Optimal Maintenance Thresholds to Perform Preventive Actions by Using Multi-Objective Evolutionary Algorithms

Round 1

Reviewer 1 Report

The topic of the paper and the propose idea to solve the problem is interesting. However, section 5, which is the core of the paper should be definitely improved, as much information critical for understanding the paper is not presented.

Are the profit (P) and maintenance cost (C) expressed in the same quantity (in EUR)? Is the purpose to minimize the overall cost of the production? If so, do you really need multi-objective optimization, as in a matter of fact we have only one criterion expressed by P-C?

What is the length of the chromosome? What are the parameters encoded in the chromosome? Those in Tables 1-4? So what are the values of them shown in the tables? The optimal values? If so, of which point of the Pareto Front?

Table 5: please explain what do you understand by selection rate, crossover rate and mutation rate (e.g. 0.75 is what, the probability of changing any position or single position in the chromosome?)

Figure 3: what is on the vertical axis? Maintenance cost?

Some other remarks:
lines 30-31 "almost no emphasis has been given" or "almost no emphasis was given"
line 61 "by an effectiveness"
line 120 "the stopping criteria used has been the convergence of the result after 5 generations" - can you please explain this better?
line 158 "as it models using" ?
lines 164-168 please reformulate the text and split the sentence into several ones to make it clear.

Author Response

REVIEWER 1, ROUND 1

Responses to Reviewer 1

We are very grateful for your constructive comments, criticism, suggestions, and references. We have done our best to address them all. We believe that, as a result, the paper has substantially improved. Below we provide point-by-point responses to your comments.

English language and style

( ) Extensive editing of English language and style required
( ) Moderate English changes required
(x) English language and style are fine/minor spell check required
( ) I don't feel qualified to judge about the English language and style

Comments and Suggestions for Authors

The topic of the paper and the propose idea to solve the problem is interesting. However, section 5, which is the core of the paper should be definitely improved, as much information critical for understanding the paper is not presented.

Again, thank you for your revision as well, as it improves significantly the quality of our work. We respond to each of the comments/questions formulated one by one in the following lines:

Are the profit (P) and maintenance cost (C) expressed in the same quantity (in EUR)?

Thank you for the observation. Correct, both terms are expressed in EUR. We did not realize that the tiff version (not the excel version, but the tiff one) of Figure 3 did not include the unit for the cost (in the graph both terms are expressed in thousands of euros). Thank you for paying attention to that, we have corrected Figure 3 so that both terms, P and C have now their units.

Is the purpose to minimize the overall cost of the production? If so, do you really need multi-objective optimization, as in a matter of fact we have only one criterion expressed by P-C?

Yes, we do consider that we need a bi-objective optimization with these two criteria as we did in other similar papers. The main ratio to be optimized in business is the Return Of Investment or ROI (which is given by the following division: ROI=net profit / liabilities). The rest of the ratios are partially optimal. We will comment two examples:

a)    In companies and research papers people focuses on minimizing costs. For example, maintenance managers must confront maintenance expenses versus the unavailability cost of the machinery they save. Nevertheless, in some cases the margin of their products is so huge that optimal values can justify increases in maintenance costs that only cost savings cannot.

b)    In some cases a profit maximization can request a proportionally huge effort in terms of money that must be kept (in work in progress or stock value, maintenance expenses, quality control and so on). Depending on the moment, companies may have fluctuating cash limitations

For the above-mentioned reasons we think that the bi-objective optimization makes sense, as it does not only focus on profit maximization, but also it tries to keep costs under control.

In response to your comment, we have included in the next paragraph to line 120 a full explanation of why we have proposed this optimization problem:

“In this optimization approach, maintenance managers’ and plant managers’ purposes are considered jointly: maintenance managers usually try to minimize costs related to equipment inefficiencies (C(x)), whereas plant managers aim at maximizing the profitability of the plant (P(x)). It is widely known that multi-objective optimization should be complementary with respect to measures taken into consideration. In this case C(x) and P(x) are defined as complementary, since Y is defined as a constant value, so the cost terms of C(x) do not have influence on it. In a real system, Y is consequence of the sale price and all the productive and logistic costs, including the ones formulated in the equipment model. But, if the model had to consider C(x) to obtain Y, other costs, such as logistics, management and raw material costs should be considered. It is worth remarking that this very same joint C(x) and P(x) optimization approach was applied to the optimization of preventive maintenance in [9].”

