Enhancing System Safety and Reliability through Integrated FMEA and Game Theory: A Multi-Factor Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Thank to the author’s contribution to the filed of safety assessment in this and previous studies. This manuscript presents an advanced approach that synergizes FMEA with game theory, offering a robust framework for holistic risk analysis. To verify its adaptability, a case study about complex healthcare system was made a further analysis.

 

Author Response

Thank you for your valuable and kind feedback. 

Reviewer 2 Report

Comments and Suggestions for Authors

The topic of the article is very interesting and is in line with the goals and scope of the journal. However, I suggest a revision of the article according to the following comments.

 

1.The Abstract can still be improved. It is important to emphasize the main results, conclusions, and scientific contribution of the paper. Please revise the summary to strengthen this information.

2.According to the instructions for authors of the journal Safety, citations to research papers in the text must be indicated numerically with straight brackets, so I suggest replacing the curly brackets with straight brackets.

3.The research objectives are not clearly defined at the end of the introduction, and the research questions to be answered by the results of this work are not mentioned. The authors must clearly state how the contribution of this paper differs from work already done in this area. The introduction should conclude with some hypotheses, the main conclusions and scientific contributions to other studies in the field. At this stage, it is not clear what research question the authors are trying to answer. For example, it states, "This research stands out for its groundbreaking contributions in two primary domains. First, we pioneer the integration of Game Theory within the framework of FMEA, uniquely tailoring it to prioritise failure modes. This innovative approach adds a fresh dimension to the risk assessment discourse. Second, we present a novel method incorporating Pythagorean fuzzy uncertain linguistic variables. This technique is employed to calculate risk factor scores, thereby elevating the accuracy and efficacy of the entire analytical process." In my opinion, these goals are too vague. What are the problems mentioned in the previous text of the introduction that this paper aims to address? Please underline this information at the end of the introduction.

4.Section 2.1 needs to be reworded; a section cannot be just a list of bullet points. Consider adding two or three paragraphs to this subsection.

5.In section 2.3, please explain the meaning of the variables Z1 and Z2 when the concept of Nash equilibrium is described.

6.On page 5, line 243, check the citation brackets, there is an additional curly bracket that is not needed, chek this in all manuscript.

7.The position of Figure 1 must be on the page on which it is called up for the first time, i.e. place Figure 1 on page 6

8.In the methodology proposed by the authors, which is presented on page 8, point (i), the authors point out that it is necessary to identify the least significant risk factor. The authors also suggest that these risk factors be identified by decision makers through a qualitative approach. Does it make sense to consider risk factors with low significance in risk analysis and risk management? Clarify this question in the manuscript. I also ask if these decision makers are using any tools (e.g. FMEA) to determine the criticality of these factors, or do they just rely on their opinion? Explain this question in your manuscript. In practice and with a qualitative approach, is there a consensus in determining these risk factors? What does the model look like in situations where there is no consensus?

9.Page 10, immediately after definition 3, there are a number of expressions that need to be numbered, the bullets need to be removed. Review the entire article on this topic.

10.How does the proposed model take into account the barriers to mitigation and prevention?

11.In the proposed methodology, the authors use the traditional FMEA risk variables, including the detectability variable. How does the proposed model account for the ability to mitigate or/and prevent a failure mode once it has been detected? The detectability variable aims to measure the ability to detect a particular failure mode. However, the ability to deal with the detected failure is not measured by this variable. To what extent is this aspect taken into account in this proposed methodology? Explain this question in the manuscript.

12.The authors repeatedly mention risk factors, describe the authors' perception of risk factors in the manuscript or cite a standard that contains the definition of risk factors used in this paper.

13.The definitions in section 3.2 are based on the work cited in references 121, 122-125. I suggest that this section be moved to Section 2 where it deals with the literature review.

14.The paper lacks a discussion. The authors have not discussed and interpreted the results in relation to previous studies. The results of the proposed model should be compared with the results of major models that prioritize failure modes for the same risk scenario to highlight the advantages in terms of the application of the model or in terms of the accuracy or significance of the results obtained.

15.The authors must highlight the limitations of the study (proposed model) and the simplifications/assumptions adopted.

