Integrating the Taguchi method and the multiattribute decision-making method to optimize the surface mount technology solder paste printing thickness process

Abstract

In order to meet the demand for the current consumer electronic products, the improvement of the surface mount technology is an important trend. This study used the Taguchi method to develop different level schemes of the surface mount technology solder paste printing process parameter in order to obtain the conditions of parameter combinations of the surface mount technology solder paste printing process parameter. However, the Taguchi method of experimental configuration requires multiple trials to obtain the surface mount technology solder paste printing process parameter, which may require considerable cost and time. Therefore, this study attempted to use two multiattribute decision-making methods, gray relational analysis, and technique for order preference by similarity to ideal solution evaluating method, in order to determine a group of optimal experimental schemes from among the established multiple experimental schemes using the Taguchi method. This study also used the process capability parameter to verify the research methods. The experimental results showed that surface mount technology solder paste printing thickness process capability (C_pk) value has improved from 0.59 to 1.53, which could improve product quality. The Taguchi and two multiattribute decision-making methods have proven that the model can effectively obtain the surface mount technology solder paste printing thickness process parameter.

Keywords

Surface mount technology gray relational analysis technique for order preference by similarity to ideal solution solder paste printing thickness process capability

Introduction

In response to the present trend of miniaturization of consumer electronic products, electronic components are becoming smaller, resulting in higher demand for surface mount technology (SMT) technology. The defect ratio of SMT is 75% in the solder paste printing process. In other words, the SMT yield rate can be maintained at a certain level only if the solder paste printing process is correctly done, the solder paste printing process as shown in Figure 1. However, it is difficult to make the printing process correct. It can also be said that solder paste printing process is the core of the entire SMT technology. Ramkumar et al.¹ proposed that the amount of fallen solder, pad design, hole design, circuit board surface coating, solder paste type, component placement method, and circuit temperature of the weld are the most important factors of the SMT process. The stencil hole design includes the hole shape and size. The hole may be a rectangle, oval, pentagon, and double trapezoid, and the size may be of 80%, 90%, and 100% of the soldering pad. Pan et al.² proposed 50 factors that may affect solder paste printing and argued that the selection of variables is very important, as there are many variables. Finally, six variables affecting the solder paste retention, including the size of the stencil hole, the hole shape, circuit board surface coating, stencil thickens, solder paste type, and printing speed, are selected. The experimental results suggested that hole size and stencil thickness are two key variables. Yang³ proposed 19 variables affecting solder paste printing by printing parameters and solder paste and, finally, summarized stencil thickness, component spacing, stencil hole size, mold release height, mold release speed, squeeze pressure, solder viscosity, and solder paste particle size as the input values of the neural network. The experiments of Ramkumar et al.¹ focused on the stencil hole design, including the shape and the relative proportion of the hole size against the soldering pad.

Figure 1.

Solder paste printing process: (a) start, (b) printing, and (c) complete.^1–3

A present study by Yang⁴ used discrete-event simulation to create a 300-mm semiconductor manufacturing flow and executed a factorial experiment of three factors based on uniform design, including direct ratio, stocker capacity, and the number of machine load ports. Finally, using the dual-response surface method, the most important of the three factors and best performance were determined. The results show promise for the proposed tool-to-tool transportation strategy in solving practical application. Wazed et al.⁵ developed simulation models for a multistage production system under common processes in an uncertain situation created by machine breakdown and quality variation. Few simulation models are developed based on a live case from a company. The models are verified and validated with the historical data of the company and by face validity. Taguchi approaches for orthogonal array are used in designing experiments. The experimental settings are executed in WITNESS, a simulation package. It is observed that variations in the levels of common processes in the system have significant impact on production quantity and cycle time. There is strong interaction among the common processes and the batch size in lancing stations. Padhi and Mohapatra⁶ aim to present a combined fuzzy analytical hierarchical process (AHP) and simple multiattribute ranking technique (SMART) approach to deal with contractor selection problems in government procurement auctions. The proposed approach utilizes a set of 10 attributes for the evaluation of a contractor. In this approach, the attributes of both past performance and present status of the contractor are considered, wherein the selection attributes are qualitative and/or quantitative types, which are inhibiting and/or enabling in nature. Claudio and Okudan⁷ in their study present an exploratory work using a hypothetical example of a decision-making methodology, namely, multiattribute utility analysis, for health care. The hypothetical sample problem presented involves patient prioritization in an emergency department (ED), where several patients require immediate attention, and all have the same acuity level. The utility theory is selected for this application in order to appropriately account for uncertainties in the decision problem.

