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Proceedings of the 2023 Winter Simulation Conference
C. G. Corlu, S. R. Hunter, H. Lam, B. S. Onggo, J. Shortle, and B. Biller, eds.
MODELING MULTIVARIATE RELATIONS IN MULTIBLOCK SEMICONDUCTOR
MANUFACTURING DATA USING PROCESS PLS TO ENHANCE PROCESS
UNDERSTANDING
Geert van Kollenburg
Richard Verhoeven
Mike Holenderski
Nirvana Meratnia
Eindhoven University of Technology
Groene Loper 3
Eindhoven, 5612AE, NETHERLANDS
Daniele Pagano
STMicroelectronics s.r.l.
Stradale Primo Sole, 50
Catania, 95121, ITALY
ABSTRACT
The complexity of manufacturing process data has made it more challenging to extract useful insights. Data-
analytic solutions have therefore become essential for analyzing and optimizing manufacturing processes.
Path modeling, also known as structural equation modeling, is a statistical approach that can provide
new insights into complex multivariate relationships between process variables from different stages of
the manufacturing process. The incorporation of expert process knowledge and subsequent interpretation
of model results can facilitate communication between stakeholders, promoting lean manufacturing and
achieving the sustainability goals of Industry 5.0. This paper describes the use of a path modeling algorithm
called Process Partial Least Squares (Process PLS) to gain new insights into the relationships between
equipment data from several machines within the semiconductor manufacturing process. The methods
used in this study can assist manufacturers in understanding the relations between different machines and
identify the most influential variables that may be used to develop soft-sensors.
1 INTRODUCTION
The semiconductor industry plays a vital role in modern society, with increasing demand for smaller and
more powerful computer chips and electronic devices. Computer chips are made in hundreds at a time on
silicon wafers. The manufacturing process involves multiple stages, including wafer fabrication, deposition,
lithography, and etching (Timings 2021). Each stage involves multiple process steps and each step may be
dependent on the performance of the previous steps. Variations in any of the hundreds of steps can affect
the final product performance, yield, and reliability (Melhem et al. 2015). The complexity and dependency
of the manufacturing processes, together with the abundance of process data has resulted in an increasing
demand for data analytic solutions to analyze and optimize these processes.
Statistical models and machine learning algorithms can provide valuable insights into the manufacturing
processes. Yet most data-analytic applications do not model the relationships between the many process
steps, but instead focus on predicting specific outcomes like product quality or yield (Biegel et al. 2022;
Sanchez-Marquez and Vivas 2020; Dupret et al. 2005) in order to control the manufacturing processes.
Path modeling, also known as structural equation modeling (SEM), is a valuable approach that can identify
multivariate relationships between process variables from various steps of the manufacturing process (van
Kollenburg et al. 2020; Hair Jr et al. 2021).
Path modeling enables the identification of key factors that contribute to the overall variability of the
manufacturing processes. By incorporating all relevant variables and dependencies between manufacturing
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
steps, path models can reveal new insights into the complex relationships between process variables and
their impact on the manufacturing process (Vinzi et al. 2010). Path modeling can assist manufacturers in
identifying the root causes of process variations, implementing corrective actions, and identifying areas
for improvement. Real-time process optimization will become possible when models identify strong
relationships between specific process variables and a defect-causing situation later in the process (Arteaga
and Ferrer 2002).
Path modeling is particularly useful in process analytics as they allow for the incorporation of expert
process knowledge in an intuitive manner. This facilitates communication between data-analysts and
manufacturing operators and such explainability is critical if models are to be integrated into personnel’s
routine work (Meindl et al. 2021; Cagliano et al. 2019). The inclusion of knowledge of process experts and
subsequent interpretation of model results provides a unique opportunity to promote lean manufacturing
(Tortorella et al. 2019). Collaboration between humans and data-analytic solutions is a core aspect of the
sustainability goals specified for Industry 5.0 (Breque et al. 2021). Investing in a working environment,
where workers can interact with data-analytics in an intuitive way can lead to increased value creation in
manufacturing processes (Cifone et al. 2021; Senoner et al. 2022).