16.Conclusions should be updated with further findings, limitations, and future extensions.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Dear Reviewer,

Thank you for your thoughtful and detailed feedback on our manuscript. We highly appreciate your recognition of the article's alignment with the journal's goals and scope. We have carefully considered each of your suggestions and have made comprehensive revisions accordingly:

1. Enhanced Abstract: The abstract has been extensively revised for greater clarity. It now explicitly highlights the key results, the novel contributions of our research, and the broader scientific implications, thereby offering a concise yet comprehensive overview of the study's value.

2. Citation Format Adjustment: We have meticulously revised the citation format throughout the manuscript, replacing all instances of curly brackets with straight brackets, aligning with the journal's citation style guidelines.

3. Refined Introduction with Clear Objectives: The introduction has been restructured to articulate the research objectives and questions more distinctly. We have also delineated how our work diverges from existing research, detailing the unique contributions our study offers to the field, specifically addressing the gaps identified in earlier sections of the introduction.

4. Expanded Section 2.1: Section 2.1 has been transformed from a bullet-point list into a more traditional narrative structure. This section now contains elaborative paragraphs that provide a richer context and a deeper understanding of the listed points.

5. Detailed Explanation of Variables Z1 and Z2: In Section 2.3, we have included a comprehensive explanation of the variables Z1 and Z2 within the Nash equilibrium framework, offering a clearer understanding of their roles and significance in our research.

6. Consistent Citation Formatting: We have corrected the citation error on page 5, line 243, and thoroughly reviewed the entire manuscript for consistency in citation formatting, ensuring adherence to the journal's guidelines.

7. Optimal Placement of Figure 1: As per your recommendation, Figure 1 has been relocated to its first point of reference within the text on page 6, ensuring a smoother reader experience.

8. Clarification on Risk Factor Significance and Decision-Making Process: We have expanded the discussion around the identification of less significant risk factors in the methodology section. This includes a detailed explanation of the qualitative approaches and tools used by decision-makers in assessing risk factor criticality, along with insights into how consensus is reached in situations with varying opinions.

9. Revised Formatting for Expressions and Bullets: We have replaced the bullet points with numbered expressions immediately after Definition 3 and conducted a comprehensive review of the entire manuscript to ensure consistent and appropriate formatting.

10. Incorporation of Mitigation and Prevention Barriers: A new section has been added to explain how the proposed model considers barriers in mitigation and prevention strategies, thereby enhancing the depth of our methodological approach.

11. Elaboration on Detectability and Mitigation/Prevention: The manuscript now includes an elaborate discussion on how the proposed model accounts for not just the detection of failure modes but also their mitigation and prevention. This provides a more holistic view of the risk management process.

12. Detailed Description of Risk Factors: We have added a section that specifically addresses our perception of risk factors, along with references to standards and definitions that underpin our approach.

13. Rearrangement of Definitions to Literature Review Section: The definitions previously located in Section 3.2 have been moved to the literature review section (Section 2), providing a more logical and coherent flow of content.

14. Comprehensive Discussion Section: A new, more robust discussion section has been added, where we compare and contrast our results with significant existing models. This section aims to highlight the unique advantages and accuracy of our proposed model in the context of the existing literature.

15. Inclusion of Study Limitations and Assumptions: A detailed section outlining the limitations and assumptions of our study has been included, providing a transparent and honest appraisal of our research approach.

16. Revised and Enhanced Conclusions: The conclusion section has been thoroughly updated to reflect the new findings, discuss the limitations identified, and suggest potential avenues for future research.

We trust that these extensive revisions have addressed your concerns and significantly enhanced the manuscript's quality. We are eager to see our revised work contribute to the journal and the broader academic community.

Thank you once again for your valuable input and for the opportunity to improve our manuscript.

Reviewer 3 Report

Comments and Suggestions for Authors

The article is factually correct. I have no comments on the layout of the article. The study concerns current scientific issues. The article presents an advanced approach that combines FMEA with game theory. In this way, it was proposed to reduce the shortcomings of the classic FMEA method.

Suggestions for improvements.

-) Please state clearly in the abstract what was the purpose of the study? Who and what can the results from the article be useful for?

-) I suggest not ending the subsection with bullet points, e.g. 2.1. Please add the ending of the subchapter.

-) In the text before Fig. 1 should be a reference to the number of this fig. I propose to supplement this reference and apply this principle throughout the article.