As the experimental configuration of the Taguchi method requires multiple trials to obtain an SMT solder paste printing process parameter, it may require considerable time and cost. The technique for order preference by similarity to ideal solution (TOPSIS) concept considers the set of optimal attributes of m attributes in n schemes in order to develop a comprehensive performance and chooses the optimal scheme using the positive ideal solution and negative ideal solution. Gray relational analysis constructs the optimal attributes in the case of uncertain and incomplete information in scheme selection in order to mine and understand the relationships between different schemes and attributes through analysis and computation to select the attribute combination of the optimal scheme.^8–19

Research method and case analysis

Based on the multiple experimental schemes established by the experimental configuration of the Taguchi method, this study interviewed 10 experts (including one assistant manager of the Manufacturing Department, two managers, five section managers, and two engineers of the SMT Department of a company) and used two multiattribute decision-making methods (TOPSIS and gray relational analysis) to determine a group of optimal experiments, while using the process capability index ( $C_{pk}$ ) to verify the proposed research method. In the SMT printing process, solder paste thickness has a significant impact on the quality of SMT. The uniformity of the printed circuit board (PCB) on the same board has become the most important characteristic of the parity product. This study measured the SMT process and solder paste thickness uniformity at five points, in the upper, middle, lower, left, and right parts of the PCB board, by defining ((the highest point − the lowest point)/(average of the five points) = solder paste thickness uniformity). According to expert opinions and analysis, this study summarized eight SMT solder paste printing process quality control factors, as shown in Table 1, as the key quality characteristic schemes of priority concern for improvement, then calculated and assessed customer quality demands, and conducted importance analysis of the quality characteristics.^3,8–19

Table 1.

Factor analysis of SMT solder paste printing thickness process.

Factor		Range	Current status
Control factors	A: scraper material	A1: steel; A2: rubber	A1
	B: solder paste metal proportion	B1:Sn/Ag3.5; B2:Sn/Ag3.0/Cu0.5; B3:Sn-2Ag-0.5Cu-2Bi	B2
	C: scraper pressure (Nt)	10–17	13
	D: scraper angle (°)	40–70	50
	E: scraper speed (r/min)	5–30	15
	F: mold release speed (mm/s)	0.2–0.6	0.3
	G: printing spacing/angle (mm)	0.4–0.8	0.5
	H: flux (%)	2–10	3
Fixed factors	Working temperature (°C)	20–25	21
	Working humidity (%)	45–50	46
	Printing stencil thickness (mm)	0.1–0.15	0.15

To explore solder paste thickness $C_{pk}$ improvement, nominal-the-best characteristics are used. The nominal-the-best signal-to-noise (SN) ratio after inference is defined, as shown in equation (1), where $\bar{y}$ is the experimental data of average and s is the standard deviation¹³

S N_{NTB} = 10 \cdot \log_{10} (\frac{{\bar{y}}^{2}}{s^{2}})

(1)

Process capability is measured by the $C_{pk}$ index: if C_pk≥ 1.33, it is qualified.¹⁹ The solder past thickness data of 100 groups of sample PCB boards are randomly selected from mass-produced products in order to calculate the process capability index as C_pk = 0.59 < 1.33, which indicates that the process is unstable, the process capability is insufficient, and there is room for improvement.

Gray relational analysis

The degree of relationships among subsystems or elements could be evaluated through gray relational analysis,²⁰ and important influential factors to the development trend are then determined in order to learn the major features of the system through the following steps.

Step 1: normalize original data.

Normalize by dividing the original data $x_{i} (k)$ with the mean value of the sequence, as shown in equation (2)

r_{i} (k) = \frac{x_{i} (k)}{\sum_{k = 1}^{N} \frac{x_{i} (k)}{N}}, i = a, \dots, d k = A, \dots, N

(2)

Step 2: designate the standard sequence and calculate the difference sequence.

