Review Reports - Uncertainty-Driven Reliability Analysis Using Importance Measures and Risk Priority Numbers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

It seems that most of the content in the full text is described subjectively using some words, and reliability analysis is conducted using importance measurement and risk priority level driven by uncertainty. The full text does not clearly explain what these uncertainties specifically refer to? What factors are causing this uncertainty, subjective cognition or random environment? If subjective cognition is the cause, then which theory among uncertainty theory, fuzzy theory, interval theory, etc. should we use as the research tool. If it is caused by a random environment, then we should use probability theory as a mathematical tool to model reliability and calculate importance measures and risk priorities. And apply a case study to numerically simulate the method proposed in the article to verify the rationality and effectiveness of your proposed method. Now it seems that the model you proposed was not found in the article. What theory was used as a mathematical tool to calculate the data results in the paper? Suggest that the authors to revise the entire text to make it more convincing to read.
The structure of the article is fine, but the content of each section can be a bit confusing to read. For example, in the third part of the article - Methods, can the authors use some mathematical expressions to present the proposed methods to readers. The fourth part of the article also has the same problem. Suggest authors to make revisions.
What does the abbreviation SWCCT refer to? It is recommended to clearly explain its meaning when it first appears in the text.
What are the rankings in Table 3 based on? Is it an industry standard? Or is it the result of engineering practice experience? Or is it artificial ranking?
The failure mode is shown in Figure 5. Is this overall failure model subjective? Is there still a theoretical or practical basis? If it is subjective, please explain the physical basis for this assumption. If there is evidence, it is recommended to cite the corresponding literature. In addition, it is recommended to clarify in the text how the parameter values in the figure are obtained, whether they are assumed based on human experience or have practical application basis.
Are the data in Tables 4 and 6 the results obtained from experiments? Or is it real data collected during actual operation? Please explain clearly in the text.
In the last paragraph of page 13 of the article, it is believed that "Table 4 shows that the failure assessment is consistent with the FMEA, as the heavy- 405 duty truck system is responsible for 83% of the total SWCCT failures." How was this data obtained from Table 4? Please provide a detailed explanation.
How was the data in Figure 7 calculated? Please explain clearly in the text.
Please provide a reasonable explanation for Figures 6 and 7 in the text. What do these figures illustrate? Please explain the meaning of the methods and models proposed in the article.
Please explain the effectiveness of the model proposed by the authors based on the data in the article. What data and indicators can demonstrate the effectiveness of your proposed model method? Please provide a detailed explanation in the conclusion section of the article.

Author Response

Thank you for the suggestions. The modifications to the text are highlighted in yellow within the document. In this document, there is a specific answer to the question.

Comments 1: It seems that most of the content in the full text is described subjectively using some words, and reliability analysis is conducted using importance measurement and risk priority level driven by uncertainty. The full text does not clearly explain what these uncertainties specifically refer to? What factors are causing this uncertainty, subjective cognition or random environment? If subjective cognition is the cause, then which theory among uncertainty theory, fuzzy theory, interval theory, etc. should we use as the research tool. If it is caused by a random environment, then we should use probability theory as a mathematical tool to model reliability and calculate importance measures and risk priorities. And apply a case study to numerically simulate the method proposed in the article to verify the rationality and effectiveness of your proposed method. Now it seems that the model you proposed was not found in the article. What theory was used as a mathematical tool to calculate the data results in the paper? Suggest that the authors to revise the entire text to make it more convincing to read.

Response 1: Thank you for this important request for clarification. We revised the manuscript to state explicitly that the uncertainties treated are parametric (statistical) uncertainties arising from finite failure records and operational variability. The mathematical framework is probability theory: lifetime parameters are estimated by maximum likelihood (MLE), parameter uncertainty is quantified via the observed information matrix (asymptotic normal approximation), and uncertainty is propagated via Monte Carlo simulation through the Fault Tree / Reliability Block Diagram. These details and equations are now in Sections 3.2–3.4 and Appendix A. The case study applies the numeric workflow component; we compute reliability, after we evaluate system reliability via FTA or RBD, to compute IMs, and finally synthesize with FMEA by pairing each prioritized component with its top failure modes and RPNs, and report medians and 95% intervals (see Section 4.4).

Comments 2: The structure of the article is fine, but the content of each section can be a bit confusing to read. For example, in the third part of the article - Methods, can the authors use some mathematical expressions to present the proposed methods to readers. The fourth part of the article also has the same problem. Suggest authors to make revisions.