-) Please consider making the figure more detailed. 1. In my opinion, you can add input and output data, you can add a start and an end (like in an algorithm or a flowchart). From each field (including Listing current... and Determining ... in Pre-Step) we should reach the end of the process. This is not the case now.

-) I propose the text from Fig. 1. between 3 and 3.1 transform into a subchapter.

-) I recommend not ending subsections with a figure.

-) Please describe the axes in Fig. 3.

-) I propose not to finish the subsection of Fig. (e.g. Fig. 3).

-) If possible, add more practical implications in the summary.

In my opinion, the article can be published after implementing the proposed improvements.

I am not qualified to assess the quality of English in this paper

Author Response

Dear Reviewer,

Thank you for your comprehensive review and positive feedback on the article titled "Integrating FMEA and Game Theory for Enhanced System Safety and Reliability in Healthcare." I greatly appreciate your recognition of the factual correctness of the article and its contribution to current scientific discussions by advancing the combination of FMEA with game theory.

In response to your valuable suggestions for improvement, I have undertaken the following revisions:

1. Abstract Clarification: The abstract has been revised to clearly state the purpose of the study. It now explicitly outlines who the intended audience is and how they might benefit from the findings of this research.

2. Subsection Formatting: The formatting of subsections, particularly 2.1, has been modified to ensure that they do not end with bullet points. A conclusive sentence has been added to each to provide a proper ending to the subchapters.

3. Figure References: References to Figure 1 and all other figures have been thoroughly reviewed and included in the text preceding each figure. This ensures clarity and ease of understanding for readers as they navigate through the article.

4. Enhancing Figure Details: Figure 1 has been enhanced to include input and output data, along with a clear start and end point, similar to a flowchart. This modification ensures a comprehensive understanding of the process flow and addresses the current lack of connectivity between steps.

5. Text and Figure Organization: The text between Sections 3 and 3.1, previously encapsulated in Figure 1, has been transformed into a subchapter for better clarity and structural flow.

6. Subsection and Figure Separation: Subsections have been revised to ensure they do not conclude with a figure. This change provides a smoother narrative flow and allows for more detailed textual conclusions in each subsection.

7. Figure Axes Description: The axes in Figure 3 have been clearly described to enhance understanding and provide context for the data presented within the figure.

8. Subsection Conclusion: The practice of ending subsections with figures, such as Figure 3, has been revised. Subsections now end with explanatory text to provide a more comprehensive and coherent reading experience.

9. Practical Implications in Summary: The summary has been expanded to include more practical implications of the study, highlighting its relevance and potential applications in real-world scenarios.

I am confident that these revisions have significantly improved the manuscript, addressing each of your insightful suggestions. Your feedback has been instrumental in enhancing the overall quality and clarity of the article.

Thank you once again for your constructive critique and endorsement for publication post-improvements. Your guidance has been invaluable.

Reviewer 4 Report

Comments and Suggestions for Authors

This article introduces and demonstrates a methodology integrated FMEA and Game theory to enchance system safety and reliability in a complex healthcare unit under the emergency condition. The following suggestions are provided for the author to consider and correct:

1) Equation 5 was repeated in Page.9, but equation 17 was missed. Recheck the equation order after revision, please.

2) There are some cited references format in the content is wrong (L237, L243, L255, L261). The cited references no. 66 and no.127 replace by "Theory of Games and Economic Behavior"(L221) and "Zhang and Xu (107)"(L400), respectively. The cited reference no.66 in "Reference section" (L966-967) suggest to correct.

3) The description of ranking of failure modes in L603-604 and L712-713 are not consistent.

4) Correct the "AHP" (L316) to "Analytic Hierarchy Process (AHP)".

5) Correct the "Spearman coefficient" (L763) to "Spearman correlation coefficient".

6) The codes of decision makers in Table 2 (L570) and Table A of Appendix A (L828-829) are not consistent with the description of Definition 7 (L469-473).

Author Response

Dear Reviewer,

Thank you for your insightful and constructive feedback on the article titled "Integrating FMEA and Game Theory for Enhanced System Safety and Reliability in Healthcare under Emergency Conditions." Your meticulous review and valuable suggestions have significantly contributed to refining the quality and accuracy of the manuscript.