What is the length of the chromosome? What are the parameters encoded in the chromosome?

We have reformulated section 5.1 to explain the length of the chromosome and the parameters within. The parameters encoded in the chromosome are the three w_c and M_min:

where w_c is the level of deterioration of the monitored component when a preventive maintenance (PM) action for reducing its wear/age will be performed, ranging from 1 to 260 days (integer)

and

M_min represents the minimum days (integer value) between two PMs. That is to say, if the maintenance wear or age reduced in a component via PM is small, a replacement of the component will be performed, so that the age tends to zero. M

We realize that without this explanation it is almost impossible to understand the problem, so we added this explanation in line 144. Thank you for the remark. We hope we made it better this time.

Those in Tables 1-4? No, not exactly. So what are the values of them shown in the tables? The optimal values? If so, of which point of the Pareto Front?

The values shown in Tables 1-4 are the constants needed for this optimization problem.

It could be that the fact that we did not explain sufficiently the chromosome has made you understand that values of Table 2 (parameters related to the effectiveness and length of the PREVENTIVE maintenance) are activities to be optimized. But this is not true. Take into account that when a component reaches its w_c age, a PREVENTIVE maintenance activity is performed in order to reduce its age or deterioration level. We hope that with this new explanation, the text becomes more understandable, but if further explanation is needed please let us know.

Table 5: please explain what do you understand by selection rate, crossover rate and mutation rate (e.g. 0.75 is what, the probability of changing any position or single position in the chromosome?)

You are right, we focused more on the use of the algorithm (on the application) rather than in the details. The selection rate represents the percentage of the best individuals of the solution matrix that will be selected to be ‘potential parents’ of the forthcoming generation. The crossover rate is the probability of exchanging genetic material between two parent individuals. In this case, the crossover probability indicates in which percentage a single point crossover will be applied. For the mutation, to be honest, we did not explain ourselves correctly. The term mentioned in the text is the mutation probability and not the mutation rate. The mutation probability indicates the percentage of the cases in which mutation will be applied after having performed crossover. The mutation rate whereas represents the percentage in which mutation is applied. In our case, it has been considered a standard-of-use 1/n as the mutation rate, being n the number of bits in the encoding of the decision variable.

We have included this explanation in line 157.

Figure 3: what is on the vertical axis? Maintenance cost?

Correct, as it has been stated before, we missed that detail, and we have updated Figure 3.

Some other remarks: Thank you for all of them. They have been taken into account and the paper has been improved.

lines 30-31 "almost no emphasis has been given" or "almost no emphasis was given",

It has been corrected, sorry for the mistake

line 61 "by an effectiveness", It has been corrected, sorry for the mistake

line 120 "the stopping criteria used has been the convergence of the result after 5 generations" - can you please explain this better? Yes, it has been commented that the simulation stopped after having no improvements in the result matrix in 5 consecutive generations

line 158 "as it models using" ? We have reformulated the sentence to make it understandable.

lines 164-168 please reformulate the text and split the sentence into several ones to make it clear. We have split and reformulated the text. We hope we made it clear enough this time.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper presents a work the uses multi-objective evolutionary computation algorithm, i.e., NSGA II to solve the maintains problem. The authors simulate it using two objective functions, i.e., cost and profit. The idea and motivation of the work have the potential value to further investigate, however, the presentation, methodology, and evaluation are rather poor to appeal the originality and contribution to the society in current version. 

First, it needs an explanation on cost and profit modelling, why these two functions are modelled as such form, please clarify this issue. 

Second, the authors use NSGA II as the optimizer for the problem, however, the parameter setting, e.g., crossover rate, and mutation rate are weird in optimization research field, it needs to consider furthermore for a better parameter setting. 

Third, the evaluation is very poor to stand as an academic work, it needs several trails evaluations and make a statistical conclusion, it needs to improve. 

fourth, the presentation of whole paper is hard to follow and understand, please ask an English native speaker to give it a proofread before review. 

I am sorry, but I have to reject this version of the work, it is hard to accept it in current stage of this work. 