Response 2: We appreciate this helpful suggestion. The revised Section 3 now includes the main equations for parameter estimation, system reliability, and importance measures. Section 4 also presents the computational steps and formulas used to obtain the reported results, improving clarity and traceability. We have clarified the numerical handoff across stages in Methodology. Section 3 is now structured as 3.1 From System Characterization to FMEA, 3.2 From FMEA to System Reliability, 3.3 From System Reliability to IMs. Each step is operationalized with equations, explicitly linking the outputs of one subsection to the inputs of the next. We also added a one-line computation chain at the first reference of Figure 1 to make the data flow explicit:

Numerically, the workflow after qualitative assessment proceeds as: estimate lifetime parameters for each component, compute reliability, evaluate system reliability via FTA or RBD, and compute IMs. Explicit formulas for IMs (Birnbaum, RAW, RRW, FV, Criticality), Monte Carlo propagation steps, and the rank-stability metric (top-k frequencies). Results (Section 4) now show the exact computations used to produce tables and figures. These edits improve reproducibility and readability..

We added mathematical expressions for parameter estimation, reliability functions, IM formulae, Monte Carlo propagation, and rank-stability metrics in Section 3 and in the Results where needed. (See Sections 3.2–3.4 and equations near Figure 1.)

Comments 3: What does SWCCT mean?

Response 3: We thank the reviewer for noticing this omission. The abbreviation SWCCT now appears fully defined at its first mention as Solid Waste Collection and Compaction Trucks, and it is also included in the new section Abbreviations list.

Comments 4: What are the rankings in Table 3 based on? Is it an industry standard? Or is it the result of engineering practice experience? Or is it artificial ranking?

Response 4: Thank you for requesting this clarification. We now explicitly state in Sections 4.1–4.3. Table 3 rankings are derived from the methods stated in the manuscript: RPN rankings come from FMEA expert scores (Severity, Occurrence, Detection) provided by the company’s maintenance staff; IM rankings derive from computed Importance Measures (Birnbaum, RAW, RRW, FV, Criticality) using the fitted reliability models.

Table 3 combines two sources: (a) RPN rankings, based on Severity/Occurrence/Detectability scores obtained from the company’s FMEA workshops with maintenance staff; and (b) IM rankings, computed from fitted reliability models (see Sections 4.1–4.3 and Table 3 caption). The provenance of each ranking is now explicitly stated.

Comments 5: Is Figure 5 failure mode subjective? Basis and parameter values?

The failure mode is shown in Figure 5. Is this overall failure model subjective? Is there still a theoretical or practical basis? If it is subjective, please explain the physical basis for this assumption. If there is evidence, it is recommended to cite the corresponding literature. In addition, it is recommended to clarify in the text how the parameter values in the figure are obtained, whether they are assumed based on human experience or have practical application basis.

Response 5: Thank you for this request for the source and justification. We clarified that the failure modes in Figure 5 come from the company’s FMEA records and were validated with field technicians (see Section 3.1). Parameter values in the figure are labelled according to origin: those estimated from operational data are derived via MLE (Appendix A); S/O/D scores and any expert estimates are identified as expert-derived in the figure caption and Section 3.1. We also added references to standard FMEA practice where appropriate.

Comments 6: Are the data in Tables 4 and 6 the results obtained from experiments? Or is it real data collected during actual operation? Please explain clearly in the text.

Response 6: Thank you for this request for clarification. Tables 4 and 6 present results computed from real operational failure records provided by the Solid Waste Management Company. This is now stated in Section 4 and in Appendix A, which details data sources and preprocessing.

Comments 7: In the last paragraph of page 13 of the article, it is believed that "Table 4 shows that the failure assessment is consistent with the FMEA, as the heavy-duty truck system is responsible for 83% of the total SWCCT failures." How was this data obtained from Table 4? Please provide a detailed explanation.

Response 7: Thank you for requesting a precise explanation. We appreciate the reviewer’s observation. The statement regarding the 83% contribution of the heavy-duty truck system (HDTS) has been clarified in the revised version. This percentage was not extracted directly from Table 4 but from the aggregation of subsystem-level failure probabilities obtained through the Fault Tree Analysis (FTA) model. Each subsystem’s failure probability was computed by propagating the individual component reliability distributions through the system structure function. The HDTS accounted for approximately 83% of the total system failure probability when these probabilities were normalized with respect to the top-event failure of the SWCCT.

