Digital Maturity of SMEs in the EU: Leaders and Laggards of Luxembourg’s Manufacturing Ecosystem

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The research work presented in the paper made use of the EU Digital Maturity Assessment Tool (EU DMAT) to empirically evaluate the digital maturity of manufacturing SMEs in Luxembourg.  The research was conducted on a sample of 30 companies, which is in line with similar studies available in literature, also with respect to the overall size of Luxembourg's manufacturing sector.

The discussion and analysis of related work (Section 1.2) is sound and comprehensive.  The authors' observation that there is a lack of empirical studies of digital maturity specifically aimed at the manufacturing sector and leveraging a standardized assessment method, which provided the underlying motivation for their work, is supported by the literature analysis they conducted.

The statistical methods and tools used throughout the paper are rather standard, and hence, not an element of novelty per se.  However, they were used correctly and adequately described, barring some notational inconsistencies better discussed in the following.

The discussion of experimental results (Section 4) is sound for the most part, but for the adoption of KPIs and the use of AI, as indicated in the following. The discussion of the limitation of the study the authors provide in the conclusion if comprehensive and technically sound.

Notational inconsistencies and methodological shortcomings:

• Equation (4) does not down-scale correctly when both W_d,q and R_i,d,q are higher than 10.  This may lead to Q_i,d,q > 10, which is out of range.  For instance, if the score of enterprise i is R_i,d,q=11 out of W_d,q=12, the denominator of (4) is min(10,12)=10, and hence, Q_i,d,q=10/10*11=11.  Given that the possibility of W_d,q being > 10 is explicitly mentioned in the manuscript (L.319-320), the formula must be rectified.
• In Equations (10) and (12), the indicator of the matrix size (n x d) must  contain only constants.  On the contrary, d is defined as a variable ranging from 1 to 6 (the DMAT dimensions) at L.384 of the manuscript.  The notation must be amended accordingly.  As a side note, this has been done correctly for n (which is a constant and represents the number of enterprises considered in the study) and i (a variable that ranges from 1 to n).
• Since one of the focal points of the study is the use of a standardized  assessment method, any "deviations from the standard DMAT usage" alluded to at lines 286-287 of the manuscript must be explicitly mentioned and their impact must be thoroughly discussed.
• L.469: How was the number of bootstrap samples (2000) selected?  The reasons behind this particular choice must be clarified because they are not self-evident from the manuscript.
• There is an significant inconsistency between Figure 6F, which mentions p<0.01, its caption, which says p<0.001, and its discussion in the main text at L.622, which also says p<0.001.  Visually, the data shown in the figure seem more consistent with p<0.01.  The figure, caption, and discussion must be amended to remove the inconsistency and provide the correct p value.
• The majority of the analysis in Section 4 is adequately supported by  experimental data.  However, although the suggestion of adopting clear KPIs given at L.698-700 sounds sensible, its relationship with the empirical assessment described in the paper is not at all clear.  The same can be said of the considerations about AI use at L.704-714.  The manuscript must be improved to clarify the relationship between empirical data and their analysis.

Minor points:

• Table 3 mentions the case *p<0.05 in the footnote, but it never appears in the table.  It is therefore unclear whether the footnote is redundant or  some data are missing in the table.
• L.133-134: "whereas [...], while important, they are": the 'they' is most  probably redundant and should be removed.
• L.137: "Thus, as we [...]": it is unclear what the 'as' is referring to, given that there is no causal relationship between the focus of the study being on empirical studies and the fact that the comparative analysis of DMA tools is available elsewhere in literature.  Consider rephrasing.
• L.206: "rigor hypotheses": should it be "rigorous hypotheses"?
• L.396: "intertia" -> "inertia"
• L.400: "cosane" -> "cosine"
• L.414: "the standard deviation": it is unclear of which variable the standard deviation has been calculated.  Please rephrase.
• L.681: "divergen" -> "divergent"
• The exclusion of sectorial analysis due to insufficient sample size and  confidentiality concerns is mentioned twice in the text (L.357-360 and  L.508-516).  Consider bringing up this point only once, for instance, in the discussion of the limitations of the study.
• Stylistically I find that the Introduction, standing at about 4 pages, is  overlong.  Please consider whether moving the Literature Review subsection, which currently accounts for about half of it, would improve readability.
• It is unclear why Section 4 consists of only a single subsection.