Minor comments:

References are not used in Abstract, please delete them and use your own words to express such conclusion. 

Figure 1 is very rough data, please format it more visualizable.

Author Response

REVIEWER 2, ROUND 1

Responses to Reviewer 2

We are very grateful for your constructive comments, criticism, suggestions, and references. We have done our best to address them all. We believe that, as a result, the paper has substantially improved. Below we provide point-by-point responses to your comments.

English language and style

(x) Extensive editing of English language and style required
( ) Moderate English changes required
( ) English language and style are fine/minor spell check required
( ) I don't feel qualified to judge about the English language and style

Comments and Suggestions for Authors

Again, we show our gratitude to your comments as they improve the paper without any doubt. We respond to each of them in the following lines:

This paper presents a work the uses multi-objective evolutionary computation algorithm, i.e., NSGA II to solve the maintains problem. The authors simulate it using two objective functions, i.e., cost and profit. The idea and motivation of the work have the potential value to further investigate, however, the presentation, methodology, and evaluation are rather poor to appeal the originality and contribution to the society in current version.

Thank you for recognizing the interest of the topic and the suggestions.

First, it needs an explanation on cost and profit modelling, why these two functions are modelled as such form, please clarify this issue. 

You are right; it requires further explanation about why we select them and why we consider them complementary. Our proposal has been to reference and adopt the text we used in Ref (Oyarbide-Zubillaga, Goti and Sanchez, 2008), where in a similar case (preventive maintenance optimization, instead of condition based maintenance) the following text was used.

In response to your comment, we have included in the next paragraph to line 120 a comment indicating that “as in other cases (Oyarbide-Zubillaga, Sanchez & Goti, 2008), a cost profit optimization has been developed”. The lines included are the following:

In response to your comment, we have included in the next paragraph to line 120 a full explanation of why we have proposed this optimization problem:

“In this optimization approach, maintenance managers’ and plant managers’ purposes are considered jointly: maintenance managers usually try to minimize costs related to equipment inefficiencies (C(x)), whereas plant managers aim at maximizing the profitability of the plant (P(x)). It is widely known that multi-objective optimization should be complementary with respect to measures taken into consideration. In this case C(x) and P(x) are defined as complementary, since Y is defined as a constant value, so the cost terms of C(x) do not have influence on it. In a real system, Y is consequence of the sale price and all the productive and logistic costs, including the ones formulated in the equipment model. But, if the model had to consider C(x) to obtain Y, other costs, such as logistics, management and raw material costs should be considered. It is worth remarking that this very same joint C(x) and P(x) optimization approach was applied to the optimization of preventive maintenance in [9].”

Second, the authors use NSGA II as the optimizer for the problem, however, the parameter setting, e.g., crossover rate, and mutation rate are weird in optimization research field, it needs to consider furthermore for a better parameter setting. 

Third, the evaluation is very poor to stand as an academic work, it needs several trails evaluations and make a statistical conclusion, it needs to improve. 

We understand that these two points are strongly inter-related, so we will try to respond to them jointly.

Regarding the second point, we did not explain it correctly, and we have made an effort to improve our explanations. We have detailed this part by describing how the selection, crossover and mutation work. In this sense, we have included the following explanation in line 157:

The selection rate represents the percentage of the best individuals of the solution matrix that will be selected to be ‘potential parents’ of the forthcoming generation. The crossover rate is the probability of exchanging genetic material between two parent individuals. In this case, the crossover probability indicates in which percentage a single point crossover will be applied. For the mutation, to be honest, we did not explain ourselves correctly. The term mentioned in the text is the mutation probability and not the mutation rate. The mutation probability indicates the percentage of the cases in which mutation will be applied after having performed crossover. The mutation rate whereas represents the percentage in which mutation is applied. In our case, it has been considered a standard-of-use 1/n as the mutation rate, being n the number of bits in the encoding of the decision variable.

For the parameter setting (end of point two), and the fact that it needs several trails evaluations and statistical conclusion, we have little space for improvement.

1-    In other works we were allowed to do it (e.g. [1][2][3][4]).

2-    Actually, we made some trials before sending the initial version of this paper and we did not observe deviations in the quality of the Pareto front. We could state that we showed a slightly faster convergence with these parameters compared to others that have been tried. Nevertheless, we could not treat it scientifically (making a Design Of Experiments, for example) as it would take too much time.