To avoid confusion, the text has been updated to explicitly explain that Table 4 reports the overall reliability of the complete SWCCT, while the 83% figure results from the FTA-based subsystem contribution analysis. The revised paragraph also references the methodological link between the reliability quantification presented in Table 4 and the component importance results shown in Figure 6. This clarification ensures that the reader can trace how the subsystem-level contributions were derived from model-based reliability propagation rather than from subjective estimation.

Comments 8: How was the data in Figure 7 calculated? Please explain clearly in the text.

Response 8: We appreciate the reviewer’s observation. Figure 7 has been replaced with a new figure that presents the Top 5 critical components and their corresponding IMs. Following the reviewer’s suggestion, the text now includes a clearer explanation of how the data were obtained. The calculation is based on the mathematical definitions of the selected IMs, as presented in the corresponding table. Additionally, the updated version incorporates the uncertainty propagation introduced in the methodological framework, allowing a more complete and transparent representation of the results.

Comments 9: How was the data in Figure 7 calculated? Please explain clearly in the text.

Response 9: We appreciate the reviewer’s observation. Figure 7 has been replaced with a new figure that presents the Top 5 critical components and their corresponding IMs. Following the reviewer’s suggestion, the text now includes a clearer explanation of how the data were obtained. The calculation is based on the mathematical definitions of the selected IMs, as presented in the corresponding table. Additionally, the updated version incorporates the uncertainty propagation introduced in the methodological framework, allowing a more complete and transparent representation of the results.

Comments 10: Please explain the effectiveness of the model proposed by the authors based on the data in the article. What data and indicators can demonstrate the effectiveness of your proposed model method? Please provide a detailed explanation in the conclusion section of the article.

Response 10: We added concrete indicators of effectiveness in Section 4.4 and in the Conclusion: (a) rank-stability metrics (top-k inclusion frequencies) indicate how consistently the same components are prioritized under parameter uncertainty; (b) interval overlap analysis for IMs identifies when rankings are statistically indistinguishable; (c) concordance analysis compares model priorities with historical maintenance priorities from the company. These indicators are reported in Tables/Figures in Section 4.4 and summarized in the Conclusion to show the method’s practical value for maintenance planning.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes a methodological framework that integrates Importance Measures (IMs) with the Risk Priority Number (RPN) to provide a more robust assessment of system reliability under uncertainty. However, it has many significant technical and conceptual flaws that undermine its scientific value. The authors may need to improve clarity, terminology, and methodological traceability and validate results using real reliability data with statistical confidence before further consideration. Currently, the framework conceptual rather than computational with descriptive but not quantitative modeling. The case study has insufficient data to support and validate the framework.

I cannot find any explicit mathematical or procedural integration presented in this study. The authors just stacks FMEA-based RPN ranking and IM-based sensitivity ranking. How the two metrics are normalized, weighted, or combined into a unified framework is unclear.
For the treatment of uncertainty, I cannot find any quantitative characterization. Qualitative terms (uncertainty-aware, variability, probabilistic rigor) are used without demonstrating uncertainty quantification like Monte Carlo simulation, Bayesian inference, or statistical confidence intervals. Therefore, uncertainty-driven is doubtful.
The method section just copy well-known textbook formulations (Birnbaum, RAW, RRW, Fussell Vesely). The paper does nothing to the novel interpretation or adaptation. This part reads more as a summary than as a contribution.
Figure 1 shows a logical connection, but a numerical implementation is absent. For FMEA, FTA, and IMs, how these results from one step jump to the next?
Please consider verify the proposed framework against established methods. For a system operating 10.44 h/day, reliability dropping to 65% after 50 hours implies a mean time to failure of less than one week. It impossible for heavy-duty vehicles.
The authors claimed that RPN ranks the cardan shaft highest, while IM ranks the pneumatic brake system highest. More indicators like normalization and weighting scheme are needed to justify it

Author Response

We thank the reviewer for the careful reading of the manuscript and the constructive remarks raised, which we have addressed in detail. The revision work has helped to improve the quality of the paper. The modifications to the text are highlighted in yellow within the document. In this document, there is a specific answer to the question.

Comments 1: I cannot find any explicit mathematical or procedural integration presented in this study. The authors just stacks FMEA-based RPN ranking and IM-based sensitivity ranking. How the two metrics are normalized, weighted, or combined into a unified framework is unclear.

Response 1: We thank the reviewer. We improved the text to clarify that RPN is used to rank failure modes based on severity, occurrence, and detectability, guiding practical mitigation strategies. In contrast, Importance Measures (IMs) assess component-level impact on overall system reliability. These indicators serve distinct analytical purposes and are not directly comparable. We reorganized the methodology section to make this issue clearer.