The aim of the work presented in this paper was to learn more about the complex connections between
distinct steps in the semiconductor manufacturing process. This paper explains the process of obtaining
features from the equipment data, analyzing the data with a path modeling method called Process PLS
(van Kollenburg et al. 2021), and evaluating different model configurations to understand the relationships
between machines. The research is presented in a way that allows the methods to be applied to other
manufacturing processes, which is why the term ’machine’ will be used throughout to describe parts of
the processes otherwise called ’tools’ or ’chambers’ and so forth.
The remainder of this paper is organized as follows. The next section discusses related work. In
Section 3 the data that was used will be explained. That Section also includes an overview of the Process
PLS algorithm and illustrates multiple model specifications. Section 4 presents the results of the analyses
using the model specifications discussed. The paper ends with a discussion and future outlook in Section 5.
2 RELATED WORK
Data-analytic applications are common in manufacturing industry (Moldovan et al. 2017). While many
applications focus on quality predictions (Köksal et al. 2011, provide an overview), statistical process
control has also been standard practice for a long time (Spanos 1992). Path models on the other hand
have mostly been used to analyze company-level indicators. Examples include analysis of environmental
practice and manufacturing performance (Tseng et al. 2008), sustainable manufacturing practices (Vinodh
and Joy 2012), front-end product design (Withanage et al. 2012), corporate governance mechanisms (Fei
et al. 2015) and marketing strategies (Sarstedt et al. 2022). To the best of our knowledge, path models
have not yet been applied to evaluate the interrelations between various part of the manufacturing process
itself.
Path models have recently been used to analyze industrial chemical production processes (van Kollenburg
et al. 2020; Offermans et al. 2021), leading to new insights into relations between process variables that
led to reduced production costs. Sensors in industrial processes provide time series. In process industry,
sensors may measure different bits of material at each point in time as the materials flows through the
machines. If properly aligned, each data point of a sensor can be related to all other data points related to
the same bit of material (Offermans et al. 2021). As such, the data is well-suited for use in correlational
methods like path models.
In semiconductor manufacturing processes, products reside at each machine for some time. This means
that many sensors each produce a time series variable per wafer. Multivariate time series can be analyzed
with statistical models like ARIMA (Hamilton 2020), upcoming data points can be predicted with deep
learning models like LSTM (Hochreiter and Schmidhuber 1997) and anomaly detection can be done with
ensemble methods (Trardi et al. 2022). These methods, however, neither consider the multiple-machine
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
nature of the manufacturing process to model the interrelations between the various sub-processes, nor
predict specific features in other time series.
To the best of our knowledge, no path modelling extensions for multi-block time series have yet been
developed to accommodate multiple target blocks (Gu and Van Deun 2019). To make use of existing path
models, the time series variables must be transformed in such a way that correlations between sets of data
become meaningful.
3 MATERIALS AND METHODS
3.1 Data
Historical equipment data from seven machines within a semiconductor manufacturing process was provided
by STMicroelectronics s.r.l. The seven machines will be referred to as Machine 1 through 7, in the order
that wafers pass through them. The data consisted of readings from 151 sensors which are distributed over
the seven machines, providing information on the production of over 2000 wafers, which all followed the
same production recipe. While details about the manufacturing steps cannot be disclosed, the goal of the
research was to relate specific observations at one machine to observations at other machines. For instance,
identifying whether an extreme value in Variable Aof Machine 1 is related to high variability of Variable B
on Machine 3.
As a pre-processing step, features of the time series variables were extracted before further analysis.
From each variable, the average value (avg), minimum value (min), maximum value (max) and the standard
deviation (std) were extracted. This means that each of the 151 time series was transformed into 4 features,
with each feature having a single value per wafer. This transformation is illustrated in Tables 1 and 2. The
data was labeled in the format M_V_feature, where Mindicates the machine at which the measurement
was done ranging from M1 to M7,Vindicates the sensor number, ranging from V1 to V151 and feature
is the label for either the avg,min,max, or std.