3-    Several researchers use parameters based on experience and expert judgement, even in the specific case of CBM (e.g. [5]). We have done the same.

Therefore, for the aforementioned reasons, we would strongly prefer to keep this trial with the selection, crossover and mutation rates mentioned in the paper.

fourth, the presentation of whole paper is hard to follow and understand, please ask an English native speaker to give it a proofread before review. A C2 level English speaker has reviewed and modified the text (please see the changes marked in a different color).

I am sorry, but I have to reject this version of the work, it is hard to accept it in current stage of this work. We hope this new version meets your expectations this time. In any case, all suggestions are welcome.

Minor comments:

References are not used in Abstract, please delete them and use your own words to express such conclusion.

Reference [2] of the previous version has been deleted, whereas reference [1] has been included in the text.

Figure 1 is very rough data, please format it more visualizable.

Yes, you are right. We took the data form the WoS (Web of Science) and we kept is as it was. Now we have reconstructed the Figure and its quality is better.

References

1.        Oyarbide-Zubillaga, A.; Goti, A.; Sanchez, A. Preventive maintenance optimization of multi-equipment manufacturing systems by combining discrete event simulation and multiobjective evolutionary algorithms. Prod. Plan. Control 2008, 19, 342–355.

2.        Goti, A.; Sanchez, A.; Oyarbide-Zubillaga, A.; Guimaraes, N.; Isa¡as, P.; Goikoetxea, A. Money based maintenance model constrained multi-objective optimization. In; IADIS Press: Lisbon, 2006; pp. 49–56.

3.        Sanchez, A.; Goti, A.; Rodriguez, V. Condition based maintenance optimization under cost and profit criteria for manufacturing equipment. In; Taylor & Francis Group: London, UK, 2008.

4.        Goti, A.; Oyarbide-Zubillaga, A.; Sanchez, A. Optimizing preventive maintenance by combining discrete event simulation and genetic algorithms. Hydrocarb. Process. 2007, 86, 115–122.

5.        Liu, B.; Liang, Z.; Parlikad, A. K.; Xie, M.; Kuo, W. Condition-based maintenance for systems with aging and cumulative damage based on proportional hazards model. Reliab. Eng. Syst. Saf. 2017, 168, doi:10.1016/j.ress.2017.04.010.

Author Response File: Author Response.docx

Reviewer 3 Report

First of all, I would like to thank the authors for their work and contribution and the editors for the possibility of participating in the review process. It is always a pleasure and always interesting. 

The article addresses a major issue in the extension of industrial implementation of CBM programs. Measuring their impact and optimizing their use by means of cost-benefit models that allow the CBM strategy to be compared with the rest of the maintenance strategy options is a fundamental aspect for which, on the other hand, clear and contrasted reference models are not usually available. 

In this sense, the content of the paper is, in my opinion, relevant and the authors present it reflecting scientific solvency and evident knowledge of the industrial reality.

Finally, it should be noted that studying the relationship between the loss or reduction of production speed and the age linked to monitoring is a relevant case and directly related to the interest of the industry when it comes to understanding the real usefulness of CBM strategies. 

Some comments

- The references provided are not sufficient. A greater number of references that scientifically endorse the paper's approach would be desirable. 

- Improve the detail of the explanation of the use case. Especially in the description of the decision variables in this case. Figure 3 should be described in greater detail and a greater explanation of the results it represents and the conclusions of these results with respect to the objective of the paper would be desirable.

- Improve Figure 1. Identify the source of the data from which these results are extracted: are they in this journal? Are they from general sources such as Scopus? 

- Improve Figure 2: More detail in the axes and in the graph so that the variables referred to in the text that can be related to the graph (wc, M, etc) are reflected more clearly.

- Enter a list of acronyms or review acronyms, as there are certain unexplained acronyms.

Author Response

REVIEWER 3, ROUND 1

Responses to Reviewer 3

We are very grateful for your constructive comments, criticism, suggestions, and references. We have done our best to address them all. We believe that, as a result, the paper has substantially improved. Below we provide point-by-point responses to your comments.

