Maintenance Optimization Model with Sequential Inspection Based on Real-Time Reliability Evaluation for Long-Term Storage Systems
Round 1
Reviewer 1 Report
This paper deals the maintenance optimization topic of the long-term storage systems based on real-time reliability evaluation. At first, the Wiener process is utilized to design a degradation model and a closed-form equation for the system is obtained by using the first passage time . In addition, the sequential inspection intervals are provided and a maintenance optimization model is presented. The topic is interest and organization of the manuscript is well balanced. Therefore I recommend to publish this article in the processes.
Author Response
Many thanks to the reviewer for taking time out of his/her busy schedule to review the paper and recommend the paper.
Reviewer 2 Report
Dear authors,
The paper investigates the issue of maintenance optimization modelling for long-term storage systems based on real-time reliability evaluation. Which is carried out by combining a Wiener process, a real-time reliability function with a real-time reliability threshold for the system, and an optimization algorithm. A case study seems to prove the validity of the proposed method.
The paper is clear and well written, however, I have some comments:
1. Improve the quality of all the figures. Except figure 2, the rest of figures are extremely difficult to read.
2. In addition, graphs of figures 8 and 9 in order to get a better view of the trends.
3. Line 236: the equation should be centered and the sentence “where […]” should start in the next line.
4. The concept “unit” is more or less clear by reading the text. However, it should be explicitly defined in the text. Is it a part? A set of parts? A system? All of them?
5. What is the reason to choose the initial values and step sizes w0=0.01, ∆w = 0.01, ∆q=0.01?
6. What physical parameters of the real gyroscope are interesting to define the estimator θk?
7. As the authors comment in the last sentence of the conclusions, like-new performance cannot be recovered after maintenance in some cases. Although this is a topic of further study, would it be feasible to introduce the non-like-new performance in the proposed model?
8. A second case study would greatly improve the quality of the paper and firmly confirm the validity of the proposed method.
Author Response
Thank you for your comments concerning our manuscript (Manuscript ID: processes-521428) entitled “Maintenance optimization model with sequential inspection based on real-time reliability evaluation for long-term storage systems”. Those comments are valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval.
Point 1: Improve the quality of all the figures. Except figure 2, the rest of figures are extremely difficult to read.
Response 1: Thank you very much for your constructive suggestions. These figures have been redrawn and further improved the resolution of the figures, hoping to meet the requirements of the paper.
Point 2: In addition, graphs of figures 8 and 9 in order to get a better view of the trends.
Response 2: We have redrawn figures 8 and 9, and present the influence of the cost parameters (CI, CP, CC, Cd) on the optimal values q* or w0* on a single figure instead of the previous four subgraphs, and the resolution of the two figures have also been improved.
Point 3: Line 236: the equation should be centered and the sentence “where […]” should start in the next line.
Response 3: We have checked all parts of the manuscript and re-edited it, ensuring equations, formats and figures right.
Point 4: The concept “unit” is more or less clear by reading the text. However, it should be explicitly defined in the text. Is it a part? A set of parts? A system? All of them?
Response 4: Thank you very much for your constructive suggestions. As we know, the long storage system is a complex system, composed of a variety of components, devices and subsystems. Taking the missile system as an example, it is mainly composed of four parts: warhead, power device, guidance system and missile body structure. The research object in this paper refers to the key units that have important influence on the long storage system, which can be the key component, such as the alloy blade of the rocket engine, or the key device in the subsystem, such as the gyroscope in the guidance system. Therefore, the unit in this paper can be either a single component, a single device or a single subsystem. In the first paragraph of Section 2, we add the explanation of the unit and modify the related sentences. Please see lines 152-163 of the paper for details.
Point 5: What is the reason to choose the initial values and step sizes w0=0.01, ∆w = 0.01, ∆q=0.01?
Response 5: Since the failure threshold w=0.6 of the gyroscope is relatively small, in order to find the optimal value w0* of the preventive maintenance threshold as much as possible, we decide to start the simulation search from a small initial value, although this will increase the time cost of the algorithm to some extent, but it can guarantee to find the optimal value of the preventive maintenance threshold. For the choice of step size ∆w = 0.01and ∆q=0.01, we consider mainly from two aspects, one is to ensure that the optimization result meets the needs of engineering practice, and the other is the time cost of the algorithm. If a larger ∆w or ∆q is selected, such as ∆w = 0.1 or ∆q=0.1, the accuracy of optimization result will be low, which cannot meet the requirements of engineering practice. On the contrary, a smaller ∆w or ∆q, such as ∆w = 0.001 or ∆q=0.001, will increase the time cost of the algorithm. So, considering both, we chose step sizes ∆w = 0.01and ∆q=0.01.
Point 6: What physical parameters of the real gyroscope are interesting to define the estimator θk?