Table 1: Illustration of the original time series that was used to create the data set used in further analyses.
Labels are given in format Machine_Variable. Each of the 151 sensors produced a variable and each wafer
thus had observations on these 151 variables. Data is shown for the first and last wafer.
Wafer 1 .Wafer 2186
M1_V1 .M7_V151 .M1_V1 .M7_V151
.774 ..499 ..746 ..166
.519 ..753 ..64 ..818
.283 ..041 ..069 ..31
.786 ..19 ..038 ..767
.294 ..196 ..092 ..05
. . . . . . .
. . . . . . .
. . . . . . .
.315 ..973 ..821 ..538
.619 ..239 ..981 ..193
.137 ..583 ..859 ..376
.324 . . .327 .
.149 . . .733
.522 . .
The columns in Table 1 represent sensor readings observed for each wafer. Each row in that Table
indicates a time point during which the wafer was in the respective Machine. Also illustrated is the fact
that not all time series were of equal length. In Table 2 each column represents a feature from the time
series and each row represents the observed value of that feature for a given wafer. The boxed number is
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
the minimum value observed in Variable 151 for Wafer 1. The encircled number indicates the maximum
value observed in Variable 1 for Wafer 2186. Each feature (min, max, avg, std) was named according to
the machine and the variable they originated from in the format ’Machine_variable_feature’. For example,
the feature M1_V1_max lists for each wafer the maximum value observed in the time series M1_V1 that
was collected at Machine 1. In the remainder of this paper, the term ’features’ will refer to the data used
in the statistical analyses, as represented in Table 2.
Table 2: Features extracted from the time series that were used in statistical analyses.
M1_V1_max M1_V1_min .M7_V151_min M7_V151_avg} M7_V151_std
Wafer 1 .786 .137 ..041 .434 .322
. . . . . . .
. . . . . . .
. . . . . . .
Wafer 2186 .981 .038 ..05 .402 .282
We excluded features that had more than 15% missing values or that had (near-)zero variance. Near-zero
variance may be related to both rare events and to uninformative data, but for the analyses presented below,
such features cannot be used. Then, we removed 26 wafers that had missing data for any of the remaining
features. To prepare the data for analysis, we standardized all features to have a mean of zero and a variance
of one. The resulting data set consisted of 562 features describing the 151 time series during the production
of 2186 wafers. This data set was used for subsequent analyses. The analyzed data and code to reproduce
the results presented below may be provided to the interested reader upon reasonable request.
3.2 Process PLS
Partial least squares (PLS), also known as Projection to Latent Structures (Wold 1982), is a family of
multivariate regression techniques used to evaluate the relationships between two or more blocks of data. PLS
models can handle large number of correlated predictor variables. A high correlation between predictors
is called collinearity and is problematic for most traditional regression techniques because it leads to
rank-deficiencies in covariance matrices.
Standard PLS regression only models the relation between two blocks of data. This could be used to
predict the data of, say, Machine 4 from the data of Machine 3 (See Figure 1a). Merging multiple blocks
into one larger block makes it possible to predict, for example, data of Machine 5 from all the data observed
in the machines preceding it (i.e. Machines 1, 2, 3, and 4 as shown in Figure 1b), but this approach does
not model the contributions of individual machines. There are also multi-block PLS extensions that can
handle multiple predictor blocks (Figure 1c), where the relation between each pair of blocks is evaluated
separately. The reader is referred to other literature for a discussion on the standard approach for the
multiple-predictor models (Biancolillo and Næs 2019).
To study the relationships between the machines, information from one machine should be utilized to
predict data from another machine, while itself being predicted by other machines. In essence, any block
of data can simultaneously act as both a predictor and a target, with several targets existing within the
model. We employ a versatile path model algorithm called Process PLS (van Kollenburg et al. 2021), which
provided information on the relations between the data from the various machines in the manufacturing
process.
Like other SEM models, a Process PLS model consists of an outer and inner model. The outer model
partitions the data into blocks. In the current context, this means that features are grouped according to
their respective machines. In Figure 2, the outer model specification is represented by the blue components
of the model and the machines as red rectangles. The inner model, represented as the green arrows in
Figure 2, is used to specify which connection between machines to include. For the remainder of this
paper, all following figures will only present the inner model.
