A Pick-and-Place Process Control Based On the Bootstrapping Method for Quality Enhancement in Surface Mount Technology

Surface Mount Technology (SMT) is a technique in electronic manufacturing to assemble electronic components on the surface of printed circuit boards. The industry has faced new challenges because of the increasing complexity of the assembly process to satisfy requirements such as lightweight, smaller size, and diverse conﬁgurations. With the usage of lead-free solder and the trend toward miniaturization in the electronics industry, the misalignment of solder paste has become more problematic. As the size of components decreases, it becomes more challenging to guarantee accurate placement and alignment during the assembly process. Self-alignment is a physical phenomenon during soldering, where components attached to soldered pads experience movement. Self-alignment can enhance the assembly quality by adjusting component positions near the desired position. However, it can lead to assembly defects, such as poor attachment and tombstoning, as components are shifted away from the pad center, resulting in an unbalanced position. Therefore, understanding and correctly using self-alignment becomes signiﬁcant in modern electronic manufacturing. This research proposes a model that collects data from inspection to estimate the self-alignment strength and ﬁnd a new placement location that can reduce component misalignment and enhance dimensional requirements for PCB assembly, such as side overhang and end overlap.


Introduction
Information and communications technology (ICT) advancement has led to the growth of sophisticated sensors, data collection systems, wireless communication tools, and decentralized computing solutions [1].Integrating physical manufacturing machinery with internet connectivity and large-scale data analysis has led to Industry 4.0 [2].Manufacturers detect bottlenecks in production processes and optimize the processes by analyzing production data collected in real time [3].New-generation information technologies are important in the global manufacturing transformation [4].
The SMT involves three processes: printing, mounting, and soldering.In the printing process, the printer machine puts solder paste onto the pads of the PCB.Next, a mounter picks and places components on pads.Finally, a reflow oven melts solder paste, making attachments between components and pads by forming solder joints.Inspection machines can be used after each process to monitor, prevent assembly failure at an early stage, and check the quality of final products.The fully monitored SMT assembly line includes six sequential operations: printer, Solder Paste Inspection (SPI), mounter, Pre-Automatic Optical Inspection (Pre-AOI), reflow oven, and Post-Automatic Optical Inspection (Post-AOI).SPI detects defects and inconsistencies of printing quality, Pre-AOI identifies misplaced or missing components before soldering, and Post-AOI determines the quality of PCB assembly by checking the solder joint quality and the degree of component misalignment [5].
With the miniaturization trend in electronic products, it becomes more frequent to observe that misalignment in mini-scale components exceeds acceptable tolerances after the reflow process [6].Advanced chip placement methods have been developed to address this issue.There are three commonly used placement methods: Placed-onpad (PP), Adaptive process control (APC), and Place-between-pad-and-paste (PB).Fig 1 shows three placement methods.PP places components directly on the pad center without considering solder paste offset.It is the traditional and prevalent method in the industry [6].APC and PB are advanced techniques that place components away from the pad center by aligning them with the observed solder paste location.APC is a technique to place components onto the solder paste location.It requires the solder paste location information from SPI and updates the mounter CAD file to place components onto the solder paste location.APC improves assembly quality by reducing the occurrence of solder bridging defects in components positioned on solder paste [7].However, since the mounter cannot place chips exactly on solder paste, APC shows a large mean and variance of component misalignment compared to PP [6].Components placed between the pad center and solder paste are located around the pad center after soldering, but those placed farther from the solder paste and the pad center show large misalignment from the pad center.PB is a rule-based strategy developed to reduce the average and variance of final misalignment by considering mounter placement accuracy [6].PB places components at the midpoint between solder paste and pads in the length direction if the solder paste offsets are greater than 20 µm.This rule was developed based on an experiment, which showed a strong selfalignment effect in the length direction compared to the width [8].Since PB places components between the solder paste and pad center, PB results in a smaller average and standard deviation in misalignment compared to APC and PP.APC and PB are advanced methods considering solder paste offset's influence on component movement, but they rely only on SPI data to guide their placement decisions.They do not consider various self-alignment patterns and distributions happening in different environments.Without using data from pre-AOI and post-AOI, APC and PB may not effectively reduce component misalignment or exacerbate the assembly quality where production lines have different self-alignment patterns and distributions.A placement control system, known as the "Mounter Optimizer Module (MOM)," utilizes real-time data from SPI, pre-AOI, and post-AOI inspection machines, as shown in Fig 2 (b).Although it uses data from all inspection machines, the practical application of MOM is restricted due to the need for the Design of Experiments (DOE) for both model training and identifying the optimal placement location.The training process requires a minimum of 2,000 placement data around the pad center, which incorporates various solder paste offsets.To determine a placement for a specific solder paste location, a minimum of 1,000 placement data points with intentional offsets is required, which can reduce assembly quality and lead to defects.The objective of this research is to develop a placement method that can reduce the variability of component misalignment after reflow soldering, minimize component misalignment by leveraging the self-alignment effect in length and width directions, and determine a new placement location using a small amount of placement data without DOE and much placement data for implementation.The proposed model addresses APC's inconsistent and unstable performance in reducing component misalignment by considering mounter accuracy.Collecting real-time data from all inspection machines and considering the self-alignment effect in both length and width direction, the proposed model has more generality than PB, a rule-based approach that assumes that the self-alignment is consistently strong in the length direction, which is not always true.The model uses the bootstrapping method to estimate the self-alignment strength.It then determines a new placement location where components can be placed in length and width direction without using DOE.
This paper is organized as follows: Section 2 reviews related background information and studies; Section 3 shows the Experimental Design, and Section 4 describes the methodologies used in this study.Section 5 includes the outcomes of the proposed model based on the experiment results.Finally, the conclusions and future works are presented in Section 6.

Related Works
In SMT, it is common for the solder paste to be misaligned during the printing process.During the soldering, components placed on the pads experience movement due to the fluid dynamic properties of molten solder paste.This movement is known as self-alignment.Self-alignment is critical in SMT because it can cause defects, such as poor attachment and tombstoning.However, it can also enhance the assembly quality by helping misaligned components to be located near the pad center [9].Therefore, understanding the self-alignment characteristics of small components during the reflow process has become critical for achieving high yield in SMT [8].However, understanding self-alignment characteristics is challenging since no distinct patterns or particular distributions exist, as shown in Fig 4.Even though it is a challenging task, it is a significant physics phenomenon that must be considered to reduce small components' misalignment.
As the SMT passive components become smaller for higher density and miniaturized packaging, self-alignment becomes more crucial in precision micro-object manipulation and chip component assembly, especially in high-density interconnect PCB [10].Researchers have been trying to build physics-based models to better understand the self-alignment mechanism of small passive components during reflow and avoid common manufacturing defects such as nonwetting, tilting, overhanging, and tombstoning [11].Wassink and Verguld developed the first self-alignment model, a simple two-dimensional force model.It focused on a straight-line solder fillet and two forces: gravity and surface tension [12].They used this model to study the tombstone effect.They aimed to understand how torques impact the chip and lead to the tombstone defect.Later, Ellis and Masada created a more complex model that considered additional forces like solder's hydrostatic and capillary pressure.This model also accounted for a curved solder fillet shape, making it closer to reality [13].Creating a numerical model for studying self-alignment is more complex than constructing two-dimensional models for analyzing the tombstoning effect.Mathematical representations often involve complex combinations of algebraic, differential, and integral equations, relying on assumptions and principles.Without electronic computation, processes had to be significantly simplified for analytical assessment of their mathematical models [14].
Over the past three decades, computers have facilitated the analysis of various real-world engineering challenges through suitable mathematical models and numerical methods.Two models are used in numerical simulations to predict component movement: one based on pressure continuity and the other on energy minimization principles.In [15], FEM, a numerical method used in energy minimization to solve complex problems, was applied to study the self-alignment of 0805 and 0603 size components.The model used the bezier curve function to define the solder joint shape and only considered surface tension force for simulation.However, this approach could only show movement in the lateral direction.In [16], an advanced model that considers different forces, including hydrostatic and capillary pressure, gravity, dynamic friction, and surface tension, was developed.The model simulated how the components moved in length and width directions.Other simulation models, such as Surface Evolver (SE) and ANSYS, were applied to investigate the self-alignment effect.SE was implemented to study the degree of restoring force of the component [17], and ANSYS was used to investigate the self-alignment effect of lead-free solder during the reflow phase on board [18].Models built based on FEM, SE, and ANSYS simulate the component movement based on the energy minimum principle.A surface tension model using the Continuum Surface Force (CSF) was introduced [19].Without determining the final solder fillet shape, the model simulated the component movement using Computational Fluid Dynamics (CFD), which analyzes fluid flow and interactions within a system.
While many studies have explored the theoretical aspects of component movements during soldering, there remains a need for clear justification to tackle the practical challenges of self-alignment in real-world scenarios [9].Due to the complexity and variability of manufacturing processes, data-driven methods are employed to study self-alignment.In [20], an artificial neural network (ANN) was utilized to predict the self-alignment of 0603-size chip resistors soldered using infrared or vapor phase soldering.Components were intentionally displaced from 0 to 800 µm in width and 0 to 300 µm in length.ANNs were used to predict component self-alignment with an average error of approximately 10-20%.In [21], ANN with Bayesian regularization was trained on 1173 data samples to predict component positions, achieving an accuracy of 10-30% mean absolute error.In [9], experiments involved assembling six types of passive chip components in various size categories.A Random Forest Regressor (RFR) was used with 48 factors to predict the final component positions, resulting in average prediction errors of 13.47 µm, 12.02 µm, and 1.52 • .
Under the miniaturization trend, understanding electronic component selfalignment characteristics becomes critical for surface-mount assembly yield.As passive components' size gets smaller, quality rejects due to overhangs after the reflow appear more frequently.This is because the dimensional pass-fail criterion is set based on the amount of component misalignment regarding the size of the component and pad [8].APC is a method of placement control that collects solder location data from SPI and transmits this data to the mounters.The mounters utilize this information to update the placement program, ensuring that components are precisely positioned onto the solder deposits rather than the substrate pads.This strategy leverages the self-alignment principle to enhance production yields and reduce defects.In [7], APC improves the assembly quality by decreasing the number of solder bridging defects.However, APC shows inconsistent and unstable results in terms of component misalignment [6].Components placed between the solder paste and pad center tend to have smaller misalignment, but those placed farther from the solder paste location and the pad center have larger offset after soldering.Thus, APC shows a larger mean and variance of component misalignment than PP.In PB, a component should be placed at the midpoint between solder paste and pads in the length direction when solder paste offsets are greater than 20 µm.Due to the mounter placement accuracy, the actual component positions could be close to the pastes or the pad center if not placed at the midpoints, and the post-reflow offsets are relatively small in either situation [6].This rule-based strategy is easy to implement but cannot guarantee to find the optimal placement positions.A comprehensive framework with real-time communication between the inspection machines and the mounter is needed to identify the optimal placement option for every component.In the MOM framework, multiple placing options can be identified firstly based on the SPI machine's real-time solder paste offset information.Then, after accurately estimating the post-reflow results for each placing option with a hybrid ML model trained with historical SPI, pre-AOI, and post-AOI data, the optimal placing option will be decided by multi-step evaluation and its evaluation metrics.The model is trained with randomly selected 2,000 placement data points where components are positioned near the pad center, including different solder paste offsets caused by various printer settings.Experimental results show the effectiveness of the proposed MOM framework compared to other placement methods.The average misalignment of components placed by MOM decreased by 15% and 25% compared to the counterparts in PP for the length and width direction separately [5].

Experimental Design
The experiment is conducted in an on-site Smart Electronics Manufacturing (SEM) Laboratory production line.The line starts with an MPM Momentum printer and a Koh Young aSpire 3 Solder Paste Inspection (SPI) machine, followed by a Fuji mounter and a Koh Young Zenith pre-reflow Automatic Optical Inspection (AOI) machine.Lastly, a Heller convection reflow oven and a Koh Young Zenith post-reflow AOI machine are set in the line.Historical data on stencil printing and component offset were gathered and used in a controlled experiment to test a proposed statistical-based mounter placement control system in the SPP and P&P processes.Since passive components are widely used in electronics manufacturing, the statistical-based placement control framework focuses on the small resistor type, R0402 (400 µm × 200 µm).In this study, a total of 12 boards and 4,500 0402 resistors were utilized.We used six boards to investigate the self-alignment effect, employing 2,250 components, while the remaining six boards were used to test the model's performance.Table 1 shows three printer settings used in this experiment.A total of 12 single-sided FR-4 (woven glass and epoxy) and Hot Air Solder Leveling (HASL) PCBs were utilized in the experiment.PCB size is 160 mm × 130 mm.Board information is in Table 3.This experiment uses an Indium 8.9HF Pb-Free SAC305 solder paste and a 7-zone Heller 1707MKV-E convection reflow oven with nitrogen as the reflow atmosphere.The conveyor speed is set as 35 cm/min.The reflow recipe temperatures of the seven heating zones and one cooling zone are represented in Table 4.