Take the mean value as a standard sequence, that is, sequence 0; the difference sequence $Δ_{0 i} (k)$ indicates the absolute difference of elements k between the other sequence i and the standard sequence 0, as expressed in equation (3)

Δ_{0 i} (k) = | r_{0} (k) - r_{i} (k) |, i = 1, 2, 3, \dots k = A, \dots, N

(3)

Step 3: calculate maximal difference $Δ_{max}$ and minimal difference $Δ_{min}$ , as expressed in equations (4) and (5)

Δ_{max} = \underset{i, k}{Max} Δ_{0 i} (k)

(4)

Δ_{min} = \underset{i, k}{Min} Δ_{0 i} (k)

(5)

Step 4: calculate gray relational coefficient $γ_{0 i} (k)$ .

The relational coefficient $γ_{0 i} (k)$ is defined in the following, of which $ς$ is the adjustment factor, as shown in equation (6)

γ_{0 i} (k) = \frac{Δ_{\min} + ς \cdot Δ_{\max}}{Δ_{0 i} (k) + ς \cdot Δ_{\max}}

(6)

Step 5: calculate the gray relationship $Γ_{0 i}$ between each sequence and the standard sequence. The gray relationship $Γ_{0 i}$ is defined, as shown in equation (7)

Γ_{0 i} = \sum_{k = A}^{N} \frac{γ_{0 i} (k)}{N}

(7)

Step 6: conduct sequencing according to the gray relationship.

TOPSIS

The basic concept of TOPSIS is to define both the positive ideal solution and the negative ideal solution in order to determine the solution closest to the positive ideal solution and farthest from the negative ideal solution. The positive ideal solution refers to the criterion value of the maximum benefits and minimum costs of all alternative solutions. Contrarily, the criterion value of the minimum benefit and maximum cost refers to the negative ideal solution. The TOPSIS method can be applied in the evaluation of a decision-making matrix of m solutions with n attributes, as illustrated in the following, and the calculation steps are given in the following.¹¹

Step 1: original value normalization.

Decision makers can provide subjective value measurements of a scoring matrix composed of the attribute value of TOPSIS, as established in each scheme. Assuming that there are n schemes and m attributes, and the score of scheme j in attribute i is $x_{ij}$ , the scoring matrix is shown in equation (8)

[\begin{matrix} x_{11} & x_{12} & \dots & x_{1 j} \\ x_{21} & x_{22} & \dots & x_{2 j} \\ ⋮ & ⋮ & \dots & ⋮ \\ x_{i 1} & x_{i 2} & \dots & x_{ij} \end{matrix}]

(8)

In order to avoid the influence of extreme values, TOPSIS must standardize the scoring matrix to prevent greatly different scores among the schemes in the same attribute and eliminate the influence of different attributes with different scales on the different scopes of attribute values. Assume that $r_{ij}$ is the score after standardization, as shown in equation (9)

r_{ij} = \frac{x_{ij}}{\sqrt{\sum_{i = 1}^{n} x_{ij}^{2}}}

(9)

Step 2: establish the weighted normalization decision-making matrix.

According to the relative weight of each attribute, the scoring matrix comprising the attribute values of the schemes in each of the attributes can be converted to a weighted scoring matrix. Weight in this study is the direct scoring method; assume that $w_{i}$ is the relative weight of attribute $i$ , and $g_{ij}$ is the standardized score multiplied by the weight, thus, the weighted standardized scoring matrix is as shown in equation (10)

[\begin{matrix} v_{11} & v_{12} & \dots & v_{1 j} \\ v_{21} & v_{22} & \dots & v_{2 j} \\ ⋮ & ⋮ & \dots & ⋮ \\ v_{i 1} & v_{i 2} & \dots & v_{ij} \end{matrix}] = [\begin{matrix} w_{1} r_{11} & w_{2} r_{12} & \dots & w_{j} r_{1 j} \\ w_{1} r_{21} & w_{2} r_{22} & \dots & w_{j} r_{2 j} \\ ⋮ & ⋮ & \dots & ⋮ \\ w_{1} r_{i 1} & w_{2} r_{i 2} & \dots & w_{j} r_{ij} \end{matrix}]

(10)

Step 3: search for the positive ideal solution (A⁺) and negative ideal solution (A⁻), as shown in equations (11) and (12).