Author Response

We sincerely thank the reviewer for detailed and constructive feedback. In the following, we carefully consider all comments and fully address them in the revised version of the manuscript. Below is a step-by-step response to points describing modifications, revisions and rebuttals, including the rationale behind each correction.

Comment 1: Notational inconsistency in eq(4)...

Response 1: We appreciate the reviewer's attention to this point. In the revised version, we ensure strict bounding at [0, 10] regardless of the magnitude Wd,q by replacing the original expression in the Qi,d,q formulation and updating it in the manuscript. By replacing the original expression with a formulation that enforces proportional normalisation, we also add an explicit constraint 0≤ Qidq ≤ 10. This conforms to the EU's DMAT, where raw scores are normalised linearly to a 0-10 range, regardless of whether the maximum exceeds 10. However, the idea is only to ensure manual imputation of errors if the rater manually inserts values > 10. Lastly, the text around lines 319-321 is also rewritten accordingly. Hence, we ensured that the equation now guarantees correct down-scaling when w exceeds 10.

Comment 2: Matrix notation in Eq10 and eq12 when d cannot be both constant and variable.

Response 2: Dear, thank you for the comment. We have completely revised the description of notations. In the revised version, we introduced different indices. Instead of using i and j for the enterprise and specific dimension, respectively, we now use Di,j to describe the specific (enterprise) dimension score. This was depicted later on normalisation and standardisation of the data matrix with n x d data matrix, where Zi,j is standardised data format for enterprise i and j dimension

Comment 3: Since one of the focal points of the study is the use of a standardized  assessment method, any "deviations from the standard DMAT usage" alluded to at lines 286-287 of the manuscript must be explicitly mentioned and their impact must be thoroughly discussed.

Response 3: Dear thank you for raising the point. Actually, we explicitly stated this because unlike other members of the EDIH network throuoghout the EU, we believe we are the first ones to actually challenge manufacturing SMEs on point by point response to assure valid and reliable outputs. To assure this, we went in all of the 30 companies (the two assessors) and perform shopfloor visits and discuss with engineers, managers and staff and other responsible person to make sure the responses they provide are actually valid. The EU DMAT survey is usually performed online and subjective, this way we wanted to remove self-assessment and to be more objective, and we describe that throughout the paper.

Comment 4: L.469: How was the number of bootstrap samples (2000) selected?  The reasons behind this particular choice must be clarified because they are not self-evident from the manuscript.

Response 4: Thank you for the question. Actually, in our common practice and reported in other studies, it is usually at least 1000 bootstrapping performed, and we wanted to increase the value to achieve stable percentile and bias-corrected confidence intervals due to small sample size. However, even after increasing by double, there is no significant deviations in intervals because ultimately values converge. There is no specific subjective report. If you consider that we need to increase or decrease the value of bootstrapping performed, we are open for that.

Comment 5: There is an significant inconsistency between Figure 6F, which mentions p<0.01, its caption, which says p<0.001, and its discussion in the main text at L.622, which also says p<0.001. Visually, the data shown in the figure seem more consistent with p<0.01. The figure, caption, and discussion must be amended to remove the inconsistency and provide the correct p value.

Response 5: Thank you very much for bringing this to our attention. We have reworked the figure and the data shows high statistically signifiacnt difference which can be observed in effect size. So the value rpeorted by JASP is actually p < 0.001. Thank you for that. The figure is replaced.

Comment 6: The majority of the analysis in Section 4 is adequately supported by  experimental data.  However, although the suggestion of adopting clear KPIs given at L.698-700 sounds sensible, its relationship with the empirical assessment described in the paper is not at all clear.  The same can be said of the considerations about AI use at L.704-714.  The manuscript must be improved to clarify the relationship between empirical data and their analysis.