Methodologies
The proposed method collects data from all inspection devices to determine new component placement locations.For each printed board, the model assesses the solder paste conditions.Initially, it inspects the solder paste volume and selects those between 70% and 130%, representing good conditions according to SPI machine standards.Next, it uses interquartile range (IQR) to remove outliers that have excessive solder paste volume and offset differences.After removing outliers, the model finds potential placement options while considering printer and mounter accuracy.It further estimates the self-alignment degree by analyzing data from pre-AOI and post-AOI, calculating component displacement during the reflow process, and constructing a confidence interval.The model applies its expectation function, using the estimated self-alignment degree to predict assembly quality values for potential placement points.It evaluates the expected assembly quality for each placement location and chooses one with the highest percentage of the optimal assembly quality.Side Overhang (SO) measures component misalignment in the width direction, while End Overlap (EO) assesses misalignment in the length direction relative to component and pad dimensions

Evaluation Metrics
The proposed model makes placement decisions by gathering and analyzing inspection data from SPI, Pre-AOI, and Post-AOI.It calculates self-alignment using placement data from pre-AOI and post-AOI, employing bootstrapping methods to estimate confidence intervals.These intervals enable the model to predict expected assembly quality.It utilizes SO to find a new placement location in the width direction and EO to find a new placement location in the length direction.

Degree of Self-Alignment
Self-alignment represents the displacement happening during the reflow process.Positive self-alignment indicates that the solder paste pushes the component toward the pad center during the reflow process.Negative self-alignment makes components move

Assembly Quality Measurement
Following the IPC standard for Class 3 products, SO should not exceed 25%, and EO should be at least 25% after soldering.SO and EO are illustrated in Fig 8 .SO represents the percentage of P OST W to COM P W , and 0% indicates perfect alignment in the width direction.A positive SO refers to a positive component placement offset, and a negative SO refers to a negative component placement offset in the width direction.For example, a 10 µm offset in width direction results in a 5% SO, while a -10 µm offset leads to a -5% SO.EO indicates the percentage of P OST L concerning P AD L , P BT W , and COM P L .COM P L denotes the component's length dimension, and P BT W represents the distance between two pads.The board's pad distance is 160 µm, COM P L is 400 µm, and P AD L is 220 µm.Given this design, the ideal EO is about 55%, reflecting perfect alignment in the length direction.Components with positive misalignment will have higher EO values, whereas those with negative misalignment will show lower EO values.For instance, a component with a 10 µm misalignment in the length direction will have a 60% EO, while a component with a -10 µm misalignment will have a 50% EO.The proposed model concentrates on finding a placement location that brings more components' SO 0% and EO 55%.

Evaluating Non-Parametric Methods: A Comparative Analysis
The proposed model uses the estimated self-alignment degree to determine a new placement location.It employs bootstrapping to create a confidence interval.Jackknife, originally used to estimate estimator bias and variance, has wider applications, including constructing confidence intervals [23].The bootstrap method, another common resampling technique, approximates the sampling distribution for a parameter by repeatedly sampling the original data with replacement [24].Bootstrapping methods include percentile, bootstrap-t, and BCa, which require no predefined parameters.The smoothed bootstrap, on the other hand, relies on a defined kernel or smoothing function to estimate the distribution and draws samples from a density estimate based on the data itself [25].
Given the unknown and varied shapes of the self-alignment distribution, nonparametric methods that do not require hyper-parameter tuning, such as choosing a kernel function, were compared.In this study, we select the bootstrapping method capable of constructing precise confidence intervals even with small placement data.

Expectation Function
The proposed model aims to identify a different placing location for a given solder paste offset region by collecting information.It gathers 50 data points, calculates the self-alignment, and generates a confidence interval to estimate the median of the selfalignment degree using the bootstrapping technique.Once the confidence interval is established, the model uses its expectation function and upper and lower limits to The model assumes that the mounter placement follows a normal distribution to determine the expected value of EO using the upper and lower boundaries of the confidence interval.The Fuji mounter NXT III, which has an accuracy level of 25 µm with a 3 σ level, was used in this study.We assume the placement follows a normal distribution with a mean of 0 and a standard deviation of 8, N (0, 8).Fig 12 (c) and (d) show the distribution of mounter placement offsets for the length and width directions, respectively.Shapiro-Wilk test is conducted, and the p-value for both distributions is greater than 0.05, which shows that the placement offset distribution follows the normal distribution.