As noted, each metric yields different prioritization outcomes. RPN emphasizes failure modes within the power transmission system, whereas IMs identify brake systems as critical due to their influence on system reliability. This contrast exemplifies the complementary nature of both approaches.

Cardan shaft failure is particularly critical due to its high severity and low detectability. Such failures often result in environmental hazards, traffic congestion, and the deployment of trucks in inaccessible areas. Preventive detection remains unfeasible, as current truck systems lack adequate monitoring capabilities.

Meanwhile, brake systems were prioritized by IM’s modeling due to their failure frequency. From an operational standpoint, they are routinely inspected thoroughly before dispatching. Additionally, existing control mechanisms are sufficient to detect potential faults.

We changed the order of Theoretical Background to be consistent with the methodology and to make the relationship between these two measures clearer

Comments 2: For the treatment of uncertainty, I cannot find any quantitative characterization. Qualitative terms (uncertainty-aware, variability, probabilistic rigor) are used without demonstrating uncertainty quantification like Monte Carlo simulation, Bayesian inference, or statistical confidence intervals. Therefore, uncertainty-driven is doubtful.

Response 2: We agree and have added an explicit, quantitative uncertainty treatment. In section 3.4 (Uncertainty quantification), we model parametric uncertainty and propagate it via Monte Carlo through the FTA/RBD structure to obtain sampling distributions for subsystem failures and all IMs. We now report medians and 95% uncertainty intervals for these quantities and include rank-stability summaries (top-k inclusion frequencies).

In the Case study, Section 4.4 (Uncertainty analysis for SWCCT) details the application of this procedure to our dataset; the Results section was updated accordingly (tables/figures now display medians with 95% intervals).

Comments 3: The method section just copy well-known textbook formulations (Birnbaum, RAW, RRW, Fussell Vesely). The paper does nothing to the novel interpretation or adaptation. This part reads more as a summary than as a contribution

Response 3: We appreciate the reviewer’s observation regarding the limited interpretative and methodological contribution of the section describing Importance Measures.

We have expanded the discussion to strengthen the connection between the theoretical framework and the methodological objectives of the study. The revised text clarifies that the Importance Measures (Birnbaum, RAW, RRW, FV, and Criticality) are used to both rank components and interpret how reliability propagates through engineering systems. Each measure represents a different reliability dimension: structural dependence, vulnerability, probabilistic contribution, and relative risk relevance. This allows for a more complete understanding of how system performance responds to component behavior. These measures are then integrated with the RPN within the FMEA framework, linking reliability modeling with maintenance prioritization.

In practice, IMs are derived from system models (FT or RBD) and incorporate uncertainty analysis to account for variability in real operating conditions. The ranked components obtained from the IMs serve as input for the RPN evaluation, which identifies the most critical failure modes based on severity, occurrence, and detectability. This combined approach bridges the gap between theoretical reliability concepts and applied maintenance decisions by providing practitioners with a quantitative, structured method to allocate resources and plan interventions. These revisions ensure that theoretical discussion directly supports the modeling rationale and methodological development of the study.

Furthermore, the revised discussion section reinforces the interpretative connection between the theoretical framework and the study’s specific objectives. It now elaborates on how the application of Importance Measures and RPN provides complementary insights for uncertainty-aware decision-making, thereby strengthening the link between theoretical modeling principles and their practical implications in reliability-based maintenance engineering.

Comments 4: Figure 1 shows a logical connection, but a numerical implementation is absent. For FMEA, FTA, and IMs, how these results from one step jump to the next?

Response 4: We thank the reviewer. We have clarified the numerical handoff across stages in Methodology. Section 3 is now structured as 3.1 From System Characterization to FMEA, 3.2 From FMEA to System Reliability, 3.3 From System Reliability to IMs. Each step is operationalized with equations, explicitly linking the outputs of one subsection to the inputs of the next. We also added a one-line computation chain at the first reference of Figure 1 to make the data flow explicit:

Numerically, the workflow after qualitative assessment proceeds as follows: estimate lifetime parameters for each component, we compute reliabilities. Then, after evaluating system reliability via FTA or RBD, it is necessary to compute IMs and finally synthesize with FMEA by pairing each prioritized component with its top failure modes and RPNs.

This revision provides the requested numerical implementation linking FMEA FTA/RBD IMs.

Comments 5: Please consider verify the proposed framework against established methods. For a system operating 10.44 h/day, reliability dropping to 65% after 50 hours implies a mean time to failure of less than one week. It impossible for heavy-duty vehicles.