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
Temp.max Power.avg Chem.std Feed.min Pres.min Temp.avg
Machine 1 Machine 2
Feed.avg
a)
M1 M2 M3 M4 M5
𝐽1+ ⋯+ 𝐽4𝐽5
b)
M1
M2
M3
M4
𝐽4
𝐽1
𝐽2
𝐽3
c)
Figure 1: Examples of PLS model specifications with a single target block. The model a) uses data from
one machine to predict the data from another machine. Sub-figure b) illustrates forming a single predictor
block. Sub-figure c) shows a multi-block specification. Jmindicates the number of columns in the data of
block m. Standard PLS regression can only be used to analyse models a) and b).
The Process PLS algorithm has two main steps to find optimal predictions of all target blocks. First
the outer model is estimated by constructing lower-dimensional latent variables from the features in each
block, based on their relationships with features of target blocks. The proportion of variance in the features
of block mthat is contained in the lower-dimensional representation of that block is indicated by R2
m. In
single-target models, these R2values are equivalent to the R2values obtained in standard PLS regression
(see Figure 1a). While often called ’explained variance’, R2in PLS is better interpreted as the proportion of
variance extracted from the data to ensure optimal prediction. In the current application, the data consists
of manually extracted features. It can be expected that several features will not be informative. If much
data is redundant, interpreting absolute R2values, being a proportion of all variance in a block, should be
avoided. To ensure interpretability, Process PLS has a second step.
In the second step of Process PLS, one PLS regression model is estimated for each target block. All
blocks that predict a particular target block are used as predictors in the model. The primary result of this
step is the explained variance P2(Rho-squared). For a given block m, the explained variance is calculated
as the sum of all (partial) explained variances of every predictor block n, where nrepresents the predictors
of m. In other words,
P2
m=
n
∑P2
m.n
represents how much of the total variance in the lower-dimensional representation of the target block mcan
be predicted by (latent variables of) other blocks. Conceptually, P2
m.n, as a partial explained variance, can
be compared to the square of a regression coefficient. For instance, a P2
m.nvalue of .5 implies a regression
effect of block non mequivalent to √.5=.71. While this analogy is strictly conceptual in case of multiple
latent variables per block, it may offer readers anintuitive grasp of the meaning of the model results. Please
refer to the foundational paper of Process PLS for details (van Kollenburg et al. 2021).
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
V1.std V2.max V8.min
V9.std
V10.min
V14.avg
V15.max
V15.min
V25.min
V26.std V27.avg V39.std V40.max V41.max V77.min
V78.std
V78.avg
V90.max
V91.std
V92.max
V121.min
...
... ...
... ...
...
...
M2
M1
M7
M3 M6
M4 M5
Figure 2: Example of a Process PLS model. Data from each machine is used to predict the following
machine and each machine is used to predict data from the last machine. The outer model is represented
in blue, the machine representations are in red, and the green arrows represent the inner model.
Explaining a small yet interesting portion of the data could be more valuable than explaining a large
portion of redundant data. As a result, P2values serve as more robust indicators of the strength of
relationships between the blocks compared to R2values. Suppose the R2value of block mis R2
m=.2. Next
to limited relation with other data, factors such as collinearity or the presence of uninformative features
might have caused the R2value to be low. By calculating the P2
mand P2
m.nvalues, which are a proportion
of the R2
mvalue, we can obtain a more robust measure to determine if there is predictable data in block m.
3.3 Model Specification
The inner model of a Process PLS model can be specified in multiple ways. One strategy is to first model
the flow of the process and then, with a different model, include relationships between blocks that one
wants to explore. Modelling the flow of a wafer through the manufacturing process can be done with the
inner model specification as shown in Figure 3a. Here, the model assumes that data from each machine
is only dependent on the machine before it and that relations between machines can be explained by this
flow. From a substantive point of view, it may be unlikely that such a Markovian process is true, yet it
remains valuable for illustration purposes.