The value measurement method of TOPSIS measures the degrees of separation between each scheme and the positive ideal solution and between each scheme and the negative ideal solution as relative strength and weakness, respectively. The positive ideal solution reaches the maximum value as the larger-the-better attribute and the minimum value as the smaller-the-better attribute. In order to facilitate calculation, the smaller-the-better attribute is first adjusted to the larger-the-better attribute and then the positive ideal solution is scheme ( $A^{+}$ ), which comprises the maximum value of all attributes; thus, scheme ( $A^{+}$ ) may not be any of the existing schemes. Similarly, the negative ideal solution is scheme ( $A^{-}$ ), which comprises the minimum value of all attributes, and thus, scheme ( $A^{-}$ ) may not be any of the existing schemes

A^{+} = {(max_{i} v_{ij} | j \in J), (min_{i} v_{ij} | j \in J') | i = 1, 2, \dots, m} = (v_{1}^{+}, v_{2}^{+}, \dots, v_{j}^{+}, \dots, v_{n}^{+})

(11)

A^{-} = {(min_{i} v_{ij} | j \in J), (max_{i} v_{ij} | j \in J') | i = 1, 2, \dots, m} = (v_{1}^{-}, v_{2}^{-}, \dots, v_{j}^{-}, \dots, v_{n}^{-})

(12)

where $j = {j = 1, 2, \dots, n | j benefit criteria}$ and $j' = {j = 1, 2, \dots, n | j cost criteria}$ . The benefit criteria refer to those indicators that have higher performance values, when the values are greater. The cost criteria refer to those indicators with higher performance values, when the values are smaller.

Step 4: calculate the distances from the positive ideal solution ( $S_{i}^{+}$ ) and the negative ideal solution ( $S_{i}^{-}$ ) of various solutions. The distances from the positive ideal solution ( $S_{i}^{+}$ ) and the negative ideal solution ( $S_{i}^{-}$ ) are shown in equations (13) and (14), and $S_{i}^{+}$ and $S_{i}^{-}$ are not different from the standard deviation in statistics²¹

S_{i}^{+} = \sqrt{{\sum_{j = 1}^{n} (v_{ij} - v_{j}^{+})}^{2}}, i = 1, 2, \dots, m

(13)

S_{i}^{-} = \sqrt{{\sum_{j = 1}^{n} (v_{ij} - v_{j}^{-})}^{2}}, i = 1, 2, \dots, m

(14)

Step 5: calculate the relative approximation of various solutions to the ideal solution, as shown in equations (15) and (16).

The measured value of ${C_{i}}^{+}$ is between 0 and 1, where the closer to 1, the farther the scheme is from the negative ideal solution, and the better the scheme the closer it is to 0, the farther the scheme is from the positive ideal solution the poorer the scheme is, as shown in equations (15). In addition, it can also be defined from the perspective that the farther the scheme is from the negative ideal solution, the better the scheme is, as shown in equation (16)

{C_{i}}^{+} = \frac{S_{i}^{-}}{S_{i}^{-} + S_{i}^{+}}

(15)

{C_{i}}^{-} = \frac{S_{i}^{+}}{S_{i}^{+} + S_{i}^{-}}

(16)

where $0 < {C_{i}}^{+} < 1$ and $0 < {C_{i}}^{-} < 1$ , $i = 1, 2, \dots, m$

Step 6: rank the preference order. According to the results of Step 5, the relative performance of various solutions can be ranked, where a larger value indicates stronger preference. TOPSIS uses the relative approximate value of the positive ideal solution to rank the preference of solutions and avoids the difficulty of simultaneously comparing solutions closest or farthest from the positive ideal solution and the negative ideal solution.

Discussion

Regarding the control factors affecting the SMT solder paste thickness process, this study found fixed factors and controllable factors, as shown in Table 1, after literature review and interviews with industrial experts.^1,2,22,23

According to the discussions of the expert panel and company process engineers, the selection of factor level refers to the reliable data accumulated from previous experience, which is determined by discussion, as shown in Table 2: factor analysis of solder paste printing thickness process.

Table 2.