Response 5: We thank the reviewer. Failure records used for reliability assessment are sourced directly from the database. Considering the focus is on modeling reliability instead of availability, all failures are counted regardless of their severity. Considering the high operational demand, safety requirements, and environmental implications of any failure, the approach of modeling reliability is aligned with the policies of the SWCT company. Furthermore, the workflow of maintenance interventions also supports this practice as it facilitates the management of external warehouses and the process of continuous auditing.

It is also worth noting that some of the vehicles were reported with a failure probability distribution closely modeled with a Weibull distribution, with beta parameters near to one. This reflects typical aging behavior with a notorious increase in hazard rates. This is a reasonable explanation of the observed reliability value of 65% after 50 operational hours.

Finally, the empirical implementation of this framework in the fleet obeys the necessity of continuously prioritizing maintenance interventions. As in accordance with your comment, for the SWCT fleet, it was uncontrollable for the maintenance practice.

Comments 6: The authors claimed that RPN ranks the cardan shaft highest, while IM ranks the pneumatic brake system highest. More indicators like normalization and weighting scheme are needed to justify it.

Response 6: We thank the reviewer. Within the text, we have clarified that the issue of the failure records used for reliability assessment is sourced directly from the database. Considering the focus is on modeling reliability instead of availability, all failures are counted regardless of their severity. Considering the high operational demand, safety requirements, and environmental implications of any failure, the approach of modeling reliability is aligned with the policies of the SWCT company. Furthermore, the workflow of maintenance interventions also supports this practice as it facilitates the management of external warehouses and the process of continuous auditing.

It is also worth noting that some of the vehicles were reported with a failure probability distribution closely modeled with a Weibull distribution, with beta parameters near to one. This reflects typical aging behavior with an increase in hazard rates. This is a reasonable explanation of the observed reliability value of 65% after 50 operational hours.

Finally, the empirical implementation of this framework in the fleet obeys the necessity of continuous prioritizing maintenance interventions, as in accordance with your comment, for the SWCT fleet, it was uncontrollable for the maintenance practice

Reviewer 3 Report

Comments and Suggestions for Authors

While the manuscript addresses a timely and relevant topic with scientific value, several targeted revisions are recommended to enhance the clarity and presentation of the main arguments. To assist the authors in this process, detailed feedback has been provided in the annotated PDF. These suggestions aim to improve the precision of key concepts and reinforce the coherence of the manuscript’s structure and message, thereby increasing its suitability for publication in Applied Sciences.

1 - the abstract would benefit from placing more focus on the practical applications and broader significance of the research. Clearly emphasizing these elements would strengthen the overall impact of the study and highlight its importance for both academic and professional audiences.

2 - Acronyms are generally avoided in abstracts. It is advisable that the authors write out all terms in full in this section and introduce the related abbreviations later in the introduction, where they can be clearly explained to the reader.

3 - Several of the listed keywords appear overly long and resemble full phrases rather than clear, concise terms. The authors are encouraged to revise them to be more targeted and effective, as well-chosen keywords are essential for proper indexing and visibility in leading academic databases.

4 - The introduction provides a concise overview of the research focus, emphasizing the relevance of cutting force modeling in milling operations. However, it could benefit from a clearer articulation of the novelty and specific research gap the study aims to address. While the context is well established, the introduction would be strengthened by more explicitly positioning the contribution in relation to recent developments in the field. This would help clarify how the proposed approach advances existing knowledge and why it is timely or necessary.

5 - In the introduction, the authors provide an overview of various methods and models. I would advise them to also briefly mention the FRAM (Functional Resonance Analysis Method). They can support their argument by citing the following recent work:

-Falegnami, A. and Tomassi, A., 2025. 4 The Last Five Years (2019–2024) of FRAM Literature. Navigating the FRAM: Mastering the Functional Resonance Analysis Method for Modelling Complex Socio-Technical Systems, p.36. DOI: 10.1201/9781003518167-5

6 - The "Theoretical Background" section outlines key modeling principles and relevant prior formulations, providing a foundation for the proposed approach. However, the discussion remains somewhat generic, and the connection between the theoretical components and the specific aims of the current study could be articulated more clearly. Strengthening the link between theory and application would help justify the modeling choices and better support the rationale behind the subsequent methodological development.

7 - The "Methodology" section presents the modeling framework and computational procedures, but certain aspects would benefit from greater clarity and precision. In particular, the description of assumptions, parameter selection, and boundary conditions could be more thoroughly explained to ensure transparency and reproducibility. A clearer articulation of how each methodological step aligns with the study's objectives would improve the section's coherence and scientific robustness.

