also be employed to model a system, that is, the input can be
also viewed as a function of the output. It can be clearly interpreted from
the mathematical definition: a direct mathematical concept is O = f (I) and
a reverse mathematical concept is O = f^{1} (I), where, the O denotes
the system’s output, I denotes the system’s input and f will be mathematical
relationship between O and I. The neural networks can be used to model this
logical analysis to achieve quality optimization (Barletta
et al.., 2007; Heish, 2006; Hsieh and Lu, 2008;
Krishnaiah et al., 2006; Ozel
et al., 2007). In this study, we also apply the logical analysis
mentioned to construct the procedure and make modification. The proposed procedure
can be utilized for the conventionally experimental design and the Taguchi’s
experiment. The concept of the procedure will be given as follows.
Phase I. Determine the weight values of those multiple responses according
to the experts:
• 
Step 1: Compute the membership degree μ_{ij} according
to X_{ij} for the evaluation table which is made by several experts 
Assuming that there are n responses, m experts, evaluation value X_{ij}
of ith response for jth expert, we can construct such evaluation table. Then,
the ideal point of each criterion can be obtained by finding the maximum X_{ij}
value among each response. Next, the membership degree μ_{ij} for
each evaluation value with respect to the ideal point can be computed via the
Eq. 1:
• 
Step 2: Compute the harmonizing mean of each criterion by using
Eq. 2 
Where α will denote the degree of importance and the larger α will
represent the enlarger effect of importance. Generally, we can take α to
be 1 for simplifying the analysis.
• 
Step 3: The average weight of ith response (w_{i}) can
be computed as Eq. 4 by using e_{i}. The value
(e_{i}) of ith response can be computed as Eq. 3
by using the Eq. 2: 
Phase II. Parameter optimization
Case I: For discrete parameter combination (i.e., level combination of control
factors):
Step 1: 
Randomly select the data from the designed experiment to form
the training and the testing data set of the neural network. The ratio of
the testing/training set is about 1/4 (NeuralWare, 1990) 
Step 2: 
Determine the optimal level settings for process parameters 
TheNominalThe Best (NTB): The value of y is expected to the target
T. When the y equals to T (target), the desirability value equals to 1; if the
departure of y excesses a particular range from the target, the desirability
value equals to 0 and, such situation represents the worst case. The desirability
function of thenominalthebest can be written as the Eq. 5:
where, the y_{max} and y_{min} represent the upper/lower tolerance limits of y, s and t represent the weight value of response and the weight value can be obtained from phase I. TheLargerThe Best (LTB): The value of y is expected to the larger the better. When, they excess a particular criteria value, which can be viewed as the requirement, the desirability value equals to 1; if the y is less than a particular criteria value, which is unacceptable, the desirability value equals to 0. The desirability function of thelargerthebest can be written as the Eq. 6: where, the y_{min} presents the lower tolerance limit of y, the y_{max} presents the upper tolerance limit of y, r represents the weight of response and the weight value can be obtained from phase I. TheSmallerThe Best (STB): The value of y is expected to be the smaller the better. When the y is less than a particular criteria value, the desirability value equals to 1; if the y excess a particular criteria value, the desirability value equals to 0. The desirability function of thesmallerthebest can be written as the Eq. 7:
where, the y_{min} presents the lower tolerance limit of y, the y_{max}
presents the upper tolerance limit of y, r represents the weight of response
and the weight value can be obtained from Phase I.
• 
Train the neural network by assigning the (level setting of parameters)/(desirability
value of response) as the (inputs/outputs) of the neural network. The RMSE
(Root of the Mean Square Error) value of the training and testing phase
will be taken as an evaluation index since comparing the different network’s
architecture, i.e. the number of PEs in input layer  the number of PEs
in hidden layer the number of PEs in output layer, the learning rate, the
possible momentum, the transfer function. The architecture with the minimum
training RMSE and testing RMSE values is selected to be the optimum architecture 
For example, an experiment has three design parameters (A, B, C) with two levels
and three responses Y_{1}, Y_{2} and Y_{3}. And then,
those three responses will have different importance and it will be described
with respect to different weight value. And then, the desirability value of
response can be computed according to Eq. 57.