The Process PLS specification just discussed is not identical to having multiple two-block models. The
optimization procedure of Process PLS optimizes block representations to be as predictive as possible. For
example, Machine 2 (M2) functions as a target in the relation between M1 and M2. In a two-block model
with only M1 and M2, M2 would be optimally predicted. But since M2 functions as a predictor of M3,
the lower-dimensional representation of M2 is optimized to be as predictive as possible for M3. We stress
that if the goal of ones research is to find optimal predictions of each block of data, path modelling is not
the most optimal option. Multiple dedicated prediction models will be better suited for that purpose.
Next to modelling the flow of the wafers, it is also of interest to model the relationship between machines
that are further apart in the process. For the current application, the main interest was in predicting the
data from the last machine from each of the machines preceding it. The model specification related to this
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
M2
M1
M7
M3 M6
M4 M5
M2
M1
M7
M3 M6
M4 M5
a) b)
Figure 3: The left inner model specification represents the flow of a wafer through the manufacturing
process. The right specification includes relations of all machines with the final machine. R2
mvalues are
shown within each rectangle. The P2
m.n-values shown near the arrows indicate how much of the extracted
information in the target block can be predicted from the predictor block.
is shown in Figure 3b. The multiple-predictor, multiple-target structure is illustrative of the added value
of path modelling. That is, the many relations are estimated simultaneously and detailed information can
be gathered about which parts of the process are most strongly related to other parts, conditional on the
other relations. We also note that this method of model specification is especially interesting if the final
block of data contains quality and/or yield measurements (which it does not in the current case). In this
way, the relations between multiple machines and product quality can be studied simultaneously, which
can benefit process control optimization.
Various other model topologies beyond those presented in this paper are possible, each of which may
offer unique insights into the process. We instead present a data-driven approach to identify a simplified
model that highlights only the strongest relationships. This can be done by specifying an inner model that
estimates all effects between machines (shown in Figure 4), and removing the inner model connection
with the lowest P2value. This results in a model with one fewer connection. We repeating this process
iteratively until all remaining P2values exceeded .10. This value was subjectively chosen and is comparable
to a regression coefficient of .33. If in any iteration, a machine had no outgoing or incoming arrows, we
removed the data of that block from the data set.
4 RESULTS
The first model (Figure 31) indicated a strong relation between data from Machine 1 and Machine 2. Of
the 40% variance extracted from the data related to Machine 2 (i.e., R2
2=.40), 95% could be predicted
from features from Machine 1 (i.e., P2
2.1=.95). From a substantive point of view, this supports prior
expectations expressed by process experts and was a first confirmation that the algorithm performed as
intended. The model also showed a strong relation between (features from) Machines 5 and 6 (P2
6.5=.49)
and between Machines 6 and 7 (P2
7.6=.53). There was virtually no relation between the features from
the other Machines. Since the absolute values of R2are not meaningful in the current context (see last
paragraph of Section 3.2), these values are only shown in the figures, but not will not be discussed. The
discussions will only focus on the regression effects P2.
In the second model (Figure 3b), most effects representing the flow were highly similar to those found
in the first model. The notable exception is that the effect of Machine 6 on Machine 7, P2
7.6, dropped from
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
M2
M1
M7
M3 M6
M4 M5
Figure 4: Inner model with each machines predicting all following machines. This model was used to
iteratively find a simplified model in which all P2values are at least .10. All inner model effects that
exceeded .10 in this model specification are shown in the graph. All effects are provided in Table 3.
.53 in the first model to .18 in the second model. This decrease in P2
7.6means that part of the data that could
be explained from Machine 6 can also be explained by data from other machines. The total proportion of
variance of Machine 7 that could be explained in the second model calculated as P2
7=∑6
n=1P2
7.n=.64 (i.e.,
the sum of all effects on Machine 7) is higher than in the first model, where P2
7was .53. In the second
model, more data is being used to predict Machine 7, leading not only to a higher explained variance, but
also showing details on the contributions of each machine to the predictions of Machine 7.