8 - The inscriptions in Figure 1 are extremely small, making them virtually illegible. I recommend that the authors enlarge the text elements to ensure readability and improve the overall clarity of the figure.

9 - Figure 2 must also be significantly enlarged to be appreciated.

10 - The results section provides a range of outputs derived from the proposed methodological framework, offering quantitative insights into the modeled phenomena. However, the current structure merges the presentation of results with interpretative commentary, which risks obscuring the clarity and analytical rigor of both components. Separating the results from the discussion would significantly enhance the manuscript’s readability and improve the logical flow of the argument.

By clearly distinguishing between what the model produces and how these outcomes are interpreted in relation to the research objectives and theoretical framework, the authors would allow readers to better assess the validity and significance of the findings. Such a division would also create space for a more focused and critical reflection in the discussion section, where the implications, limitations, and potential applications of the results could be addressed more explicitly. Structuring the paper in this way would help highlight the substance of the research and improve the overall communication of its contributions.

11 - The conclusion section effectively recaps the study’s content but would benefit from a clearer focus on how the findings apply in practical contexts and their broader relevance. This part of the manuscript offers an opportunity to highlight the core outcomes and respond more directly to the research questions. Including a more detailed acknowledgment of the study’s limitations and proposing directions for future inquiry would add important perspective. Enhancing these aspects would help improve the overall clarity and impact of the conclusion.

12 - Terms like "nuanced" and "pivotal" tend to recur in texts produced with the aid of generative language tools and may reduce the stylistic distinctiveness expected in academic writing. While not incorrect, the authors are encouraged to diversify their word choice to maintain a more precise and scholarly tone.

Comments for author File: Comments.pdf

Author Response

We appreciate the reviewer for having appreciated the work, for careful reading and constructive feedback. The revisions have allowed us to enhance the quality of the manuscript. The modifications to the text are highlighted in yellow within the document. In this document, there is a specific answer to the question.

Comments 1: The abstract would benefit from placing more focus on the practical applications and broader significance of the research. Clearly emphasizing these elements would strengthen the overall impact of the study and highlight its importance for both academic and professional audiences.

Response 1: We thank the reviewer for this valuable suggestion. In the revised abstract, we have added explicit references to the practical application and broader significance of the study. The abstract now emphasizes that the proposed framework improves the identification of critical components in real-world systems, validated through a case study of Solid Waste Collection and Compaction Trucks. Furthermore, we have clarified that the framework provides a reproducible and uncertainty-aware decision-support tool applicable to complex engineered systems, thus strengthening its relevance for both academic and industrial audiences.

Comments 2: Acronyms are generally avoided in abstracts. It is advisable that the authors write out all terms in full in this section and introduce the related abbreviations later in the introduction, where they can be clearly explained to the reader.

Response 2: We thank the reviewer for this comment. All acronyms have been removed from the abstract, and terms are now written in full. An Abbreviations section has also been added to clearly define all shortened forms used in the manuscript.

Comments 3: Several of the listed keywords appear overly long and resemble full phrases rather than clear, concise terms. The authors are encouraged to revise them to be more targeted and effective, as well-chosen keywords are essential for proper indexing and visibility in leading academic databases.

Response 3: We thank the reviewer for this comment. The list of keywords has been revised for consistency with the abstract and standard indexing terms. Long expressions were simplified, and all keywords now appear explicitly or conceptually in the abstract. The new keywords are: Reliability Analysis, Importance Measures, Risk Priority Number, Uncertainty Quantification, System Criticality, Waste Collection Trucks.

Comments 4: The introduction provides a concise overview of the research focus, emphasizing the relevance of cutting force modeling in milling operations. However, it could benefit from a clearer articulation of the novelty and specific research gap the study aims to address. While the context is well established, the introduction would be strengthened by more explicitly positioning the contribution in relation to recent developments in the field. This would help clarify how the proposed approach advances existing knowledge and why it is timely or necessary.

Response 4: We thank the reviewer for this comment. This comment has been addressed in the revised version. The introduction now clearly states the specific research gap and the novelty of the proposed approach. The study introduces a methodological framework that uses reliability-based IMs to identify critical components, integrates uncertainty analysis to evaluate the reliability of component rankings, and combines these results with FMEA to identify the most critical failure modes. The framework uses reliability tools, such as FT or RBD, to quantify system reliability and propagate parameter uncertainty. The revised text emphasizes that this integration provides maintenance practitioners with a data-driven basis for prioritizing maintenance actions and reducing costs under real operational variability. These additions clarify advances in reliability analysis beyond conventional deterministic approaches and strengthen the positioning of the contribution within recent methodological developments.