The structure of the training and testing data set can be represented as follows
(where Factor_{(Level)} denotes the level label of Factor, D_{IJ}
denotes the desirability value for the Ith response for the Jth trail):
• 
Retrain the selected neural network to arrive at the steady state (i.e.,
the RMSE value will not make any change or less than the predesigned criterion)
by combining the above training and testing set in Step 1 into a training
set 
• 
Input the all possible parameters’ level settings (according to the
combination of different level) to the trained neural network, the estimated
desirability values can be obtained 
Step 3: 
If the users can not accept the estimated response
values, rechoose the parameter factors or go back Step 2 to retrain the
neural network architecture. Otherwise, the analysis procedure can stop. 
Case II: For control factor with mixed type (including the level label and
continuous value or all the continuous type):
Step 1: 
Randomly select the data from the designed experiment to form the training
and the testing data set for the neural network. The ratio of the testing/training
set is about 1/4 
Step 2: 
Determine the optimal parameter combination 
• 
Firstly, compute the desirability value of each response according
to Eq. 57. 
• 
Train the neural network by assigning (response value and the desirability
value of each response/ level setting of parameters) as the (inputs/outputs)
of the neural network. If the factor is discrete type, the output of corresponding
PE will be represented as the level number. The RMSE values of the training
and testing phase will be the evaluation index when different network’s
architectures are compared. The architecture with the minimum training and
testing RMSE values is selected to be the optimum architecture 
For example, a static experiment has three design parameters (A, B, C) with
two levels and three responses Y_{1}, Y_{2} and Y_{3}.
And, those three responses will have different importance and it can be represented
by using the different weight values. And then, the desirability value can be
computed according to Eq. 57. Herein, factor
A is discrete type and factor B and C are the continuous type. The structure
of the training and testing data set can be represented as follows (where Factor_{(Level)}
denotes the level label of Factor, Factor_{(value)} denotes the continuous
value of Factor, Y_{IJ} denotes the response value of Ith response for
the Jth trail, D_{IJ} denotes desirability of the Ith response for the
Jth trail, D_{IJ} denotes the desirability value for the Ith response
for the Jth trail):
• 
Retrain the selected neural network’s architecture to approach the
steadystate (i.e., the RMSE value will not make any change or less than
the predesigned criterion) by combining the above training and testing
set in Step 1 into a training set 
• 
The optimum parameter combination can be obtained by inputting the ideal
values or the targets, i.e., the multiple responses’ ideal condition,
the desirability value (1) and the expected weighted response to the trained
neural network 
Step 3: 
Estimate the responses’ values and determine the effect of the control
factor on responses. 
• 
Train the neural network by assigning the (level setting of parameters)/(desirability
value of response) as the (inputs/outputs) of the neural network. The RMSE
values of the training and testing phase will be the evaluation index when
different network’s architectures are compared. The architecture with
the minimum training RMSE and testing RMSE values is selected to be the
optimum architecture 
For example, an experiment has three design parameters (A, B, C) with two real
values and three responses Y_{1}, Y_{2} and Y_{3}. And,
those three responses will have different importance and it can be represented
by using the different weight values. And then, the desirability value can be
computed according to Eq. 57. Factor A
is discrete type and factors B and C are the continuous type. The structure
of the training and testing data set can be represented as follows (where Factor_{(Level)}
denotes the level label of Factor, Factor_{(value)} denotes the continuous
value of Factor, D_{IJ} denotes the desirability value for the Ith response
for the Jth trail):
• 
Retrain the selected neural network’s architecture to arrive at the
steadystate (i.e., the RMSE value will not make any change or less than
the predesigned criterion) by combining the above training and testing
set in Step 1 into a training set 
• 
Input the optimum parameter condition obtained in step 2, the estimated
response values can be obtained 
Step 4: 
If the users can not accept the estimated response values, rechoose the
parameter factors or go back step 2 to retrain the neural network 
ILLUSTRATIVE EXAMPLE
In this study, we apply an example owing to lead frame manufacturing improvement
introduced by Hsieh (2006) to demonstrate the proposed procedure. Lead frame
is a necessary material to the conventional Integrated Circuit (IC) packaging.
