## 2 State of the Art  
The review methodology is based on academic peer-reviewed publications drawn from well-known academic databases, such as ScienceDirect, Scopus, Google Scholar and Web of Science. Furthermore, the bibliometric analysis, has been chronologically limited to the period of the last five years (i.e., 2018 up to 2023). The structure of the search query applied for the literature investigation is as follows: TITLE-ABS-KEY (industry 4.0 AND \"Digital Shadow\"*\" OR \"Taguchi method\"*\" OR \"design of experiments*\") AND PUBYEAR > 2017 AND PUBYEAR > 2017. The initial search returned a total of 105 scientific articles. Among them were 52 conference papers, 38 articles, 7 conference reviews, 4 book chapters, and 4 review papers. The results obtained from the literature investigation have been processed with the utilization of the VOSviewer software (Version 1.6.19), which provides additional functionalities for the visualization of the bibliometric analysis and the clustering of the results [34]. In Figure 1 the literacy network is displayed. According to this literacy network, the main keywords include, among others, Industry 4.0, Digital Twin, Digital Shadow and DOE. Nodes are a qualitative representation of the volume of publications that mention or implement the aforementioned technologies. By analyzing the visualization of the literacy network, it can be observed that there is no visible connection between the Digital Shadow node and the DOE node, thus indicating the innovation of the presented research work, in which the authors aim to combine the above-mentioned concepts, in order to fully utilize the capabilities of advanced simulation techniques. The relationship between the major keywords with other technologies is described in the form of lines (links). These lines show with which additional technologies, or in what kind of applications, Industry 4.0, Digital Twin, Digital Shadow, and DOE are implemented. The thickness of the line is a qualitative representation of the number of implemented applications and it is described based on the resulting tree between the lines. In Figure 2, the density visualization of the publications is shown. Figure 1: Network Visualization of Literacy Topic Area. In Figure 2 the breadth of research on the subject is illustrated in the form of a heatmap. In particular, the visualization of Figure 2 is useful for unveiling the trends on which the current research effort focuses more frequently. To further improve the interpretation of the presented literature investigation results, all of the topics are grouped in three clusters, as presented in Table 1.  
With clustering, any correlation between different topics is feasible, thus making easier the recognition of non-visible linkages. For example, in Figures 1 and 2, the connections between \"DOE\", \"Industry 4.0\", and \"Digital Shadow\" are fewer, since there are limited research works combining the above-mentioned methods. However, from the clustering, it becomes apparent that they are correlated. The authors in [24] have presented three different conceptual models related to the communication and data flow between the physical system and its digital counterpart. The models are categorized in (i) Digital Model, in which the communication between the systems is performed manually (asynchronous communication), (ii) Digital Shadow, in \begin{table}
\begin{tabular}{c c c} \hline \hline
**Cluster 1** & **Cluster 2** & **Cluster 3** \\ \hline Digital Twin & Assembly line balancing & Bolted assemblies \\ “as built” design & Conceptual data model & Cloud computing \\ Design for zero-defect manufacturing & Cyber-physical model & Edge computing \\ Intelligent manufacturing & Data Analytics & Fuzzy logic \\ Mesh monitoring & Digital Shadow & Load balancing \\ Quality control & Digital supply chain & Multi responses \\ ZDM mapping & Industry 4.0 & Response time \\ Life-cycle control & Mixed-model stochastic & Smart tightening \\ Smart Manufacturing & Procurement 4.0 & Taguchi \\ \hline \hline \end{tabular}
\end{table}