The data-driven approach to find a simplified model started with the fully connected model presented
in Figure 4. The inner model effects are provided in Table 3. Due to rounding, some effects are presented
in the table as being equal (e.g., multiple entries being .00). The procedure of estimating the model and
removing the connection with smallest effect and then re-estimating the new model took 16 iterations before
all effects, P2
m.n, exceeded .10. The final simplified model is shown in Figure 5.
Table 3: Inner model coefficients (P2
m.n) from the fully connected model.
Predictors (n)
Target(m) M1 M2 M3 M4 M5 M6
M2 .84
M3 .03 .04
M4 .03 .03 .00
M5 .04 .04 .00 .01
M6 .08 .08 .00 .00 .36
M7 .09 .12 .01 .01 .24 .18
The effects in the simplified model provide interesting details on the interrelations between the machines.
The strong relations between Machines 1 and 2 is still represented well in this model, as is the relation
between Machines 5 and 6. Model simplification hardly affected the the ability to predict the data of
Machine 7 (P2
7=.63). The effect of Machines 1, 2, 4 and 6 on Machine 7 were quite similar, indicating
that each machine has a distinct relation with different parts of the data in Machine 7. This is crucial for
studying possible solutions for process control.
Detailed investigation of the results showed that M1_V7_max,M2_V76_avg,M5_V125_min
M6_V139_avg and M7_V151_min where the most important features in their respective machines
in terms of their contribution to the variance of the lower-dimensional representations. Details are provided
in Table 4, with some description of what these features represented. To give an example, M2_V76_avg
is a feature (the average) extracted from the time series Variable 76. Variable 76 reports the readings of a
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
temperature sensor during the time a wafer is in Machine 2. The average value of this sensor contributed
21.1 times more to the Process PLS model than the other features from Machine 2 contributed on average.
M2
M1
M7
M6M5
Figure 5: Simplified inner model found through iteratively removing inner model connections from a fully
specified model (Figure 4 until all P2values were at least .10. As no relations with Machines 2 and 3
reached the threshold, the respective data blocks were removed from the model.
Table 4: Anonimized names of the most important features of each block in terms of contribution to the
(simplified) Process PLS model. Feature contributions are an indication of how much variance a feature
contributes to the variance of the lower-dimensional representations. The relative contribution is calculated
as the contribution of this feature divided by the average contribution of all features in its block.
Feature Name Relative Contribution Description
M1_V7_max 8.2 The maximum value of a voltage
M2_V76_avg 21.1 Average temperature
M5_V125_min 7.4 Minimum of a certain flow
M6_V139_avg 6.1 Average pressure
M7_V151_min 20.6 Minimum of a certain speed
It is possible to evaluate which features are most important for predicting certain blocks of data.
For example, the single strongest predictor for the data in Machine 2 was feature M1_V36_std, which
indicates the variability in temperature on Machine 1 during manufacturing. The minimum of a certain
flow, M5_V125_min, was the single most important predictor of the data observed in Machine 6. For
Machine 7 the variability of a different flow, represented by feature M5_V126_std was the strongest
predictor. Without providing too many details, it may be clear that this type of information is extremely
valuable for predictive process control and obtaining valuable insights for root-cause analysis.
5 DISCUSSION
This paper showcases how path modeling can serve as a potent instrument to study relationships between
process data across production lines. This approach helped us reveal correlations between feature sets,
leading to a deeper understanding of the intricate interactions in the production process. Path models
are interpretable, and their simple topology and the ease with which models can be specified, creates an
intuitive representation of the process. By simplifying the models, we were able to identify the essential
relationships.
The findings obtained from our analyses can be applied towards creating soft-sensors or virtual metrology.
It is imperative to identify the crucial connections between features in order to determine which input
variables should be used. Subsequently, these features can be utilized to forecast the quality of end-products
van Kollenburg, Verhoeven, Pagano, Holenderski, and Meratnia
(van Kollenburg et al. 2022), leading to production optimization, cost reduction, and improvement in overall
product quality.