Control factors and levels of SMT solder paste printing thickness process.

	A	B	C (Nt)	D (°)	E (r/min)	F (mm/s)	G (mm)	H (%)
Level 1	Steel	Sn/Ag3.5	17	70	30	0.6	0.4	2
Level 2	Rubber	Sn/Ag3.0/Cu0.5	13	65	18	0.4	0.6	6
Level 3		Sn-2Ag-0.5Cu-2Bi	10	40	5	0.2	0.8	10

As suggested by the proposed research methods, the process capability index ranking of the top three schemes and the ranking of multiattribute decision-making method are the same, and the ranking of the Schemes 4 and 5 is slightly different (two multiattribute decision-making methods), as shown in Tables 3 and 4.

Table 3.

L₁₈ (2¹3⁷) experimental configuration and process capability analysis.

Scheme	Experimental factor level distribution								$C_{pk}$ (ranking)
	A	B	C	D	E	F	G	H
1	1	1	1	1	1	1	1	1	1.29 (8)
2	1	1	2	2	2	2	2	2	1.22 (10)
3	1	1	3	3	3	3	3	3	1.45 (3)
4	1	2	1	1	2	2	3	3	1.49 (2)
5	1	2	2	2	3	3	1	1	1.26 (9)
6	1	2	3	3	1	1	2	2	1.53 (1)
7	1	3	1	2	1	3	3	3	1.21 (11)
8	1	3	2	3	2	1	1	1	1.35 (5)
9	1	3	3	1	3	2	2	2	1.40 (4)
10	2	1	1	3	3	2	1	1	1.10 (14)
11	2	1	2	1	1	3	2	2	1.06 (15)
12	2	1	3	2	2	1	3	3	1.34 (6)
13	2	2	1	2	3	1	2	2	0.92 (17)
14	2	2	2	3	1	2	3	3	1.01 (16)
15	2	2	3	1	2	3	1	1	1.33 (7)
16	2	3	1	3	2	3	2	2	0.89 (18)
17	2	3	2	1	3	1	3	3	1.19 (12)
18	2	3	3	2	1	2	1	1	1.15 (13)

Table 4.

Opinions of 10 experts for multiattribute decision-making analysis.

Scheme	(1) Combination of this parameter level will not cause the average probability (%) of other costs to the company (opinions of 10 experts)	(2) Optimized average probability (%) of the combination of this experimental parameter level (opinions of 10 experts)	(3) Average material cost, labor cost, and machine cost (NT$) to be spent in this experiment (opinions of 10 experts)	(4) Average time to be spent in this experiment (h) (opinions of 10 experts)	(5) Average probability of acceptable process capability in this experiment (%) (opinions of 10 experts)	$Γ_{0 i}$ (ranking)	$C_{i}$ ⁺ (ranking)
Scheme	Relative importance of the 5 evaluation factors: 28% (average opinion of 10 experts)	Relative importance of the 5 evaluation factors: 36% (average opinion of 10 experts)	Relative importance of the 5 evaluation factors: 8% (average opinion of 10 experts)	Relative importance of the 5 evaluation factors: 6% (average opinion of 10 experts)	Relative importance of the 5 evaluation factors: 22% (average opinion of 10 experts)	$Γ_{0 i}$ (ranking)	$C_{i}$ ⁺ (ranking)
1	88	91	500	1.7	52	0.793 (8)	0.716 (9)
2	65	85	500	1.8	42	0.762 (11)	0.683 (13)
3	90	93	470	1.3	96	0.819 (3)	0.753 (3)
4	88	95	435	1.2	97	0.823 (2)	0.762 (2)
5	67	90	550	1.6	48	0.781 (9)	0.726 (7)
6	86	99	460	1.3	98	0.836 (1)	0.798 (1)
7	77	89	520	1.7	42	0.772 (10)	0.691 (12)
8	85	93	500	1.5	95	0.816 (4)	0.742 (5)
9	87	91	510	1.4	93	0.811 (5)	0.752 (4)
10	82	76	580	1.8	28	0.693 (15)	0.629 (17)
11	81	78	590	1.9	26	0.672 (16)	0.619 (18)
12	80	80	510	1.8	88	0.659 (17)	0.739 (6)
13	78	83	590	1.6	36	0.751 (12)	0.667 (14)
14	65	71	595	1.9	36	0.636 (18)	0.659 (15)
15	76	90	560	1.6	89	0.809 (6)	0.722 (8)
16	78	81	580	1.5	32	0.732 (13)	0.649 (16)
17	77	90	550	1.6	43	0.802 (7)	0.711 (10)
18	70	78	565	1.7	30	0.719 (14)	0.701 (11)