Taping process is an important operation for lead frame manufacturing. Figure
1 graphically depicts the concept diagram of the lead frame and the taping
process.
 Fig. 1: 
The concept diagram of the taping process in taping station 
The purpose of the taping process is to maintain the coplanarity of the leads
and make it to be efficiency utilized during the wire bonding.
To avoid the broken in wire bonding during the subsequent packaging, the taping strength must be monitored by the lead frame manufacturer. The height of the adhesive bleeding is another important consideration except the taping strength. During the current setting values of related process parameters for SO product series, the average taping strength is about 145 g and the variance of the taping strength is about 36 g; the average height of adhesive bleeding is 7.4 mil and the variance adhesive bleeding is 1.32 mil. The quality of taping process can not be accepted by the lead frame manufacturer. The manufacturer would like to perform the parameter optimization for simultaneously optimizing two responses: maintaining the taping strength (Y1) as 180 g and the height of adhesive bleeding (Y2) as 5 mil.
After performing a brainstorming, four control factors as pressure strength
(A), spacing (B), curing temperature (C) and dwell time (D) are chosen. For
experienced judgment, each control factors have three level settings for designed
experiments. Table 1 shows the level settings of control factors.
The current settings are denoted by underline. To reduce the experimental time
and cost, an Orthogonal Array (OA) L_{9} is selected (Taguchi,
1996). Each parameter combination will repeat five trails, hence, 45 data
are observed.
The presenting settings are denoted as underline. In this illustrative example,
the control factors nearly have a continuous form, thereby accounting for why
the optimal control values can be studied. Hence, the case II of the proposed
approach will be performed. To simplify the proposed approach, the neural network
package software, i.e., Neural Professional Plus/II [15], is used to develop
the required networks. It is a C based simulator that provides a system for
developing various neural network models.
Table 1: 
The level settings of the control factors 

Table 2: 
The evaluation result of five experts 

Before, we perform the parameter optimization, we discussed with the senior
engineers to determine the importance degree of those two responses. And then,
five senior engineers and managers were grouped to determine the related importance
about those two responses by using the scale five. And, the evaluation result
of those five experts will be given in Table 2. For each response,
Likert’s 5 scales was applied into achieving evaluation. Restated, score
5 will denote the most importance and score 1 will denote the less importance
with the respect response. Next, the phase I of our proposed procedure will
be taken to compute the suitable weight values as 0.6024 (for taping strength)
and 0.3976 (for the height of adhesive bleeding).
Next, ten trials (this example includes fortyfive trials) are randomly chosen
from the fortyfive trails to form the testing set and the remainder are used
to form the training set. This makes the proportion of testing/training to be
about 1/4. Herein, all factors will have the continuous type, we will choose
the procedure of mixed type. In such procedure, the number of PEs in the input
layer for neural network is five (including two responses, two desirability
value of those two responses and the weighted response value).
Table 3: 
The RMSE of the training and testing for step2 

*Denotes the optimum neural network’s structure 
Table 4: 
The RMSE of the training and testing for step3 

*Denotes the optimum neural network’s structure 
The number of output PEs for neural network will be set as four (including
four control factors with the continuous type). These two responses in this
case are NTB type, hence, the Eq. 5 will be used to derive
the additional information. Due to that the weight values of those two responses
were obtained as 0.6024 and 0.3976, the parameter of s (or t) in Eq.