Finally, a new paragraph (lines 92 - 113) and a bridging sentence were added to better position the contribution within recent developments and show how the framework links statistical inference, uncertainty propagation, and decision support.

Comments 5: In the introduction, the authors provide an overview of various methods and models. I would advise them to also briefly mention the FRAM (Functional Resonance Analysis Method). They can support their argument by citing the following recent work:

Falegnami, A. and Tomassi, A., 2025. 4 The Last Five Years (2019–2024) of FRAM Literature. Navigating the FRAM: Mastering the Functional Resonance Analysis Method for Modelling Complex Socio-Technical Systems, p.36. DOI: 10.1201/9781003518167-5

Response 5: We appreciate the suggestion. We carefully reviewed the proposed reference on FRAM (Functional Resonance Analysis Method). Our study, however, develops and evaluates a probabilistic, component-level reliability framework (FMEA → FTA/RBD → IMs) with explicit parametric uncertainty treatment. FRAM is a systems/socio-technical Safety-II approach used to model functional variability in work processes; it is not employed, extended, or compared in our methodology or results, and its constructs do not inform our modeling choices (parametric TTF, structure functions, importance measures).

To keep the Introduction coherent and methodologically faithful, we restrict citations to techniques that are directly used or analytically connected to our framework. Adding FRAM would imply a scope that we do not cover and could confuse readers about the paper’s contributions. For these reasons, we have not included the FRAM citation. We note that FRAM may be valuable in future work focused on socio-technical performance variability, but it lies outside the present paper’s objectives.

Comments 6: The "Theoretical Background" section outlines key modeling principles and relevant prior formulations, providing a foundation for the proposed approach. However, the discussion remains somewhat generic, and the connection between the theoretical components and the specific aims of the current study could be articulated more clearly. Strengthening the link between theory and application would help justify the modeling choices and better support the rationale behind the subsequent methodological development.

Response 6: We changed the order of Theoretical Background to be consistent with the methodology and to make the relationship between these two measures clearer, and we have expanded the discussion to strengthen the connection between the theoretical framework and the methodological objectives of the study. The revised text clarifies that the Importance Measures (Birnbaum, RAW, RRW, FV, and Criticality) are used to both rank components and interpret how reliability propagates through engineering systems. Each measure represents a different reliability dimension: structural dependence, vulnerability, probabilistic contribution, and relative risk relevance. This allows for a more complete understanding of how system performance responds to component behavior. These measures are then integrated with the RPN within the FMEA framework, linking reliability modeling with maintenance prioritization.

Furthermore, we create a new section named discussion. In this section reinforces the interpretative connection between the theoretical framework and the study’s specific objectives. It now elaborates on how the application of Importance Measures and RPN provides complementary insights for uncertainty-aware decision-making, thereby strengthening the link between theoretical modeling principles and their practical implications in reliability-based maintenance engineering.

Comments 7: The "Methodology" section presents the modeling framework and computational procedures, but certain aspects would benefit from greater clarity and precision. In particular, the description of assumptions, parameter selection, and boundary conditions could be more thoroughly explained to ensure transparency and reproducibility. A clearer articulation of how each methodological step aligns with the study's objectives would improve the section's coherence and scientific robustness.

Response 7: We appreciate the reviewer’s observation and have strengthened clarity and precision in the Methodology as follows:

Assumptions and boundary conditions: We added the following paragraph at the end of section 3.4: “General assumptions: Unless stated otherwise, component failures are treated as statistically independent (dependences are represented by the FTA/RBD structure function); lifetime parameters are time-homogeneous over the analysis horizon; oper-ating conditions are stationary within the mission window; repairs are not modeled (focus on reliability rather than availability). Candidates’ lifetimes, families, and parameter estimation follow Section 3.2; IM are computed as in Section 3.3. and para-metric uncertainty is quantified and propagated as in Section 3.4. Dataset-specific assumptions (e.g., mission time, data sources) are detailed in the Case study.”

Parameter selection: In Section 3.2 (From FMEA to system reliability), we clarify the parameter-estimation protocol: MLE for candidate lifetime families (Exponential, Weibull, Gamma), model choice via goodness-of-fit (e.g., Kolmogorov-Smirnov), and, where informative, AIC/BIC. Appendix A presents the best models fitted and parameters to replicate the Reliability analysis and uncertainty quantification.