The 18 groups of schemes, as shown in Table 3, have been confirmed to obtain $C_{pk}$ values. After identifying the optimal process state, using the proposed research method, the optimal parameter combination of SMT solder paste printing thickness is Scheme 6 of A₁B₂C₃D₃E₁F₁G₂H₂. The confirmation experiment is to verify whether the average value, as predicted by the optimal conditions, is valid, in order to ensure that the optimal factor level combination has been determined. The expected target value of SMT solder paste printing thickness in this study is 80 ± 3 mm. This experiment conducts three confirmation trials (as shown in Table 5) to calculate the expected SN ratio and CI₁ under the optimal conditions: SN/CI₁ (confidence interval) = [37.506 ± 5.7672] = [31.7388, 43.2723].

Table 5.

Response value and SN ratio in confirmation trials.

Experiment number	Observed value in the experiment (mm)				SN ratio
	1	2	3	4
1	81	79	79	80	38.44
2	81	80	81	80	42.89
3	79	81	79	81	36.81

SN: signal-to-noise.

Therefore, the expected SN ratio confidence interval in the confirmation experimental trials is SN/CI₂ = [30.0618, 44.6812]. In the above confirmation experiments, all SN ratios fall in the 95% confidence interval, indicating that the experimental results are successful.

After preliminary analysis and fine-tuning of the final analysis of the process conditions, it is found that SMT solder paste printing thickness and process conditions are correlated to a considerable extent. After standardization of the manufacturing process, it is found that the SMT solder paste printing thickness process capability $C_{pk}$ has been improved from the original 0.59 to 1.53 (as shown in Figure 2). The p-value of the sampling thickness normal test after improvement is 0.388 > 0.05, suggesting that distribution is normal. Hence, it improves the quality stability of the SMT solder paste printing thickness and satisfies customer required accuracy.

Figure 2.

SMT solder paste printing thickness process capability.

Table 3 shows that the ranking of process capability index ( $C_{pk}$ ) is slightly different, as Scheme 1, when ranked with either of the two multiattribute decision-making methods used in this study, meets the practical requirements provided in $C_{pk}$ , as shown in Tables 3 and 4; the SMT production process involves many complex and extensive dependent variables, such as machines, materials, and work environment, rendering it more complex than traditional manufacturing processes; thus, control and improvements of dependent production variables affecting product quality become important subjects in the industry. The solder paste printing thickness process is an important process affecting product assembly quality, which requires the cooperation of many factors, and poor welding arises from the solder paste printing thickness process. Hence, the research findings of this study confirm the selection of steel (A₁) as scraper material, Sn/Ag3.0/Cu0.5 (B₂) as solder paste metal proportion, 10 Nt (C₃) as scraper pressure, 40° (D₃) as scraper angle, 30 r/min (E₁) as scraper speed, 0.6 mm/s (F₁) as mold release speed, 0.6 mm (G₂) as printing spacing/angle, and 6% (H₂) as flux; thus, a better process capability ( $C_{pk}$ ) of 1.53 can be obtained for the solder paste printing thickness process.

Conclusion

This study integrated the Taguchi method and multiattribute decision-making method (gray relational analysis method and TOPSIS evaluating method) in order to determine the optimal experimental level combination for SMT solder paste printing thickness for manufacturing processes. The empirical results suggested that SMT solder paste printing thickness process capability $C_{pk}$ has been improved from the original 0.59 to 1.53 and enhanced product process capability and quality. The experimental cost was lowered and time was shortened to effectively reduce the defect rate, production costs, and product delivery time. The experimental results of this study can provide a reference to the SMT industry for improving the product quality.^{1,2,11,12,16,18,21,24–26}

Footnotes

Declaration of conflicting interests

The author declares that there is no conflict of interest.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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