Adopting New Machine Learning Approaches on Cox’s Partial Likelihood Parameter Estimation for Predictive Maintenance Decisions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

My comments are given as follows:

1. The literature review with regard to PHM and/or CBM can be significantly improved. There have been various recently published studies on this topic, such as  A hybrid repair-replacement policy in the proportional hazards model, A recursive method for the health assessment of systems using the proportional hazards model, A dynamic inspection and replacement policy for a two-unit production system subject to interdependence, Joint optimization of lot sizing and condition-based maintenance for a production system using the proportional hazards model,  Condition-based maintenance with dynamic thresholds for a system using the proportional hazards model,  Optimal condition-based maintenance with general repair and two dependent failure modes, etc.

2. The definition of parameters following a formula should not be placed in another paragraph. For example, "Where X_{max}^* is the maximum value..." should be replaced by "where X_{max}^* is the maximum value..."

3. How to use the proposed approach for CBM decision-making can be further discussed.

4. The data in Table 1 can be explained.

5. The goodness-of-fit test results should be given to show whether the obtained estimates can be accepted.

Comments on the Quality of English Language

The English expression of this paper is good.

Author Response

Please see the attachment. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

While the article presents an elaborate methodology for adopting new machine learning approaches on Cox's partial likelihood parameter estimation for predictive maintenance decisions, there are several areas that warrant criticism and potential improvements:

1. The innovativeness of this research in comparison to existing literature must be explicitly highlighted in the Introduction.

2. The article lacks a detailed theoretical foundation for the chosen machine learning algorithms (Gradient Boosting, Random Forest, Genetic Algorithm) and their suitability for the specific problem at hand. Providing more contexts on why these algorithms were selected and how they address the challenges of parameter estimation in Cox's partial likelihood would enhance the theoretical grounding of the methodology.

3. When referencing theories or formulas in the article, attention must be paid to their interconnections. For example, α^ipc, ϵ, and Z_i(t) should be explained and cross-verified. This applies throughout the entire manuscript. Additionally, it is recommended that the authors provide a flowchart detailing the entire analytical process to facilitate reader understanding.

4. The data used in the case study are derived from an electrical distribution company in Chile. The data captured in Table 1 must be explained in the article, such as electric demand, C2H4, etc., and clarification should be provided on why this data was collected. They should possess special analytical significance in the study or be explained if not.

5. The case study is limited to a specific industry, and the article lacks discussion on the generalizability of the proposed methodology to other industries or contexts. Including a discussion on the external validity of the results and potential challenges in applying the methodology to different scenarios would be valuable.

6. Physical quantities in relevant Tables must be labeled with units, such as in Tables 1, 8, 10, 12, etc.

7. The final application is only described in Figures 1 and 2, and it has not been compared with current research. Consequently, the significance or key findings of this study cannot be effectively highlighted in this study.

8. The conclusion should be concise and quantitatively highlight the innovativeness and contribution of this research.

Author Response

Please see the attachment. 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript investigated innovative non/semi-parametric approaches to address the problems of boundaries assessment and initial value strategy in the predictive maintenance decision scenarios. The authors' research is interesting and could bring a boost to the field. The contribution is outstanding and evident, both in the context of the application and in the methodological analysis. This manuscript could almost be accepted, but it would do well to consider the following questions.

-- The title of the manuscript should not be followed by a period.

-- I think the highlight part is good, but it's not clear if MDPI is allowed to have this.

-- In the ‘Case Study and Discussion’ section，the authors are encouraged to introduce results from other literature for comparison. On one hand, this would highlight the advantages of the proposed method, and on the other hand, readers would be able to better understand the research motivations of this paper.

-- The references are dated and it is recommended that they be updated.

Author Response

Please see the attachment. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed my comments properly. I have no further comments or questions.

Reviewer 2 Report

Comments and Suggestions for Authors

The reviewer checked the manuscript of machines-2804328-v2 carefully. It is apparent that some contents from the manuscript have been improved according to the reviewer’s suggestions. The second revised comments are recorded as follows:

 1. The innovativeness of this research in comparison to existing literature must be explicitly highlighted in the introduction.

Reviewer’s 2nd comment: Modifications have been made to the Introduction, Literature Review, and other sections to explicitly clarify the main contributions previously stated in the Highlights subsection.

2. The article lacks a detailed theoretical foundation for the chosen machine learning algorithms (Gradient Boosting, Random Forest, Genetic Algorithm) and their suitability for the specific problem at hand. Providing more contexts on why these algorithms were selected and how they address the challenges of parameter estimation in Cox's partial likelihood would enhance the theoretical grounding of the methodology.

Reviewer’s 2nd comment: It has been corrected via the advice of the reviewer.

3. When referencing theories or formulas in the article, attention must be paid to their interconnections. For example, α^ipc, ϵ, and Z_i(t) should be explained and cross-verified. This applies throughout the entire manuscript. Additionally, it is recommended that the authors provide a flowchart detailing the entire analytical process to facilitate reader understanding.

Reviewer’s 2nd comment: A flowchart has been added at the beginning of Section 3 ('Model Formulation'), detailing the analytical process to enhance reader understanding. Additionally, a new sub-section, 3.1 ('Data Preparation'), has been incorporated into this manuscript.

4. The data used in the case study are derived from an electrical distribution company in Chile. The data captured in Table 1 must be explained in the article, such as electric demand, C2H4, etc., and clarification should be provided on why this data was collected. They should possess special analytical significance in the study or be explained if not.

Reviewer’s 2nd comment: Corrections have been made based on the reviewer's advice, including adjustments to Table 1 and providing additional explanations in lines 390 to 398.

5. The case study is limited to a specific industry, and the article lacks discussion on the generalizability of the proposed methodology to other industries or contexts. Including a discussion on the external validity of the results and potential challenges in applying the methodology to different scenarios would be valuable.

Reviewer’s 2nd comment: New analyses discussing the generalizability of the proposed methodology have been added at the end of the Case Study and Discussion section. Similar efforts have been made for Tables 13 and 14.

6. Physical quantities in relevant Tables must be labeled with units, such as in Tables 1, 8, 10, 12, etc.

Reviewer’s 2nd comment: It has been corrected via the advice of the reviewer.

7. The final application is only described in Figures 1 and 2, and it has not been compared with current research. Consequently, the significance or key findings of this study cannot be effectively highlighted in this study.

Reviewer’s 2nd comment: No comments.

8. The conclusion should be concise and quantitatively highlight the innovativeness and contribution of this research.

Reviewer’s 2nd comment: The Conclusions section has been rewritten to clarify the innovativeness and contributions, following the advice of the reviewer.

Proposed changes must be marked in different colors to make it easier for reviewers to verify.