I am pleased to inform you that the necessary revisions have been made in accordance with your recommendations:

1. Equation Order: The repetition of Equation 5 and the omission of Equation 17 have been rectified. The order of equations has been thoroughly reviewed and corrected to ensure sequential coherence and clarity.

2. Citation Errors: The formatting errors in the cited references (specifically at Lines 237, 243, 255, 261) have been corrected. References no. 66 and no. 127 have been accurately replaced with "Theory of Games and Economic Behavior" (Line 221) and "Zhang and Xu (107)" (Line 400), respectively. Additionally, the citation for reference no. 66 in the References section (Lines 966-967) has been amended as suggested.

3. Consistency in Failure Mode Ranking: The previously inconsistent descriptions of failure mode rankings in Lines 603-604 and 712-713 have been aligned for uniformity and accuracy.

4. Terminological Clarifications: The abbreviation "AHP" on Line 316 has been expanded to "Analytic Hierarchy Process (AHP)," and the term "Spearman coefficient" on Line 763 has been updated to "Spearman correlation coefficient" for enhanced clarity and precision.

5. Uniformity in Decision Maker Codes: The discrepancies in the codes of decision makers between Table 2 (Line 570) and Table A in Appendix A (Lines 828-829) have been addressed, ensuring consistency with the description provided in Definition 7 (Lines 469-473).

I appreciate your thoroughness in reviewing the manuscript and your commitment to enhancing the scholarly rigor of our work. Your guidance has been invaluable in ensuring that the article meets the highest standards of academic excellence.

Reviewer 5 Report

Comments and Suggestions for Authors

The paper is interesting but there are some flaws worth improving:

The paper mentions a Game Theory-based approach, but the specific application and how game theory is integrated into the FMEA methodology are not thoroughly explained. A more detailed description of the game theory model and its components would enhance clarity.

The negative Spearman correlation coefficient between the Game Theory-based approach and the Linguistic-based method raises questions. A negative correlation may indicate a lack of agreement between these methods, and further clarification or justification for this observation is necessary.

The suggestion for future research to explore different game theory classes lacks clarity on the criteria for selecting the most appropriate class. Providing guidelines or factors that should be considered in this selection process would strengthen this recommendation.

Elaborate on the importance of comparing various linguistic variables. Clearly articulate the research questions or hypotheses driving this comparison and explain how it contributes to the robustness of the proposed methodology.

If introducing imaginary Risk Priority Numbers (RPNs), provide a strong theoretical and practical justification. Explain how this addition improves risk assessment and decision-making in a way that is more effective than traditional RPNs.

Comments on the Quality of English Language

It's ok

Author Response

Dear Reviewer,

Thank you for your insightful comments and the opportunity to further refine our paper. Your feedback is invaluable in enhancing the overall quality and clarity of our research. We have addressed each of your points as follows:

1. Detailed Integration of Game Theory in FMEA: We acknowledge the need for a clearer explanation of how Game Theory is integrated into the FMEA methodology. The paper has been revised to include a comprehensive description of the Game Theory model, detailing its components, the rationale behind its selection, and the specifics of how it complements and enhances the traditional FMEA process. This expansion aims to provide a thorough understanding of the innovative aspect of our approach.
2. Clarification of the Negative Spearman Correlation: Upon careful consideration, we have identified several reasons why a detailed exploration of the negative correlation was not included in the manuscript:

• Manuscript Length Constraints: The most significant constraint we faced was the length of the manuscript. Currently, our paper, including the two appendices, is approximately 18,000 words long, which is already at the upper limit of what is permissible for our submission. Delving into a detailed analysis of the negative correlation would require a substantial expansion of the text, thereby exceeding the word limit and potentially compromising the readability and coherence of the paper.
• Focus and Scope of the Study: Our primary focus in this research was to introduce and validate the integration of Game Theory within the FMEA framework and the novel use of Pythagorean fuzzy uncertain linguistic variables. This focus determined the scope and boundaries of our analysis. While the negative correlation is an intriguing observation, it fell outside the central aim of our study, and a thorough investigation of this aspect would have diverted attention from our main objectives.
• Complexity of Analysis: Analyzing the negative correlation in depth involves a multifaceted examination of both methodologies, possibly requiring additional data collection and complex statistical analysis. Given the already intricate nature of our study, integrating this additional layer of analysis would not only have lengthened the manuscript but also added a level of complexity that might detract from the clarity and directness of our primary findings.
• Future Research Opportunity: We believe that the investigation of this negative correlation presents an excellent opportunity for future research. It can be explored in a separate, dedicated study that specifically focuses on understanding the dynamics and implications of this observation. This approach would allow for a more detailed and targeted exploration without the constraints of the current manuscript's length and focus.