Response 6: Dear, thank you for pointing this out. We outline what should be a logical steps based on empirical data and practical in-house (shopfloor) tours throughout these companies. Mainly, we consider that KPIs is most important for understanding pain points and gaps in their processes, after that AI scaling with follow. Hence, we placed more discussion on institutialisation and operationalisation of KPIs, where identified gaps and necessity of AI (such as adopting ML tools for regression and classification for implementing predictive maintenance, predicting improvement in processes based on product quality) will logically follow. Please see highlighted line numbers 696-713.

Minor points:

Comments: 

• Table 3 mentions the case *p<0.05 in the footnote, but it never appears in the table.  It is therefore unclear whether the footnote is redundant or  some data are missing in the table.
• L.133-134: "whereas [...], while important, they are": the 'they' is most  probably redundant and should be removed.
• L.137: "Thus, as we [...]": it is unclear what the 'as' is referring to, given that there is no causal relationship between the focus of the study being on empirical studies and the fact that the comparative analysis of DMA tools is available elsewhere in literature.  Consider rephrasing.
• L.206: "rigor hypotheses": should it be "rigorous hypotheses"?
• L.396: "intertia" -> "inertia"
• L.400: "cosane" -> "cosine"
• L.414: "the standard deviation": it is unclear of which variable the standard deviation has been calculated.  Please rephrase.
• L.681: "divergen" -> "divergent"

Response: Dear, thank you very much for this additional support in improving the quality of reporting. We have considered all suggestions and revised the article accordingly. We really appreciate the comments! In Table 3, we left 0.05, as is usual practice (and consistent throughout our tables), to maintain consistency with the reporting of p-values. However, each value is either high above 0.05 (e.g., > 0.01 or > 0.001), and in one case, it is lower than 0.05. The remaining suggestions have been revised.

Comment: The exclusion of sectorial analysis due to insufficient sample size and  confidentiality concerns is mentioned twice in the text (L.357-360 and  L.508-516).  Consider bringing up this point only once, for instance, in the discussion of the limitations of the study.

Response: Dear reviewer, thank you for bringing this to our attention. We have retained only this information in the analysis of the results and removed it from the methodology section.

Comment: Stylistically I find that the Introduction, standing at about 4 pages, is  overlong.  Please consider whether moving the Literature Review subsection, which currently accounts for about half of it, would improve readability.

Response: We thank you for your comment. However, given that we build our arguments for gaps, and consequently aims and objectives of the study mainly from our synthesis of systematic literature review, we considered for readability more appropriate to maintain it within the introduction as the reader has a first-hand insights into our argumentation scheme.

Comment: single subsection...

Response: Section 4 was already in four subsections, however, the first one was bolded as level 1 heading. We have now changed according to MDPI style format.

Lastly, we would like to express extreme gratidue for your time and effort in helping us improve the quality of the manuscript. We strongly appreciate the support of this reviewer!

Reviewer 2 Report

Comments and Suggestions for Authors

This study focuses on the digital maturity of small and medium-sized enterprises (SMEs) in Luxembourg's manufacturing sector. Based on the six dimensions of the European Union's Digital Maturity Assessment Tool (DMAT), an empirical study was conducted on 30 sample enterprises using methods such as repeated - measures Analysis of Variance (ANOVA) and Principal Component Analysis combined with Hierarchical Clustering on Principal Components (PCA - HCPC). The research conclusions emphasize that strategic and human factors at the organizational level are the core drivers of digital maturity, and technical and sustainability dimensions can only exert their maximum effectiveness on this basis.

Required Revisions for the Paper are shown in the following:

1、Refine the interpretation of cluster analysis: After identifying two clusters through PCA - HCPC, specific enterprise cases should be further integrated to illustrate the best practices of "Leaders" and the key bottlenecks of "Laggards in detail, so as to provide more specific support for practical guidance.

2、Clarify whether the distribution of sample enterprises in terms of scale, years of establishment, and sub - industries is consistent with the overall structure of Luxembourg's manufacturing industry. Supplement the detailed description of the sampling method to reduce doubts about sampling bias.

3、Standardize the annotation of abbreviations at their first occurrence: Some abbreviations in the paper (such as MLOps, which stands for Machine Learning Operations; KPI, which stands for Key Performance Indicator) are not fully explained when they first appear. It is necessary to supplement the annotation of their full names to facilitate readers' understanding.