Expectation Function of Side Overhang
In Equations 1 and 2, to calculate the self-alignment, the placement offset measured after the reflow process is subtracted from the placement offset measured before the reflow process.Using both the lower and upper bounds of the self-alignment confidence interval, we can calculate the final position of the component.For instance, if the lower bound of the confidence interval is -10µm, implying negative self-alignment, we would subtract -10µm from the placement distribution.This shift would recenter

Expectation Function of End Overlap
To calculate the expected value of EO, we assume that the mounter placement follows a normal distribution.Therefore, we can determine the final position of the component by subtracting the placement offset in pre-AOI and the self-alignment effect.
After accounting for the shift, we estimate the EO distribution using Equation 4, based on Equation 6.The variables used in these equations include COM P L (component length), P BT W (distance between two pads), P AD L (pad length), and M N T L (mounter setting in the length direction), which represents one of the possible placement options shown in Calculate expected value of SO for each mnt w using SA W,LB , SA W,U B .
• N SO,LB (mnt w , SA W,LB ) = N ( Calculate the area between -5 and 5 N SO (mnt w , SA W ) • P SO,LB = −5 ≤ N SO,LB (mnt w , SA W,LB ) ≤ 5 4: Choose mnt w that has the highest PSO .

Experimental Results
Self-alignment is critical in SMT because it can cause defects such as overhanging and tombstoning by moving components away from the pad center.Conversely, it Algorithm 2 Update mounter placement setting in length direction Require: • Printer setting in length: P RT L • Printer and mounter accuracy: P RT ACC , M N T ACC • Standard deviation of mounter accuracy: M N T ST D • Component and pad length dimension: COM P L , P AD L • Distance between pads: P BT W • Lower and upper bounds of self-alignment in length: SA L,LB , SA L,U B Ensure: A new placement setting in length Find possible placement options in length (M N T L ) Calculate expected value of EO for each mnt l using SA L,LB , SA L,U B .
• N EO,LB (mnt l , SA L,LB ) = N ( , M N T ST D P AD L ) Calculate the area between 50 and 60 N EO (mnt l , SA L ) 4: Choose mnt l that has the highest PEO can improve assembly quality by making components self-assemble perfectly on or near the desired position [9].The trend toward miniaturization in electronics requires tighter placement control to meet SMT connection criteria.As passive component sizes become smaller, overhang rejects after reflow occur more frequently.The pass-fail criterion is based on the offset between the component and pad dimensions.
In SMT, the printer does not always put solder paste in the pad center, as shown in Fig 3 (a).Solder paste misalignment causes small passive components more significant misalignment after soldering.Fig 3 (c) and (d) show solder paste offset based on different printer settings.It shows that when the printer setting is around the pad center, component misalignments after soldering are close to the pad center.However, when the printer setting is out of the pad center, components are more likely to be shifted away from the pad center.Self-alignment is calculated using Equation 1 and Equation 2 by subtracting the placement offset observed from pre-AOI and post-AOI.The proposed framework optimizes placement settings using self-alignment characteristics.The model will implement different placing strategies for each direction depending on self-alignment characteristics.It updates the mounter setting closer to the solder paste for positive self-alignment and in the opposite direction for negative self-alignment.The new placement setting is found based on the printing and mounting accuracy of equipment to find a new placement setting for the solder paste offset around the printer setting.5 shows the results of SO and EO for each method under different printer settings.We measured 200 components for each method and calculated SO and EO.
As shown in Table 5, MOM performs better in both SO and EO in both printer settings.For printer setting (60 µm, 60 µm), MOM shows 4% and 3% improvement in   Previously, the proposed model finds new placement settings for the given printer settings within the pad center and the printer settings.In the lab experiment, components have positive self-alignment in width and negative self-alignment in length direction.In other words, solder paste pushes components in width and pulls them in length direction.To reduce the final misalignment, the model updates the mounter setting towards the solder paste in the width direction by the estimated self-alignment degree.Therefore, the model can help components to have better attachment with the solder paste by making them touch the solder paste more and be placed around the pad center in the width and length direction after soldering.
We tested our model using the DOE dataset from [5] to see how the model performs under different environments.The dataset shows strong negative self-alignment in the length and width direction as shown in Fig 15.Due to the dominant negative selfalignment in length and width, we tested our model by releasing the model restrictions.The model tries to find a placement location within ± 25 µm.We restricted our placement settings since we can make all placement within SO(25%), which is the minimum dimensional requirement for the given mounter accuracy 25 µm.For the given solder paste offset, the model updates mounter settings where it expects to have the highest SO[-5%, 5%] and EO[50%, 60%].
Fig 17 shows a new placement setting for the given printer setting.Table 6 shows the proposed model performance in SO and EO.The table shows the proposed model shows better performance in SO compared to PP.The proposed model does not show significant improvement in EO compared to PP.For printer settings (30 µm, 0 µm), the proposed MOM shows 9% improvement for EO[50%, 60%].For printer settings (30 µm, -30 µm), the proposed MOM shows 12% improvement for EO[50%, 60%].