5 will be set as 0.6024 (for addressing Y_{1}) and 0.3976 (for addressing
Y_{2}). Table 3 shows the options for determining
the network’s architecture and the structure 594 is chosen for having
the better performance (training’s RSME ≅ 0.196 and testing RMSE ≅
0.263) with the learning rate being 0.125, the momentum value being 0.8, transfer
function being sigmoid function, learning rule being deltabardelta rule and
learning epochs being 5000. Retrain the chosen network’s structure by
combining the training and testing set to arrive at 5000 epochs. Then, inputting
the ideal values (180, 5, 1, 1) to the trained network, the optimum parameter
combination derived from neural network can be obtained: [pressure strength,
spacing, curing temperature, dwell time] = [(P0.51 ) kg cm^{2}, (S0.46)
mil, (C3.6) min, (t+1.5) sec].
Next, for obtaining the estimates of those two responses and determining the
effect of the four control factors in step 3, the second neural network is constructed
by assigning the (parameter combination/desirability value) to be the (inputs/outputs)
of the network. The training and testing set are randomly selected to arrive
at the (testing/training) proportion of 1/4. Table 4 shows
the options of the network and the structure 462 is chosen for having the
better performance (training’s RSME ≅ 0.124 and testing RMSE ≅
0.195). Retrain the second network chosen by combining the training and testing
set to arrive at the situation of the weighted value having no any change. The
estimated desirability values can be obtained by inputting the optimum parameter
combination obtained in step 2 to the second network.
Table 5: 
The result of the confirmation experiment 

The estimated responses of the taping strength and the height of adhesive bleeding
can be transferred by using Eq. 5 to be 179.25 g and 4.95
mil. The estimated response values significant achieve the desired quality,
the engineers can accept it and permit to perform the confirmation experiment.
Although, the estimated optimal parameter setting is denoted as [(P0.51) kg cm^{2}, (S0.46) mil, (C3.6)°C, (t+1.5)sec], the actual parameter setting is determined as [(P0.5) g cm^{2}, (S0.5) mil, (T4) mil, (t+1.5)sec] due to that it is hard to directly set the operating parameter by using the predicted recommendation. Finally, the confirmed experiments for the proposed procedure are performed. Table 5 shows those results. The average value of the taping strength is 185.3g and the average height of adhesive bleeding is 4.82 mil. They are close to the target value (180 g, 5 mil) than the current result. The result obtained from the confirmed experiments for the proposed procedure indicate that using the proposed approach can efficiently enhance the product quality, thereby confirming the proposed approach’s effectiveness. The process engineers can accept the results from the optimal parameter setting as [(P0.4) g cm^{2}, S mil, (T3)°C, (t+1.5)sec]. Moreover, the variances of the two responses (taping strength’s variance is about 2.79 g and the height’s variance is about 0.193 mil) for the confirmation experiment are significantly less than that of the current settings. Although, only one experiment is employed in this study, the validity of the proposed approach can still be verified. CONCLUSION
In this study, an optimization procedure based on ANNs modeling technique with
the different importance degrees for multiple responses is proposed. The proposed
approach can not only be employed in conventional experimental design, but Taguhci’s
experimental design is also can be performed. The proposed approach can provide
several metrics: (1) The continue parameter’s optimum condition can be
obtained since the control factor being quantitative form; (2) The importance
degrees (or the weight values) of those multiple responses can be included into
the parameter optimization. And, the consistency and difference among those
multiple responses can be considered well in this proposed procedure and (3)
The ANNs operation can be viewed as a blackbox processing, hence, the practitioners
can rapidly and easily applied it via any ANNs software, especial for those
engineers having the limited statistical training. In addition, we will suggest
collect more experimental data to train neural networks, the higher neural network's
modeling capability may be achieved. The engineers can efficiently optimize
the multiresponse problem in the field of the quality improvement by employing
the proposed optimization procedure.

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