4、Correct the consistency of chart annotations: The legend explanations of some charts (such as Figure 3 and Figure 6) are not clear enough. It is suggested to supplement the meanings of coordinate axes and the annotations of data sources to ensure that the charts are fully consistent with the descriptions in the main text.

5、Streamline the redundant expressions in the references: The formats of some existing references are inconsistent. The citation format can be standardized uniformly, and the references that are weakly related to the core of the research can be deleted to focus on the key studies related to digital maturity and manufacturing SMEs.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

Comment 1: Refine the interpretation of cluster analysis: After identifying two clusters through PCA - HCPC, specific enterprise cases should be further integrated to illustrate the best practices of "Leaders" and the key bottlenecks of "Laggards in detail, so as to provide more specific support for practical guidance.

Response 1: We thank the reviewer for bringing this point to our attention. We agree that anchoring the interpretation of clusters in concrete, enterprise-level patterns enhances the practical relevance of the findings. However, signed Terms and Conditions and confidentiality constraints prevent the disclosure of identifiable cases. Still, we have strengthened the narrative by incorporating anonymised, pattern-based examples consistent with observed profiles. For leaders, we highlight practices such as establishing strategy deployment, documenting human capital development, and implementing data governance. For laggards, we consider structural barriers such as informal decision-making, absence of digital skills planning and training, fragmented data landscapes, and difficulty aligning digital priorities with business value. Please see the completely revised Section 4.4, 'Divergent SME Maturity Profiles,' which we have revised to ensure that recommended pathways are grounded in actual observed practices and supported by empirical evidence.

Comment 2: Clarify whether the distribution of sample enterprises in terms of scale, years of establishment, and sub - industries is consistent with the overall structure of Luxembourg's manufacturing industry. Supplement the detailed description of the sampling method to reduce doubts about sampling bias.

Response 2: We appreciate the opportunity to clarify this matter. The sample of 30 SMEs was contacted from the prior LDIH database of manufacturing enterprises, which includes all firms participating in digitalisation programmes coordinated by Luxinnovation. The sample distribution is proportionally consistent with the overall Luxembourg manufacturing structure in terms of SME size classes (micro, small, medium), dominant subsectors (metals, plastics, machinery, chemicals) and typical age profiles of Luxembourg industrial firms. Participation was voluntary, and recruitment followed a census-based invitation rather than convenience sampling, reducing selection bias. We have added a detailed description of this procedure and explicitly stated how the sample compares to the distribution. Please see highlighted revised lines 238-248 in the revised version of the manuscript.

Comment 3: Standardize the annotation of abbreviations at their first occurrence: Some abbreviations in the paper (such as MLOps, which stands for Machine Learning Operations; KPI, which stands for Key Performance Indicator) are not fully explained when they first appear. It is necessary to supplement the annotation of their full names to facilitate readers' understanding.

Response 3: We have revised MLops and KPIs, and we will fully explain them when they first appear. Additionally, we made further changes to the manuscript, explaining the importance of institutionalising KPIs for both leaders and laggards. Please see the revised version of the manuscript, lines 692-716.

Comment 4: Correct the consistency of chart annotations: The legend explanations of some charts (such as Figure 3 and Figure 6) are not clear enough. It is suggested to supplement the meanings of coordinate axes and the annotations of data sources to ensure that the charts are fully consistent with the descriptions in the main text.

Response 4: We have completely revised the caption and chart annotations to explain the coordinate axes and annotations within the graph. Additionally, as we noticed an error in Figure 6 (reporting p < 0.01, when it should be p < 0.001 on the F part of the figure), we have revised the figure and the caption accordingly. We have revised both captions to explain each part of the figure presented, aligning them with the text discussion.

Comment 5: Streamline the redundant expressions in the references: The formats of some existing references are inconsistent. The citation format can be standardised uniformly, and the references that are weakly related to the core of the research can be deleted to focus on the key studies related to digital maturity and manufacturing SMEs.

Response 5: We have reworked the references and removed those that are loosely related. In our reference system, we did not use manual entry of references; instead, we utilised Mendeley, which already provided the reference citation style for Technologies.

Lastly, we would like to express sincere gratitude and appreciation to the reviewer for their feedback, which helped us improve the quality of the manuscript!