Conclusion and Future Work
The electronics manufacturing industry faces increasing challenges that complicate materials selection and assembly processes.The demand for modern electronic products with features such as lighter weight, smaller size, higher quality, and high pin count is growing [26].SMT has undergone miniaturization and cost reduction efforts, especially for higher-density packaging [27].
In SMT, it is common for the placement of solder paste to not align correctly with the existing SMT.As shown in Fig 3 (a), a panel comprising three boards displays different distributions of solder paste offset.With the ongoing trend of miniaturization in electronics and the increased use of lead-free solder, such misalignment of solder paste can cause component misalignment, particularly in smaller cases.During the reflow process in SMT, the attached components on the soldered pads may experience movement, which is called self-alignment.
Self-alignment is an important factor in SMT, as it can improve or degrade the assembly quality.Components moving away from the pad center can lead to defects such as tombstoning or overhanging, while self-alignment can result in perfectly selfassembled components.As the size of passive components decreases, the frequency of quality rejects due to overhangs after reflow increases, making it crucial to understand self-alignment characteristics.However, self-alignment is a complex phenomenon that does not follow a specific distribution.While it may be challenging to define the selfalignment distribution, it is important to consider it to minimize the final misalignment of small components.
The study introduces a new placement method that addresses the limitations of advanced placement methods.APC improves assembly quality by placing components closer to the solder paste, but this method is sensitive to the actual placement positions, resulting in inconsistent results.The proposed model addresses the sensitivity to the placement location of APC by considering both mounter placement accuracy and the solder paste offset region.The experiment results in [6] demonstrate that PB decreases the average and standard deviation of component misalignment, but its effectiveness can be limited in cases where self-alignment in the width direction is stronger than in the length direction.In contrast, the proposed model estimates the self-alignment degree in both directions and has greater generality than PB.Furthermore, unlike the AI-based MOM in [5], which requires a large amount of DOE data for training and finding the optimal placement location, the proposed method uses a bootstrapping method to estimate self-alignment degree with a small sample size and aims to improve assembly quality cost-effectively using data from all inspection machines.
The current placement control system is limited in several ways.It currently identifies new placement locations for optimal solder paste conditions within the range of 70% to 130%.Future improvements should focus on expanding this range to 50% -70% and 130% -150%, as well as enhancing the model's comprehension of self-alignment behaviors for varying solder paste volumes.While the proposed model is cost-effective for panel-level production, there may be more optimal solutions for each component in board-level production.PB and AI-based MOM are more appropriate for providing an optimal placement location for board-level production.The proposed method is that it needs to consider cases where negative self-alignment is strong, which could limit opportunities for improving product reliability.In cases where component misalignment is reduced, the product's fatigue life can be increased [28].Therefore, the current model may lose an opportunity to increase product reliability in strong negative self-alignment cases.While the proposed method effectively enhances assembly quality, there may be better placement locations than the placement location generated.Thus, it is necessary to transition to an intelligent control system that can achieve side overhang close to 0% and end overlap close to 55%.Gathering diverse placement data for a given solder offset region is essential to leverage machine learning to find an optimal placement location.However, placing components without considering the self-alignment effect can harm the product.In the future, instead of randomly placing components to collect data, the proposed model will be an initial step as a data collection technique.According to experimental findings, the proposed model was able to gather alternative placement data for a given solder offset region beyond placing components at the pad center.Consequently, using the current model as a data collection approach, the goal is to introduce an AI-based placement control system that is economical and risk-free.
Fig 3 (a) shows three boards with uneven solder paste offset distributions, where the solder paste of the second board is around the pad center, while the first and third boards show misalignment.Under the miniaturization trend, solder paste misalignment can significantly influence component misalignment, especially in small-scale components.In Fig 3 (b), components placed on larger solder paste offsets have larger misalignment after soldering.

Fig. 3
Fig. 3 (a) Solder paste offset distributions in panel production.(b) Component misalignment for different printer settings.Blue: solder paste location.Orange: component position before soldering.Red: Component position after soldering.

Fig. 4
Fig. 4 An illustration of various shapes of self-alignment distributions in length and width.
. The flowchart is shown in Fig 5 and schematic diagram is shown in Fig 6

Fig. 5
Fig. 5 An illustration of the flowchart of the proposed model.

Fig. 6
Fig. 6 An illustration of the schematic diagram of the proposed model.(a) Collect data from inspection machines.(b) Calculate the self-alignment.(c) Estimate the median of the self-alignment degree using BCa.(d) Evaluate each placement location using expectation functions to find the best placement location in length and width.(e) Update the mounter placement location based on the proposed statistical-based MOM.

Fig. 7 Fig. 8
Fig. 7 (a) Negative self-alignment.A component is moving toward the solder paste.(b) Positive self-alignment.A component is moving toward the pad center.

Fig 9 (
a) and Fig 10 (a) show the most positively and negatively skewed self-alignment distributions from our lab experiment results and doe data in [5].Fig 9 shows the coverage rate of non-parametric methods for positively skewed self-alignment distribution.BCa shows the best performance in covering the true median of the sample.Fig 10 shows the coverage rate of non-parametric methods for negatively skewed selfalignment distribution.BCa shows the best performance in covering the true median of the sample for both positively and negatively skewed self-alignment distribution.Fig 11 shows that after collecting 50 placement data, the confidence interval width becomes less than or equal 10 µm.Since BCa can reach the coverage rate of 100% for both positive and negative cases with confidence interval width 10 µm, the proposed model collects 50 data points and implements BCa to construct the confidence interval to estimate the median of the self-alignment degree.

Fig. 12
Fig. 12 An illustration of mounter placement options for the given mounter and printer accuracy & mounter placement distribution in length and width.(a) An illustration of mounter and printer accuracy.(b) An illustration of placement options in length and width.(c) Placement distribution in length direction.(d) Placement distribution in a width direction.

Fig. 13
Fig. 13 An illustration of expectation function of width direction.(a) A new placement setting in the width direction.(b) Expected chip offset after soldering using lower and upper bounds of the confidence interval.(c) Expected side overhang(%) using lower and upper bounds of the confidence interval.

Fig. 14 Algorithm 1 • 1 :
Fig. 14 An illustration of expectation function of length direction.(a) A placement setting in the length direction.(b) Expected placement offset after soldering using lower and upper bounds of the confidence interval.(c) Expected end overlap(%) using lower and upper bounds of the confidence interval.
The proposed model finds a new placement location by estimating the strength of the self-alignment.To enhance the assembly quality by decreasing the final component misalignment after soldering, it is important to understand the characteristics of selfalignment.Fig15 (a)  and (b) show the length and width self-alignment distributions of the DOE dataset in[8].Components tend to move toward the solder paste during the reflow process.However, the strength of the component movement is greater for the DOE dataset.Fig15 (c) and (d)show the length and width self-alignment distribution of our lab experiment.In the DOE dataset, components move toward the solder paste, while components move toward the pad center in the lab experiment.We test our proposed model to check if it can find a new placement location using its expectation function under two different environments.

Fig. 15
Fig. 15 Self-alignment distribution of the DOE dataset [5] and lab experiment.(a) Length in DOE dataset.(b) Width in DOE dataset.(c) Length in the lab experiment.(d) Width in the lab experiment.

Table 1
Printer settings and range of solder paste offset for each setting.nano-coatingstainlesssteel stencil guarantees that the solder paste offsets on each PCB are identical.The stencil thickness is 76.2 µm, and the frame is 29×29 inch.Stencil aperture information is in Table2. A

Table 2
Size information of the stencil's aperture.

Table 3
Size information of the board.

Table 4
The temperature setting for each zone in the reflow oven.

Table 5
The SO and EO results of PP and the proposed model based on the lab experiment dataset.

Table 6
The SO and EO results of PP and the proposed model based on DOE data.