Step-objective alignment: This alignment is made explicitly in two existing places:

- Immediately after the first reference to Figure 1: “Numerically, the workflow after qualitative assessment proceeds as: estimate lifetime parameters for each component, we compute reliabilities, after we evaluate system reliability via FTA or RBD, to compute IMs, and finally we synthesize with FMEA by pairing each prioritized component with its top failure modes and RPNs.”

- At the closing bridge paragraph at the end of Methodology, which reiterates the transition and explicitly notes that parametric uncertainty propagation (Section 3.4) yields interval estimates and rank stability:“As summarized in Figure 1 and detailed in Section 3.1-3.4, the transition from qualitative to quantitative analysis proceeds by estimating component lifetimes mod-els, assembling the system structure function via FTA/RBD, computing IMs, and prop-agate parameter uncertainty to obtain interval estimates.”

- These focused edits make assumptions explicit, specify parameter-selection rules, and clarify boundary conditions and objective alignment, thereby improving transparency, reproducibility, and coherence.

Comments 8: The inscriptions in Figure 1 are extremely small, making them virtually illegible. I recommend that the authors enlarge the text elements to ensure readability and improve the overall clarity of the figure.

Response 8: Figure 1 has been redrawn.

Comments 9: Figure 2 must also be significantly enlarged to be appreciated.

Response 9: Figure 2 has been redrawn.

Comments 10: The results section provides a range of outputs derived from the proposed methodological framework, offering quantitative insights into the modeled phenomena. However, the current structure merges the presentation of results with interpretative commentary, which risks obscuring the clarity and analytical rigor of both components. Separating the results from the discussion would significantly enhance the manuscript’s readability and improve the logical flow of the argument. By clearly distinguishing between what the model produces and how these outcomes are interpreted in relation to the research objectives and theoretical framework, the authors would allow readers to better assess the validity and significance of the findings. Such a division would also create space for a more focused and critical reflection in the discussion section, where the implications, limitations, and potential applications of the results could be addressed more explicitly. Structuring the paper in this way would help highlight the substance of the research and improve the overall communication of its contributions.

Response 10: We appreciate the reviewer’s observation. In response, the manuscript was restructured to clearly separate the results from their interpretation. A new Section 5. Discussion was added to ensure this distinction.

The Results section now focuses only on presenting the quantitative outputs of the proposed framework, including system reliability evaluation, uncertainty propagation, and failure mode prioritization. In the section, we made a new figure to present the critical component use IM.

The new Discussion section interprets these results in the context of the study’s objectives, highlighting their methodological relevance, implications for maintenance planning, and practical applications.

Comments 11: The conclusion section effectively recaps the study’s content but would benefit from a clearer focus on how the findings apply in practical contexts and their broader relevance. This part of the manuscript offers an opportunity to highlight the core outcomes and respond more directly to the research questions. Including a more detailed acknowledgment of the study’s limitations and proposing directions for future inquiry would add an important perspective. Enhancing these aspects would help improve the overall clarity and impact of the conclusion.

Response 11: We appreciate the reviewer’s observation. The Conclusion section was revised to clearly emphasize the practical relevance of the findings and their connection to the research objectives. The updated version now highlights how the results can be applied in maintenance planning and reliability management, explicitly addresses the study’s limitations, and outlines directions for future research to extend the proposed framework.

Comments 12: Terms like "nuanced" and "pivotal" tend to recur in texts produced with the aid of generative language tools and may reduce the stylistic distinctiveness expected in academic writing. While not incorrect, the authors are encouraged to diversify their word choice to maintain a more precise and scholarly tone.

Response 12: Thank you for the suggestion. We reviewed the manuscript and replaced vague and AI-like terms with clearer wording, without changing the technical content. Representative edits include:

Introduction: “pivotal” central; “uncertainty-aware” under uncertainty / uncertainty-informed; “cross-pollination” Theoretical Background: removed unneeded intensifiers (e.g., notably and highly); in subsection 2.1 “insightful”decision-relevant (only when linked to a concrete result). Methodology: “uncertainty-aware prioritization” prioritization that accounts for uncertainty and “probabilistic rigor” probabilistic modeling (MLE with goodness-of-fit). Case study: “robust testbed” relevant testbed, “granular understanding” detailed understanding. Results: “significant effects ”large effects, “uncertainty-aware median” median under uncertainty, and “confirms the robustness” confirms the stability. Where appropriate, we also preferred quantitative sentences (medians, 90% intervals) over emphasis words.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The paper has been significantly improved after revision, and it is recommended to accept and publish it.

Reviewer 3 Report

Comments and Suggestions for Authors

Comments addressed