English language and style

( ) Extensive editing of English language and style required
( ) Moderate English changes required
(x) English language and style are fine/minor spell check required
( ) I don't feel qualified to judge about the English language and style

Comments and Suggestions for Authors

First of all, I would like to thank the authors for their work and contribution and the editors for the possibility of participating in the review process. It is always a pleasure and always interesting. 

The article addresses a major issue in the extension of industrial implementation of CBM programs. Measuring their impact and optimizing their use by means of cost-benefit models that allow the CBM strategy to be compared with the rest of the maintenance strategy options is a fundamental aspect for which, on the other hand, clear and contrasted reference models are not usually available. 

In this sense, the content of the paper is, in my opinion, relevant and the authors present it reflecting scientific solvency and evident knowledge of the industrial reality.

Finally, it should be noted that studying the relationship between the loss or reduction of production speed and the age linked to monitoring is a relevant case and directly related to the interest of the industry when it comes to understanding the real usefulness of CBM strategies. 

Thank you once more for your support and valuable comments. The recognition received from you reinforces the idea of working on this research topic of productive speed loss.

Again, we also show our gratitude to your comments as they improve the paper without any doubt. We respond to each of them in the following lines:

- The references provided are not sufficient. A greater number of references that scientifically endorse the paper's approach would be desirable. 

The paper has been completed adding the latest and most relevant papers in the field. We have added the following references:

New references

1.          Accorsi, R.; Manzini, R.; Pascarella, P.; Patella, M.; Sassi, S. Data Mining and Machine Learning for Condition-based Maintenance. Procedia Manuf. 2017, 11, 1153–1161, doi:10.1016/J.PROMFG.2017.07.239.

2.          Azadeh, A.; Asadzadeh, S. M.; Salehi, N.; Firoozi, M. Condition-based maintenance effectiveness for series-parallel power generation system - A combined Markovian simulation model. Reliab. Eng. Syst. Saf. 2015, 142, doi:10.1016/j.ress.2015.04.009.

3.          Noman, M. A.; Nasr, E. S. A.; Al-Shayea, A.; Kaid, H. Overview of predictive condition based maintenance research using bibliometric indicators. J. King Saud Univ. - Eng. Sci. 2018, doi:10.1016/J.JKSUES.2018.02.003.

Cites to these three references have been added as well.

-          Line 22: “Data availability coming from the effect of IoT devices is an influencing factor pushing research in the field of CBM, as the existing ICT solutions simplify the on-field collection of large amount of data [1].”

-          Line 27: “In addition to what it is shown in Figure 1, Ref. [3] performs a quantitative review of predictive condition based maintenance research using bibliometric indicators to show the increasing interest the topic is generating”.

-          Line 34: “These studies promote the creation of implementation frameworks for CBM such as the one proposed in Ref. [1], appropriate for complex production systems based on data mining and machine learning”.

-          Line 41: “Azadeh et al. [2] sustain that most existing literature either discussed on CBM optimization of single component system or focuses on technical issues about condition monitoring equipment and diagnosis, but in this approach a multi-component system will be approached”.

- Improve the detail of the explanation of the use case. Especially in the description of the decision variables in this case. Figure 3 should be described in greater detail and a greater explanation of the results it represents and the conclusions of these results with respect to the objective of the paper would be desirable.

Yes, you are right. Another reviewer has pinpointed this weakness and we have re-written this part. We hope we made it sufficiently well this time, but any suggestion will be welcome.

- Improve Figure 1. Identify the source of the data from which these results are extracted: are they in this journal? Are they from general sources such as Scopus? 

They come from the WoS (Web of Science), and we have remarked it. We have reformatted the image as it is a direct copy-paste of the WoS and the quality was not good enough before.

- Improve Figure 2: More detail in the axes and in the graph so that the variables referred to in the text that can be related to the graph (wc, M, etc) are reflected more clearly.

We have reformatted everything, as it was not clear enough before.

- Enter a list of acronyms or review acronyms, as there are certain unexplained acronyms.

Certainly, we did it as it helps to understand and trace the paper in a better way.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The text has been significantly improved, especially by improving Figure 2 and adding lines 121, 145-149 and 159-165. I think, the paper can be published in its current version.

Reviewer 2 Report

My comments have been addressed, so I recommend acceptance after an English proofread by a native speaker.