Response 6: In the storage process of the long-term storage system, due to the influence of environmental stress and other factors (temperature, humidity, gravity, atmospheric pressure, chemical corrosion, etc.), the deformation of the motor bearing in the gyroscope will occur to a certain extent, resulting in the gradual increase of the drift coefficient of the gyroscope. When the drift coefficient exceeds the upper limit, namely the failure threshold, the gyroscope is considered to be invalid. In this paper, the drift coefficient of the gyroscope during the k-th inspection is denoted as μk , and it is assumed that it obeys normal distribution μk ~N(ak , Dk); the increment of drift coefficient during each inspection is denoted as ηk, and it is assumed that it obeys normal distribution ηk ~N(0, Qk). The diffusion coefficient in the Wiener process is σk. So, we can define the estimator θk. You can also refer to literature [28] for a detailed explanation of the estimator θk.
28. Si X S, Wang W, Hu C H, et al. A Wiener-process-based degradation model with a recursive filter algorithm for remaining useful life estimation. Mech. Sys. Sig. Pro. 2013, 35, 219-237. DOI: 10.1016/j.ymssp.2012.08.016.
Point 7: As the authors comment in the last sentence of the conclusions, like-new performance cannot be recovered after maintenance in some cases. Although this is a topic of further study, would it be feasible to introduce the non-like-new performance in the proposed model?
Response 7: We think it will be feasible. Due to our current research on this aspect is still in the exploratory stage, limited to the research capabilities and levels, considering the units cannot be restored as new after maintenance, it will increase the complexity of the model, which makes the difficulty of solving the model increase. Therefore, in this paper, we simplified the model and assumed that the units would recover as new after maintenance. However, there are many related studies on the imperfect maintenance and non-periodic inspection of units, and these studies can provide some methods and ideas for our future research in this paper. In addition, the development of related intelligent optimization algorithms can also support future research in this paper. Therefore, we believe that it is feasible to introduce the non-like-new performance in the proposed model.
Point 8: A second case study would greatly improve the quality of the paper and firmly confirm the validity of the proposed method.
Response 8: In the section of case study (Section 6), we have added a research case of an alloy blade commonly used in rocket engines. Optimization results are obtained through simulation calculation, and sensitivity analysis of relevant parameters is carried out. In this way, the validity of the proposed model is verified from two levels: device level and component level, together with the case study of gyroscope. For a detailed analysis of the maintenance optimization of alloy blades, please refer to Section 6.2.
We tried our best to improve the manuscript and made a lot of changes in the manuscript. These changes will not influence the content and framework of the paper. We appreciate for the reviewer’s warm work earnestly, and hope that the correction will meet with approval.
Thanks again for your time!
Yours sincerely,
Senyang Bai
Author Response File: 
Author Response.docx
Reviewer 3 Report
The manuscript investigates the issue of maintenance optimization modelling for long-term storage systems based on real-time reliability evaluation. The authors use the Wiener process to establish a performance degradation model for one critical unit of a long-term storage system. The sequential inspection intervals are dynamically determined by combining the real-time reliability function with a real-time reliability threshold for the system. Furthermore, a maintenance optimization model is established for the critical unit based on update process theory. Finally, an example is considered to illustrate the validity of the proposed model.
The manuscript is very well written and presented and the idea is interesting. The mathematical formulation is well documented, the numerical results are clearly presented, and the conclusions are supported by the preceding material (theoretical and practical). A comment that the authors may consider is the following:
In Section 4.2 when the maintenance strategy is given. More precisely at lines 260-263 the authors assume that “after preventive maintenance (PM), the performance state of the unit will be restored to the same level as when the unit was new, the degradation level will also return to the initial state, and the update cycle of the system will be recalculated from 0“.
However, the “new” state will contain a mixture of systems of different ages, depending on how recently each system returned to this state. Is it possible to take the above argument under consideration? A comment or short discussion on this issue will be nice to be included in the manuscript.
Author Response
Thank you for your comments concerning our manuscript (Manuscript ID: processes-521428) entitled “Maintenance optimization model with sequential inspection based on real-time reliability evaluation for long-term storage systems”. Those comments are valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval.
Point 1: In Section 4.2 when the maintenance strategy is given. More precisely at lines 260-263 the authors assume that “after preventive maintenance (PM), the performance state of the unit will be restored to the same level as when the unit was new, the degradation level will also return to the initial state, and the update cycle of the system will be recalculated from 0“.
However, the “new” state will contain a mixture of systems of different ages, depending on how recently each system returned to this state. Is it possible to take the above argument under consideration? A comment or short discussion on this issue will be nice to be included in the manuscript.
Response 1: Thank you very much for the constructive suggestions. In order to reduce the complexity of the model and better derive the analytical expression of the optimization model, we assumed that the performance state of the unit would be restored to the same level as when the unit was new after preventive maintenance (PM), but this was somewhat inconsistent with engineering practice. As the reviewers had said, this is a problem that deserves our consideration.
Therefore, in the second paragraph of the conclusion (Section 7), we take the above argument under consideration and give the reasons for this assumption, then point out that considering imperfect maintenance will be a topic for further study. Please refer to the second part of the conclusion (Section 7) for specific modification.
We tried our best to improve the manuscript and made a lot of changes in the manuscript. These changes will not influence the content and framework of the paper. We appreciate for the reviewer’s warm work earnestly, and hope that the correction will meet with approval.
Thanks again for your time!
Yours sincerely,
Senyang Bai
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
The authors have followed all my recommendations and I consider the paper is suitable for publication in the present form.