Our research showed the importance of addressing co-linearity in process data in complex systems like
production lines. We illustrated the methodology using a basic feature selection method, which likely missed
key relations between the time series. Directly integrating time series into a path modeling framework
would better capture complex relations and result in more accurate models. Until this becomes possible,
a priori filtering is needed.
6 CONCLUSION
The multitude of possible relations between time series features makes multivariate cross-correlation
infeasible for our purposes. Path modelling allowed us to use domain-specific insights to enhance the
effectiveness of our models and better understand the relations in the data. Although our current model
has shown some success in addressing our research questions, there is a need for a better-fitting model that
can account for complex interactions between variables not anticipated by domain experts. A promising
direction for future research is the extension of path modeling to tensor-based regression models (Liu
et al. 2021), which may overcome the limitations of manual feature selection by capturing higher-order
relationships in the data.
For future research, we suggest developing a neural-network-based path modeling combined with tensor
data representations from manufacturing processes. Such methods could improve model performance by
learning complex relationships between different types of data. Incorporating expert knowledge into
the model may become even more crucial to ensure interpretability. Neural network models, capable of
adapting to changes and discovering hidden data patterns, could offer more robust solutions to manufacturing
challenges.
ACKNOWLEDGMENTS
This work was in part supported by ECSEL Joint Undertaking, under grant agreement No 826589. The
authors express their gratitude to Paola Giuffre, Caterina Genua and Daniele Li Rosi for their consultation
with respect to the manufacturing process and data presented in this paper. OpenAI’s ChatGPT (GPT-4)
was used to proofread the presented text, checking for spelling and grammar. In no way were algorithms
used to create original content or to generate ideas.
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AUTHOR BIOGRAPHIES
GEERT VAN KOLLENBURG is Assistant Professor at Eindhoven University of Technology in the Netherlands. he has worked
with national and international market leaders to develop data-driven solutions for sustainable chemical and semiconductor
industries. His expertise spans statistical process control, structural equation modelling, chemometrics, and more. His dedication
to sustainability and expertise in statistics and machine learning have led to innovative approaches for predictive and prescriptive
analytics. Email address: g.h.v.kollenburg@tue.nl. Website https://research.tue.nl/nl/persons/geert-van-kollenburg
RICHARD VERHOEVEN is a University Researcher and IT Developer at the Department of Mathematics and Computer
Science at the Eindhoven University of Technology in the Netherlands. He has worked together with national and international
partners on the topics of component based systems, wireless sensor networks, internet of things and hardware-in-the-loop
simulations. Email address is p.h.f.m.verhoeven@tue.nl. Website is https://research.tue.nl/nl/persons/richard-verhoeven
DANIELE PAGANO, is Funding Project Manager at STMicroelectronics s.r.l. He has covered various position and responsibilities
in Catania Wafer Fab Operations (Lithography, Dry Etching, APC & SPC, Epitaxy, Process Control), Past experiences in collabora-
tive projects like IMPROVE (2012), INTEGRATE (2015), MADEin4 (2022) and nowadays HiCONNECTS, SATURN, IPCEI. He
is author and co-author of several publications on journals and international conferences. E-mail adress is daniele.pagano@st.com
MIKE HOLENDERSKI is an assistant professor at the Department of Computer Science and Mathematics at the Eindhoven
University of Technology in the Netherlands. He did his PhD in Computer Science on the topic of multi-resource management in
embedded real-time systems. His current research focuses on reliable and trustworthy machine learning for process optimization
and control and hybrid data/knowledge driven modelling of high-dimensional data. His e-mail address is m.holenderski@tue.nl
and homepage is https://www.tue.nl/en/research/researchers/mike-holenderski.
NIRVANA MERATNIA is Full Professor of Pervasive Computing at Eindhoven University of Technology in the Netherlands.
Her research covers various aspects of computing including distributed machine learning and AI, embedded/edge AI, data-driven
networking and smart sensor systems. She has been involved in several national and international projects addressing (distributed)
computation and intelligence in the context of Internet of Things and Cyber Physical Systems creating societal and economic
impacts. Her e-mail address is n.meratnia@tue.nl