Criteria for Selecting Game Theory Classes: In the section suggesting future research on different classes of Game Theory, we have now included specific guidelines and factors for selecting the most appropriate game theory class. This addition provides clarity on the criteria that researchers should consider, such as the nature of the decision-making environment, the complexity of the system under study, and the specific objectives of the risk assessment.

Comparing Various Linguistic Variables: We have elaborated on the importance of comparing different linguistic variables in the context of risk assessment. This includes articulating the research questions or hypotheses that drive this comparison and explaining how this analysis contributes to the robustness and reliability of the proposed methodology. This clarification aims to highlight the significance of linguistic variable analysis in enhancing the depth and accuracy of risk assessments.

Justification for Imaginary RPNs: Thank you for your thoughtful feedback regarding the introduction of imaginary Risk Priority Numbers (RPNs) in our manuscript. We appreciate the importance of providing a strong theoretical and practical justification for any new methodological introduction, particularly when it represents a significant departure from traditional practices.

However, after careful consideration and review of the research objectives, we have concluded that the introduction of imaginary RPNs may not align well with the core focus of our study. Our decision is based on several key considerations:

1. Alignment with Research Goals: The primary aim of our study is to explore the integration of Game Theory within the FMEA framework and the application of Pythagorean fuzzy uncertain linguistic variables. Introducing a concept like imaginary RPNs, while innovative, might diverge significantly from our central research theme. We believe that maintaining a clear focus is crucial for the coherence and impact of our study.
2. Complexity and Scope: Incorporating imaginary RPNs into our analysis would add a layer of complexity that may extend beyond the scope of the current paper. Our research is already rich in novel methodologies and theoretical perspectives, and we are concerned that adding another complex element could potentially overburden the narrative and dilute the primary message of our research.
3. Theoretical Justification: While imaginary RPNs could offer a novel approach to risk assessment, the theoretical grounding for their application in our specific context is not as robust as we would like. Without a strong theoretical basis, we risk undermining the scientific rigor of our study.
4. Practical Implications: The practical implications of implementing imaginary RPNs in real-world scenarios are not fully clear at this stage. Given that our research aims to offer actionable insights for practitioners, we must be cautious about introducing concepts that may not have immediate or clear practical applications.
5. Future Research Potential: We acknowledge the potential of imaginary RPNs in enhancing risk assessment and decision-making processes. However, we believe that this concept would be better explored in a dedicated study where it can be examined in depth, without the constraints of the current research focus.

In light of these considerations, we have decided to adhere to the conventional use of RPNs in our study. We believe this approach maintains the clarity and relevance of our research, ensuring that our contributions are both meaningful and directly applicable to the field.

We believe these revisions address the concerns you have raised and significantly strengthen the paper. Our goal is to ensure that the research presented is both transparent and robust, offering valuable insights into the integration of Game Theory with FMEA for risk assessment.

Thank you once again for your constructive critique, which has been instrumental in enhancing the quality of our work.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

After analyzing the revised version of the article "Enhancing System Safety and Reliability through Integrated FMEA and Game Theory: A Multi-Factor Approach", it can be stated that the authors have significantly improved the article.

In this sense, I believe that the article in the revised version meets the necessary requirements to be published in the journal Safety.

Sincerely,

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Thank you. 

Reviewer 3 Report

Comments and Suggestions for Authors

The article has been improved in line with your suggestions. In my opinion, the study, in its current form, is suitable for publication.

Author Response

Thank you. 

Reviewer 4 Report

Comments and Suggestions for Authors

The references of no.66 (L1178-1179) and no.128 (L1303-1304) do not amend correctly. Accept this revised manuscript after minor correction.

Author Response

Thank you. It is corrected now. 

Reviewer 5 Report

Comments and Suggestions for Authors

Authors made good job to improve the paper.

Comments on the Quality of English Language

It's ok.

Author Response

Thank you.