An Analytic Approach to the Cox Proportional Hazards Model for Estimating the Lifespan of Cutting Tools

Round 1

Reviewer 1 Report

After reviewing the manuscript ID JMMP-741791, titled "An Analytic Approach to the Cox Proportional Hazards Model for Estimating the Lifespan of Cutting Tools", please find below my remarks:

1. The paper structure is very good with clearly identified sections and subsections that present the selected topic and the work that has been carried out in a straightforward manner. The same applies to all Tables and Figures which are clearly captioned, labeled and easy to read while visualizing the results efficiently.

2. The written language is very good with almost no spelling/grammar errors throughout the paper. Only 3 could be found: in the introduction, line 30 instead of "...provide aid as for..." it should read "provide aid for...". Similarly, on page 6, line 159 instead of “It is can also…” it should read “It can also …”. Finally, on line 174 “…which can be analytically be satisfied…” should read “…which can be satisfied analytically…”.

3. The paper’s main contribution is a transformation of the cutting speed data using a logarithmic expression so as to improve the quality of fit of the Cox Proportional Hazards model when it comes to predicting the useful life of a cutting tool used in turning processes. This paper builds on the authors’ previous work where such a transformation was not used, leading to some limitations of the model’s performance for different areas of the wear evolution curve. The current paper provides a sound mathematical/analytical approach and the included results that compare the fit of the model with and without the proposed transformation support this approach with evidence.

However, section 4.2 that presents the numerical validation procedure could provide some further information regarding the generation of the tool degradation trajectories. Specifically, it is not explained how the parameters of this procedure were chosen (number of trajectories per cutting speed value, range of cutting speeds and discretization etc.). It is also not clear under which criteria the total of 4000 trajectories were further separated in the learning and control sets (each with 2000 trajectories).

Summarizing, I think that the paper can be accepted for publication after the above minor revisions have been made.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The article  "An Analytic Approach to the Cox Proportional Hazards Model for Estimating the Lifespan of Cutting Tools" is in subject of JMMP.

An article presents an interesting way of prediction tool life of cutting edge.  I have some comments to authors.

Comment 1

  In introduction you analyse of 33 references including some actual (2016 year).

But in the years that followed, another topic appeared in the field, including the use of neural networks to predict edge wear and also to recognize wear from the image obtained from the camera.

Please add some references from this area of research.

Comment 2

On 4 page you wrote " The depth of cut is kept constant at 1.5 mm and the feed at 0.18 mm/rev. The cutting speed is first kept constant at 340 m/min for the 29 degradation trajectories, then the experiment is repeated at different cutting speeds. The degradation evolution paths of the cutting inserts with machining time is represented in Figure 3. In this figure, the time slicing relative to the piecewise approach are highlighted.   Can you explained it? Where are results?  

Comment 3  

Bye the way I also suggest to consider organising the article so that usually the research technics and methods are presented in Materials and Methods chapter  

Comment 4  

I propose remove Fig. 1and Fig. 2 -these are issues generally known to the specialist in the subject. By the way in Fig 1 you present different values ​​of Vb, but in the article you use Vbcrit, which parameter is used the largest, average?     I also suggest to consider organizing the article so that the research technique and methodology are in one place in practice, chapter is used Materials and Methods  

Comment 5

In chapter 3 you write

This equation must be developed to achieve a clear answer, but two assumptions must be made at this point in order to obtain the analytic expressions that can be compared:
1. the hazard baseline function is fitted on a Weibull distribution
2. the Mean Up Time of the experimental sample that allowed to fit the Cox PH Model follows eq. (7)

I propose use in this place the bulletting

Comment 6

Figure 4. Prognosis for cutting tools with and without logarithmic transformation

I propose change of Fi.4 description on more detailed. What you prognosis?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf