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Risk Analysis and Evaluation of Nuclear Security Radiation Events in Spent Fuel Reprocessing Plants

Sustainability 2023, 15(1), 781; https://doi.org/10.3390/su15010781

by Cuiyue Wei, Shoulong Xu^*

, Shuliang Zou

, Fang Zhao^*

, Zhiwei Qin, Hanfeng Dong and Zhixiong Hou

Reviewer 1:

Belal Almomani

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Reviewer 4:

Masaki Ozawa

Sustainability 2023, 15(1), 781; https://doi.org/10.3390/su15010781

Submission received: 11 October 2022 / Revised: 25 December 2022 / Accepted: 30 December 2022 / Published: 31 December 2022

(This article belongs to the Special Issue Human and Organizational Factors in Complex Systems)

Round 1

Reviewer 1 Report

I do not recommend publishing this manuscript owing to the lack of scientific value and technical strength. The authors seek to quantify the risk concerning nuclear security rather than nuclear safety. However, the method of determining the basic events considering the expert score system and the frequency of concurrence by only 30 experts would include some bias in determining the main elements of risk (probability & severity). The description of the fault tree analysis (FTA) section is lengthy and hard to follow, and the scientific observations and explanations are not crisp. For instance, what is the purpose of calculating the minimum diameter set since the minimum cut set is already found? The fuzzy comprehensive system method also does not deliver further insight to the readers. Overall, the literature review, novelty, coherence of the analysis, visualizations, novel findings and discussion, and English language of this manuscript have not reached the minimum quality requirement for publishing.

Author Response

Response to Reviewer 1 Comments

Thank you for your letter and for the reviewers′ comments concerning our manuscript. Those comments are helpful and very valuable for revising and improving our manuscript, as well as the important guiding significance to our researches. We have studied the comments carefully and have made substantially revised which we hope meet with your approval. The revised manuscript is completed under the revised format. The revisions and the detailed responses to the reviewers' comments are as following:

Point 1: I do not recommend publishing this manuscript owing to the lack of scientific value and technical strength.

Response 1: Thank you for this valuable feedback. Our research uses knowledge from the field of safety science and engineering to analyze the significance and risk of nuclear security radiation events at spent fuel reprocessing plants and individual plant areas. Conclusion confirms the importance of computer nuclear security events is the highest and the importance of theft events is the lowest. The risk of the main process area is the highest, the risk of the front area is the lowest, and there is a 1.5 times relationship. The research method of this paper can be put real numbers or probabilities on different events, which many lead to accidental situations, so it can be used as a guideline (on of them) how to distribute money and manpower in nuclear installations to mitigate risk.

Point 2: The authors seek to quantify the risk concerning nuclear security rather than nuclear safety.

Response 2: I'm apologize I didn't write a good literature review in the introduction, which led to your misunderstanding. This paper focuses on the risk analysis and evaluation of "nuclear security" radiation events in spent fuel reprocessing plants, and discusses the importance of eight basic nuclear security events, such as radioactive dispersal device and computer nuclear security. We are deeply sorry for this mistake, so we have completely revised the introduction of the article, especially emphasizing the difference between "nuclear safety" and "nuclear security". Nuclear security is defined as the prevention and detection of, and response to, theft, sabotage, unauthorized access, illegal transfer, or other malicious acts involving nuclear material, other radioactive substances, or their associated facilities. The definition of nuclear safety is different, which is the achievement of proper operating conditions, prevention of accidents or mitigation of accident consequences, resulting in protection of workers, the public and the environment from undue radiation hazards. A key difference between nuclear safety and security is intentionality. Accidents related to nuclear safety are unintentional, whereas nuclear security incidents are clearly intentional and undertaken with a specific motive.

Point 3: The method of determining the basic events considering the expert score system and the frequency of concurrence by only 30 experts would include some bias in determining the main elements of risk (probability & severity).

Response 3: Thank you very much for your suggestion. According to this suggestion, we have modified and supplemented the article. First of all, the selection of 30 experts is conditional. Different weights are given to experts according to their educational background, professional title, length of service and other factors to ensure their professionalism. Secondly, the selection of expert scoring method is based on evidence. The expert scoring method has the advantages of simplicity, flexibility and practicality. It is suitable for solving complex practical problems with less data and lack of information, and can realize qualitative assessment of the occurrence probability and consequences of identified events. Therefore, this method is suitable for use in complex nuclear environments such as spent fuel reprocessing plants. Finally, the conclusion that this article wants to obtain is not an accurate probability, but a system that can analyze the risk ofeach region in the spent fuel reprocessing plant. According to this conclusion, we can reasonably allocate the protective forces of regions with different hazard levels, so as to achieve the effect of saving resources.

Point 4: The description of the fault tree analysis (FTA) section is lengthy and hard to follow, and the scientific observations and explanations are not crisp. For instance, what is the purpose of calculating the minimum diameter set since the minimum cut set is already found?

Response 4: Thanks for your helpful suggestions and your suggestions make the manuscript more meaningful and rigorous. According to your suggestion, we have modified and improved the research and analysis part of the fault tree as a whole, deleted the redundant content, and added the content lacking analysis. The specific changes have been attached below.

Construct FTA for Nuclear Security Radiation Events

Assuming that the probability of a nuclear security radiation event in the spent fuel reprocessing plant is 1, the nuclear security radiation event fault tree of the spent fuel reprocessing plant is established through the analysis of the radioactive leakage problem in the whole plant and the response of each part to the accident after nuclear leakage, as shown in Figure 1. The corresponding top, middle, and base event descriptions in Figure 1 are shown in Table 4.

Figure 1. Nuclear security fault tree for spent fuel reprocessing plant

Table 4. Nuclear security radiation event letter symbols and corresponding events

Number	Incident	Number	Incident
T	Nuclear security radiation incident	M₁₀	Support equipment failure
M₁	Radioactive release event	M₁₁	Lose
M₂	Emergency failure	X₁	Radioactive dispersal device
M₃	Leakage of high level of waste liquid	X₂	Computer nuclear security
M₄	Container leak	X₃	Destruction of nuclear facilities
M₅	Transit system leakage	X₄	Transportation nuclear security
M₆	Overfeeding	X₅	Internal threat
M₇	Auxiliary device failure	X₆	Potential threat
M₈	Monitoring equipment failure	X₇	Illegal transfer
M₉	Test instrument failure	X₈	Theft

The top event of the fault tree is the nuclear security radiation event of the spent fuel reprocessing plant, and the eight types of events such as the radioactive dispersal device are the basic events. In case of radioactive leakage or emergency failure after the accident, the top event will occur. The radioactive leakage event is caused by the radioactive dispersal device event or the leakage of high-level liquid waste, while the leakage of high-level liquid waste is caused by the leakage of a container or transfer system or excessive feeding. When the nuclear facility destruction event and potential threat event occur at the same time, the container will leak. The simultaneous occurrence of transportation nuclear security incidents and illegal transfer incidents will lead to leakage of the transfer system. The simultaneous occurrence of an internal threat event and a potential threat event will lead to the failure of auxiliary equipment. When it or a computer nuclear security event occurs, it will lead to excessive feeding. Emergency failure is due to the occurrence of computer nuclear security events or potential threats, internal threats or failures of regulatory equipment. The failure of supervision equipment is caused by the failure of detection instruments or support equipment. Illegal transfer or theft will lead to the loss of radioactive sources, which will lead to the failure of detection instruments or support equipment when it occurs at the same time as the destruction of nuclear facilities.

3.1. Structure Function of Fault Tree

The top event is represented by T, then the fault tree structure function T= is a function of X₁, X₂, … X₈, whilst gate"·" is multiplication or gate"＋" is addition.

The structure function of the fault tree is:

T=X₁+X₃*X₆+X₄*X₇+X₂+X₅*X₆+X₂+X₆+X₅+X₃*(X₇+X₈)+X₃*(X₇+X₈)

=X₁+X₂+X₅+X₆+X₃*X₇+X₃*X₈+X₄*X₇

From the result of structure function T, the minimum cut set can be obtained:

{X₁}, {X₂}, {X₅}, {X₆}, {X₃,X₇}, {X₃,X₈}, {X₄,X₇}

The minimum cut set is the set of the minimum basic events that can cause the top events to occur. That is, if one of the status values of X₁, X₂, X₅ and X₆ is 1, the status value is 1, indicating that the top event occurs; similarly, if the status values of X₃ and X₇ are 1 at the same time, the status value is 1; if the state values of X₃ and X₈ are 1 at the same time, the state value is 1;if the state values of X₄ and X₇ are 1 at the same time, the state value is 1.

3.2. Importance analysis of the Fault Tree

The importance analysis includes the structural importance, probabilistic importance, and critical importance. Among them, the structural importance degree is qualitative analysis, the probability and critical importance degree is quantitative analysis. The combination of qualitative analysis and quantitative analysis is an effective way to analyze all kinds of basic nuclear security incidents in spent fuel reprocessing plants.

Therefore, the importance analysis of the above fault tree is carried out. See (3.1-3.3) for the formula [23] of structural importance, probability importance and critical importance.

(3.1)

(3.2)

(3.3)

Among them, represents eight basic events, and n represents the number of basic events, that is, n=8. Q represents the probability of occurrence of the top event, and q represents the probability of occurrence of each basic event.

The order of structure importance is as follows:

I(X₁)=I(X₂)=I(X₅)=I(X₆)>I(X₃)=I(X₇)>I(X₄)=I(X₈)

This basic event structure importance ranking result description is as follows: basic event X₁ radioactive dispersal device, X₂ computer nuclear security, X₅ internal threats, X₆ potential threats have the greatest impact on the occurrence of nuclear security accidents, followed by X₃ destruction to nuclear facilities and X₇ illegal transfer incident, X₄ transport nuclear security and X₈ the incidence of theft have the least impact on the occurrence of nuclear security accidents.

Therefore, it can be concluded that structural importance: radioactive dispersal device = computer nuclear security = internal threat = potential threat > destruction to nuclear facilities = illegal transfer > transportation nuclear security = theft

The probability importance is:

X₁=0.640,X₂=0.648,X₃=0.130,X₄=0.068,X₅=0.640,X₆=0.640,X₇=0.156,X₈=0.062

The order of probability importance is:

Ig(X₂)>Ig(X₁)=Ig(X₅)=Ig(X₆)>Ig(X₇)>Ig(X₃)>Ig(X₄)>Ig(X₈)

The result of probability importance ranking of the basic event is described as follows: reducing the probability of the basic event X₂ computer nuclear security event can quickly reduce the probability of the top event, the least sensitive event is the X₈ theft event.

Therefore, it can be concluded that the probability importance is as follows: computer nuclear security > radioactive dispersal device = internal threat = potential threat > illegal transfer > destruction to nuclear facilities > transport nuclear security > theft.

The critical importance is: X₁=0.176，X₂=0.193，X₃=0.036，X₄=0.028，X₅=0.176，X₆=0.176，X₇=0.046，X₈=0.018

The order of critical importance is:

(X₂)>(X₁)=(X₅)=(X₆)>(X₇)>(X₃)>(X₄)>(X₈)

The critical importance of this basic event ranking result description is as follows: the rate of change of the probability of occurrence of the basic event X₂ computer nuclear security event has the largest change rate to the probability of occurrence of the overhead event, and the event that has the least impact on the rate of change in the probability of occurrence of the overhead event is the X₈ theft event.

Therefore, it can be concluded that the critical importance is as follows: computer nuclear security > radioactive dispersal device = internal threat = potential threat > illegal transfer > destruction to nuclear facilities > transport nuclear security > theft.

Of the comprehensive quantitative and qualitative factors, it can be concluded that importance analysis of computer nuclear security is the biggest, which should be paid more attention to in daily operation and management; importance analysis of theft isminimal, but it may happen.

Point 5: The fuzzy comprehensive system method also does not deliver further insight to the readers.

Response 5: The purpose of this article is to solve the problem of risk analysis for each plant area of spent fuel reprocessing plant, so as to invest the most appropriate preventive force to achieve the purpose of saving resources, rather than improving and deeply exploring the fuzzy decision-making method.

Because the data related to nuclear security incidents in spent fuel reprocessing plants are difficult to obtain and fuzzy, we find that fuzzy decision-making method is more suitable for the study of such issues after literature search and analysis.

Point 6: Overall, the literature review, novelty, coherence of the analysis, visualizations, novel findings and discussion, and English language of this manuscript have not reached the minimum quality requirement for publishing.

Response 6: I'm apologize I didn't write a good literature review in the introduction, and the coherence and novelty of the article are not reflected. According to the suggestions of several reviewers, the introduction has been completely revised, and the problems in the article have also been revised and improved. For the problem of English language, we have used the editing service of your journal to polish it. It is hoped that this revision can meet the requirements of publication.

Thank you for your professional and insightful comments. We hope our modifications and responses can satisfy you and meet the publication requirements!

Author Response File: Author Response.pdf

Reviewer 2 Report

Good paper, providing all necessary information related to the Risk Analysis and Evaluation of Nuclear Security Radiation Events in Spent Fuel Reprocessing Plants

The paper contains all the necessary elements of the peer-review papers. The authors have applied scoring method and evaluate the possibility of eight basic nuclear accident types in each area. The interpretation of the results, discussion, and conclusions are reliable.

Author Response

Response to Reviewer 2 Comments

Point: Good paper, providing all necessary information related to the Risk Analysis and Evaluation of Nuclear Security Radiation Events in Spent Fuel Reprocessing Plants.

Response: Thank you very much for your recognition of this article. As the biggest support of this article, we are very moved by your suggestions, and we would like to express our heartfelt thanks to you! At the same time, we also combined the suggestions of other reviewers to further optimize and improve the article, making the article more perfect from different angles.

Author Response File: Author Response.pdf

Reviewer 3 Report

(*) General comments:

This paper presents a probabilistic assessment of spent fuel reprocessing plant (SFRP) in terms of a risk for the occurrence of proposed eight security-related accidents. The methods of expert knowledge, in form of a weight allocation table based of different experts level, combined with a cut-set of fault tree analysis was applied to SFRP which was divided in four main areas, including additional subdivisions, for the purpose of risk quantification of basic events. For that purpose, basic (not comprehensive) methods of probability theory and fuzzy logic were used. The obtained results confirmed that the main process area has the highest risk degree, i.e. about 1.5 times higher compared to the pre-plant area, which was expected result.

However, the numerical findings in the manuscript are not presented in a clear and logical way, with missing references throughout the entire text! Only ref.[1] and [3] were used. The Introduction section is poorly written with missing relevant and general work in the field (besides Chinese authors) so rewriting it is mandatory. It should state what was already done and what's new in this paper which can be interpreted as a "step-forward". The English writing/style should go through another iteration, since the paper is packed with a very long and unclear sentences. The theoretical approach is vaguely described, with inconsistent subscripts on main quantities; more over all variables should be in italic and same font size as the text. Many presented equations, Figures and results don't have any comments or explanations regarding to the text, so they just "hung in the air". Some portions of the text are written in small figure-caption font. So to summarize, this presented methodology has a potential to put real numbers (probabilities) on different events, which many lead to accidental situations, so it can be used as a guideline (on of them) how to distribute money and manpower in nuclear installations to mitigate risk. To address this in a clear way, the presented manuscript should be rewritten in a more clear fashion and supplemented with missing elements.

(*) Specific comments:

The following numbers stated in brackets are denoting line number in the manuscript - authors are encouraged to fully address the following:

(15) small font of "nuclear accident types" should be corrected

(19) FTA should be "Fault Tree Analysis"

(21) Maybe "comprehensive" term is to strong, consider replacing it throughout the text with "elementary" since you are using basics of the aforementioned methods (probability, statistics, fuzzy logic, etc.).

(29-30) the first sentence has a small font size

(34-40) to long and an very unclear sentence, consider breaking into several more meaningful sentences

(35) missing many references ....

(42-43) this sentence should be put at the end of the Introduction paragraph, and additional references should be included, with explained motivation for this work

(65) "is divided" should be out after "reprocessing plant"

(75) missing argumentation why these specific 8 cases? maybe additional references are missing?

(75) "litter" is typo, should be "little"

(90) consider smaller font for table 1 (and rest of the tables) to accommodate reading; "professor" should be "Professor"

(96-101) again to long and very unclear sentence, consider several shorter sentences

(102-106) again small figure-caption font

(107) missing blank after "Table 2."

(108) missing blank after "Table 3."; separation space is also needed between tables

(109) missing dot in paragraph number, i.e. "3. Construct ...." (an in all others)

(112-113) looks like sentence is 2xcopied, consider merging in "... is qualitative and quantitative analysis"

(116) missing reference(s) for the statement of investigations

(117-119) consider dismissing this, since you are again repeating this section

(123) missing blank before "so"

(125-198) This section badly needs rewriting:

- the variables should not be bold and should be in italic font

- the subscripts should be in appropriate format and consistent with text

- the main quantities should be designated with names, not with "it"

- rephrasing is needed for sentences starting with "According to..."; again (151, 157, 165, 171)

- please check in (164) strange new quantities, which are not in accordance with eq(3.1)

- missing IAEA references in (143)

- consider finishing the sentence in (146); explain the meaning of T

- the sentence in (196) sounds like copy-paste error, please revise

(199) Figure 1 has missing letters in boxes on several instances

(203) "The factor set ..."

(210) "difficult influence" should probably be "different influence", please check; missing blank before "The weight..."

(213) missing blank after "Table 4."; in table 4. "The weight" should be changed to "Weight coefficient"

(214) what is the meaning of that sentence?

(218-220) consider dismissing, you are again repeating

(206) missing dot at the end of the sentence

(227) "Through statistic and sorting..." this is no explanation, you need to describe you work, this is very unclear

(229-234) figures 2-13 are missing blank before figure caption number, and "s" for "results"; no comments are following after the figures?

(253) What is B, A, R in B = A*R? you need to describe this, and also to give comment why is important so have in text "evaluation unit" with numbers?

(280-290) again small figure-caption font

(281-285) long and unclear sentence, please rephrase

(301) consider adding "..., and the probability";

(304) why do you use term "accurate probability" since you haven't performed any comparison with alternative (similar) approaches, i.e. how can you be sure in your numbers?

(316-317) copy-paste error sentence ...

Author Response

Response to Reviewer 3 Comments

Point: This paper presents a probabilistic assessment of spent fuel reprocessing plant (SFRP) in terms of a risk for the occurrence of proposed eight security-related accidents. The methods of expert knowledge, in form of a weight allocation table based of different experts level, combined with a cut-set of fault tree analysis was applied to SFRP which was divided in four main areas, including additional subdivisions, for the purpose of risk quantification of basic events. For that purpose, basic (not comprehensive) methods of probability theory and fuzzy logic were used. The obtained results confirmed that the main process area has the highest risk degree, i.e. about 1.5 times higher compared to the pre-plant area, which was expected result.

However, the numerical findings in the manuscript are not presented in a clear and logical way, with missing references throughout the entire text! Only ref.[1] and [3] were used. The Introduction section is poorly written with missing relevant and general work in the field (besides Chinese authors) so rewriting it is mandatory. It should state what was already done and what's new in this paper which can be interpreted as a "step-forward". The English writing/style should go through another iteration, since the paper is packed with a very long and unclear sentences. The theoretical approach is vaguely described, with inconsistent subscripts on main quantities; more over all variables should be in italic and same font size as the text. Many presented equations, figures and results don't have any comments or explanations regarding to the text, so they just "hung in the air". Some portions of the text are written in small figure-caption font. So to summarize, this presented methodology has a potential to put real numbers (probabilities) on different events, which many lead to accidental situations, so it can be used as a guideline (one of them) how to distribute money and manpower in nuclear installations to mitigate risk. To address this in a clear way, the presented manuscript should be rewritten in a more clear fashion and supplemented with missing elements.

Response: Thank you for your suggestions. All your suggestions are very important, and they are of great guiding significance for my future research work.

Response 1: For the reference problem, this paper replaces all the references and cites a large number of articles in the past five years. As follows:

Wang F, Wang J, Wang J, et al. Risk monitor risk angel for risk-informed applications in nuclear power plants. Annals of Nuclear Energy,2016, 91: 142-147.
Tromm W. Nuclear energy research in Germany 2010. Research centers. Atw. Internationale Zeitschrift fuer Kernenergie,2011, 56(7): 412-418.1.
Ibrahim M, Hamdan S N, Haris M F, et al. Big data analytics nuclear security framework Conference Series: Materials Science and Engineering. IOPPublishing, 2021, 1106(1):
Gandhi S, Kang J. Nuclear safety and nuclear security synergy. Annals of nuclear energy,2013, 60: 357-361.
Jensen K, Vasko V. Inadvertent Radiation Exposures in Combat Zones: Risk of Contamination and Radiobiologic Consequences. Military Medicine, 2022,187(11-12): 303-307.
Majewski M, Nestler K, Veit D A, et al. Detection of embedded low-level radioactive shrapnel after the explosion of a radiological dispersal device in radiological emergency imaging. Health physics,2020, 119(1): 95-100.
Cho H S, Woo T H. Cyber security in nuclear industry–Analytic study from the terror incident in nuclear power plants (NPPs). Annals of Nuclear Energy, 2017,99: 47-53.
Moo J H, Chirayath S S, Cho S G. Physical protection system vulnerability assessment of a small nuclear research reactor due to TNT-shaped charge impact on its reinforced concrete wall.Nuclear Engineering and Technology, 2022, 54(6): 2135-2146.
Tao L, Wang J, Long P, et al. Probabilistic safety assessment method for spent nuclear fuel road transportation. Annals of Nuclear Energy,2020, 137:
Ni S, Zou S, Chen J. Evolutionary Game Model of Internal Threats to Nuclear Security in Spent Fuel Reprocessing Plants Based on RDEU Theory. Sustainability,2022, 14(4):
Solodov A, Williams A, Al Hanaei S, et al. Analyzing the threat of unmanned aerial vehicles (UAV) to nuclear facilities. Security Journal,2018, 31(1): 305-324.
Al Hamrashdi H, Monk S D, Cheneler D. Passive gamma-ray and neutron imaging systems for national security and nuclear non-proliferation in controlled and uncontrolled detection areas: Review of past and current status. Sensors, 2019,19(11):
Busch N. Risks of Nuclear Terror: Vulnerabilities to Theft and Sabotage at Nuclear Weapons Facilities. Contemporary Security Policy,2002, 23(3): 19-60.
LI R R. Application of risk assessment grading method in accident analysis of nuclear fuel reprocessing plant. University of South China,
Ming Sun and Wen Xiang Zheng and Xiao Bo Duan. Research on Deep Coal Seam Mining Floor Starta Water Bursting Influenced Factors Based on Analytic Hierachy Process. Applied Mechanics and Materials, 2014,3277(608-609) : 737-741.
Jin Huibin et al. Study on How Expert and Novice Pilots Can Distribute Their Visual Attention to Improve Flight Performance. IEEE ACCESS, 2021,9 : 44757-44769.
Gavrilyuk V I, Drapey S S, Kaydyk B V, et al. Nuclear security risks in Ukraine< TITLE lang=""> Piзiki y cфepi фiзiчнoї yaдepнoї бeзпeki Уkpaїнi.Nuclear Physics and Atomic Energy, 2021, 22(4): 409-414.
Wang J, Lin M. Seismic probabilistic risk analysis and application in a nuclear power plant. Nuclear Technology,2018, 203(3): 221-231.
Fahmy R A, Gomaa R I. Dynamic fault tree analysis of auxiliary feedwater system in a pressurized water reactor. Kerntechnik, 2021, 86(2): 164-172.
Hermansyah H, Kumaraningrum A R, Purba J H, et al. Safety analysis technique for system with limited data: case study of the multipurpose research reactor in Indonesia. Energies,2020, 13(8): 1975
Purba J H, Tjahyani D T S, Widodo S, et al. Fuzzy probability based event tree analysis for calculating core damage frequency in nuclear power plant probabilistic safety assessment. Progress in Nuclear Energy, 2020, 125:
LI R R. Application of risk assessment grading method in accident analysis of nuclear fuel reprocessing plant. University of South China,
Xi J, Zhao Y, Ding T, et al. Analysis Model of Risk Factors of Urban Bus Operation Based on FTA-CLR. Advances in Civil Engineering,2021.

Response 2: For the problem of introduction, we have made all modifications to the introduction to explain what we was already done and what's new in this paper which can be interpreted as a "step-forward". The introduction is as follows:

Spent fuel reprocessing is one of the key technologies to realize the sustainable development and recycling of nuclear power. Due to the particularity of nuclear power, the security of spent fuel reprocessing plants has attracted much attention. Once an accident results in the release of radioactive substances, it may seriously affect the environment and human beings, eventually causing huge economic losses and having far-reaching social impacts [1]. The analysis and evaluation of nuclear security radiation events in the spent fuel reprocessing plant can provide a scientific basis for risk prevention and reduction. Therefore, in recent years, researchers have also been actively carrying out research on nuclear security issues [2]. Nuclear security is defined as the prevention and detection of, and response to, theft, sabotage, unauthorized access, illegal transfer, or other malicious acts involving nuclear material, other radioactive substances, or their associated facilities [3]. The definition of nuclear safety is different, which is the achievement of proper operating conditions, prevention of accidents or mitigation of accident consequences, resulting in the protection of workers, the public, and the environment from undue radiation hazards. A key difference between nuclear safety and security is intentionality. Accidents related to nuclear safety are unintentional, whereas nuclear security incidents are clearly intentional and undertaken with a specific motive [4]. So far, researchers have analyzed the basic accident types of nuclear security radiation events, mainly focusing on the following aspects: attention gradually enhances the terrorist attacks of the radioactive dispersal device [5, 6], computer nuclear security breaches called cyber terrorism at nuclear facilities [7], the destruction of nuclear facilities as a result of an external attack [8], transport nuclear security with a risk of radioactive material release [9], the internal threat of one of the most serious problems in the supervision of the physical protection of spent fuel reprocessing plants [10], potential threats [11], illegal transfer of nuclear materials and other radioactive sources [12], and theft [13].

The safety system theory analysis method can be adopted to analyze and evaluate the risk of the spent fuel reprocessing device [14], which has certain feasibility. Firstly, it is necessary to determine the possibility of the occurrence of each basic event. The expert scoring method [15], which has the advantages of simplicity, flexibility, and practicality, has significant advantages in this respect. It is suitable for solving the complex practical problems of fewer data and a lack of information [16], and can achieve the qualitative assessment of the occurrence probability and consequence of the identified event [17]. In terms of the risk analysis of basic events [18], researchers have also carried out relevant research work according to different application environments. FTA is more suitable for reliability analysis and the deductive evaluation of the safety system of complex projects such as chemical and nuclear facilities [19, 20], and it has effective quantitative properties on the probability of accidents [21]. The fuzzy decision method is often used to make engineering decisions on fuzzy, imprecise, and uncertain existing data and information [22]. In the case that the probability of the basic nuclear security events in the spent fuel reprocessing plant is difficult to obtain, the fuzzy decision method has significant advantages in the internal risk assessment of the plant.

Based on eight types of basic nuclear security incidents, this paper uses the expert scoring method to quantify qualitative information in the form of frequency instead of probability. The fault tree model of nuclear security radiation events in the spent fuel reprocessing plant has been established, and the importance of each basic event has been determined. Using the method of fuzzy decision and probability-mathematical statistics, the risk of each plant in the spent fuel reprocessing plant has been studied, and the relationship between the risk degree gap among them has been obtained. The research method of this paper can be input real numbers or probabilities on different events, which many lead to accidental situations, so it can be used as a guideline (one of them) on how to distribute money and manpower in nuclear installations to mitigate risk.

Response 3: For the problem of English writing, we used the editing service of your journal to polish the full text.

Response 4: In view of the problem that the description of theoretical methods is vague and the contents of equations and graphs are not annotated, we restated these theoretical methods and annotated and analyzed all graphs and equations.

Taking fault tree analysis as an example, the revised contents are as follows:

Construct FTA for Nuclear Security Radiation Events

Figure 1. Nuclear security fault tree for spent fuel reprocessing plant

Table 4. Nuclear security radiation event letter symbols and corresponding events

Number	Incident	Number	Incident
T	Nuclear security radiation incident	M₁₀	Support equipment failure
M₁	Radioactive release event	M₁₁	Lose
M₂	Emergency failure	X₁	Radioactive dispersal device
M₃	Leakage of high level of waste liquid	X₂	Computer nuclear security
M₄	Container leak	X₃	Destruction of nuclear facilities
M₅	Transit system leakage	X₄	Transportation nuclear security
M₆	Overfeeding	X₅	Internal threat
M₇	Auxiliary device failure	X₆	Potential threat
M₈	Monitoring equipment failure	X₇	Illegal transfer
M₉	Test instrument failure	X₈	Theft

3.1. Structure Function of Fault Tree

The top event is represented by T, then the fault tree structure function T= is a function of X₁, X₂, … X₈, whilst gate"·" is multiplication or gate"＋" is addition.

The structure function of the fault tree is:

T=X₁+X₃*X₆+X₄*X₇+X₂+X₅*X₆+X₂+X₆+X₅+X₃*(X₇+X₈)+X₃*(X₇+X₈)

=X₁+X₂+X₅+X₆+X₃*X₇+X₃*X₈+X₄*X₇

From the result of structure function T, the minimum cut set can be obtained:

{X₁}, {X₂}, {X₅}, {X₆}, {X₃,X₇}, {X₃,X₈}, {X₄,X₇}

3.2. Importance analysis of the Fault Tree

Therefore, the importance analysis of the above fault tree is carried out. See (3.1-3.3) for the formula [23] of structural importance, probability importance and critical importance.

(3.1)

(3.2)

(3.3)

The order of structure importance is as follows:

I(X₁)=I(X₂)=I(X₅)=I(X₆)>I(X₃)=I(X₇)>I(X₄)=I(X₈)

The probability importance is:

X₁=0.640,X₂=0.648,X₃=0.130,X₄=0.068,X₅=0.640,X₆=0.640,X₇=0.156,X₈=0.062

The order of probability importance is:

Ig(X₂)>Ig(X₁)=Ig(X₅)=Ig(X₆)>Ig(X₇)>Ig(X₃)>Ig(X₄)>Ig(X₈)

The critical importance is: X₁=0.176，X₂=0.193，X₃=0.036，X₄=0.028，X₅=0.176，X₆=0.176，X₇=0.046，X₈=0.018

The order of critical importance is:

(X₂)>(X₁)=(X₅)=(X₆)>(X₇)>(X₃)>(X₄)>(X₈)

Response 4: For font, variable and other format problems, we also revised them in accordance with the requirements.

Specific comments:

The following numbers stated in brackets are denoting line number in the manuscript - authors are encouraged to fully address the following:

Point 1: (15) small font of "nuclear accident types" should be corrected; (29-30) the first sentence has a small font size; (90) consider smaller font for table 1 (and rest of the tables) to accommodate reading; (102-106) again small figure-caption font; (107) missing blank after "Table 2."; (108) missing blank after "Table 3."; separation space is also needed between tables; (109) missing dot in paragraph number, i.e. "3. Construct ...." (an in all others),professor" should be "Professor"; (125-198)the variables should not be bold and should be in italic font，the subscripts should be in appropriate format and consistent with text，the main quantities should be designated with names, not with "it"; (206) missing dot at the end of the sentence; (210) missing blank before "The weight..."; (213) missing blank after "Table 4."; in table 4; (229-234) figures 2-13 are missing blank before figure caption number; (280-290) again small figure-caption font.

Response 1: Thank you very much for your careful review. For the above format problems, we have made unified modifications and corrections.

Point 2: (19) FTA should be "Fault Tree Analysis"

Response 2: (20) Thank you very much for your guidance. We have corrected this problem and put it in line 20 of the document.

Point 3: (21) Maybe "comprehensive" term is too strong, consider replacing it throughout the text with "elementary" since you are using basics of the aforementioned methods (probability, statistics, fuzzy logic, etc.).

Response 3: (65) We are apologizing that the name of this method was written incorrectly due to our work mistakes. The correct method name is "fuzzy decision method", and we have modified the similar problems in the whole paper.

Point 4: (34-40) to long and a very unclear sentence, consider breaking into several more meaningful sentences.

Response 4: Since the introduction of the article has been completely revised, this paragraph has been deleted.

Point 5: (35) missing many references ....

Response 5: Due to our mistakes, there are problems in the selection and citation of references, so all the references have been revised.

Point 6: (42-43) this sentence should be put at the end of the Introduction paragraph, and additional references should be included, with explained motivation for this work.

Response 6: Thank you very much for your suggestion. We have modified this part and reflected it in the introduction.

Point 7: (65) "is divided" should be out after "reprocessing plant"

Response 7: This sentence has been revised as required, and the revised sentence is as follows:

(90) and the spent fuel pool is divided into four plant areas.

Point 8: (75) missing argumentation why these specific 8 cases? maybe additional references are missing?

Response 8: (48-53) We are sorry that we are missing references due to our mistakes. Now, the reference to eight basic events has been supplemented in References [5] -[13].

Point 9: "litter" is typo, should be "little"

Response 9: (100) We are very apologizing for our mistakes, but due to the polish of the English language, the word in the full text has been replaced with “slightly”.

Point 10: (96-101) again to long and very unclear sentence, consider several shorter sentences.

Response 10: We have made modifications as required, and the modified contents are as follows:

(120-126) The number of units with a "very small" probability of the radioactive dispersion device event, which is evaluated by each group of experts, is multiplied by the expert weight of the corresponding group. On such a basis, the probability value of the event can be calculated, the occurring likelihood of which is "very small" in the same way, the probability can be a small, slightly small, medium, somewhat large, large, or very large probability value, and the algorithm’s normalized corresponding results are obtained.

Point 11: (112-113) looks like sentence is 2xcopied, consider merging in "... is qualitative and quantitative analysis"

Response 11: We are apologizing for the repetition of the article due to our carelessness, and have revised it. The revised contents are as follows:

(180-181) Among them, the structural importance degree is qualitative analysis, the probability and critical importance degree is quantitative analysis.

Point 12: (116) missing reference(s) for the statement of investigations

Response 12: Since the previous introduction was poorly written, we did not cite the contents of the survey statement. We have now supplemented it in [5] - [13] of the references.

Point 13: (117-119) consider dismissing this, since you are again repeating this section; (218-220) consider dismissing, you are again repeating.

Response 13: Thank you very much for your suggestion. We deleted it as required.

Point 14: (125-198) This section badly needs rewriting.

Response 14: (137-229) Thank you very much for your suggestions. We have sorted out and modified this part as required. Since all the above replies have been copied, there is no repeated release here.

Point 15: (151, 157, 165, 171) rephrasing is needed for sentences starting with "According to..."; again

Response 15: These sentences beginning with "according to" have been modified accordingly, such as line 172.

Point 16: please check in (164) strange new quantities, which are not in accordance with eq(3.1)

Response 16: (194) We are apologizing that the variable was written incorrectly due to our mistakes. Now we have corrected it. Its correct form is I(X₁).

Point 17: missing IAEA references in (143)

Response 17: Thank you very much for your guidance. As the content here has been modified, the IAEA references are no longer involved.

Point 18: consider finishing the sentence in (146); explain the meaning of T.

Response 18: (143) We supplemented the explanation of the meaning of "T" The top event is represented by T.

Point 19: the sentence in (196) sounds like copy-paste error, please revise.

Response 19: Thank you for your guidance. The revised sentence is as follows: (226-229) Of the comprehensive quantitative and qualitative factors, it can be concluded that importance analysis of computer nuclear security is the biggest, which should be paid more attention to in daily operation and management; importance analysis of theft is minimal, but it may happen.

Point 20: Figure 1 has missing letters in boxes on several instances.

Response 20: We have redrawn the accident tree as follows:

The specific events represented by each number are shown in the following table.

Number	Incident	Number	Incident
T	Nuclear security radiation incident	M₁₀	Support equipment failure
M₁	Radioactive release event	M₁₁	Lose
M₂	Emergency failure	X₁	Radioactive dispersal device
M₃	Leakage of high level of waste liquid	X₂	Computer nuclear security
M₄	Container leak	X₃	Destruction of nuclear facilities
M₅	Transit system leakage	X₄	Transportation nuclear security
M₆	Overfeeding	X₅	Internal threat
M₇	Auxiliary device failure	X₆	Potential threat
M₈	Monitoring equipment failure	X₇	Illegal transfer
M₉	Test instrument failure	X₈	Theft

Point 21: (203) "The factor set ..."

Response 21: (232) We modified it as required and added "The".

Point 22: (210) "difficult influence" should probably be "different influence", please check.

Response 22: Thank you for your meticulous guidance. This problem was caused by our mistakes and has now been modified. As follows:

(238-239) Since the influence degree of each factor in the factor set on the nuclear security system is different, the weight coefficient should be considered.

Point 23: (213) "The weight" should be changed to "Weight coefficient"

Response 23: We have made modifications as required, as follows:

(240) The weight coefficient of each factor is obtained.

Point 24: (214) what is the meaning of that sentence?

Response 24: We added the analysis and interpretation of the weight set. As follows:

(239) It reflects the level of importance of each factor. (245) Taking the factor of the radioactive dispersal device as an example, it represents that the subordinate degree of this factor to "important" is 0.12.

Point 25: (227) "Through statistic and sorting..." this is no explanation, you need to describe you work, this is very unclear.

Response 25: We are apologizing that we did not clearly describe the origin of the segmented histogram before, but now we have supplemented it, as follows:

(255-261) V={small (V₁), small (V₂), small (V₃), medium (V₄), larger (V₅), large (V₆), large (V₇)}.

The probability distribution of a radioactive dispersal device event in a spent fuel pool area is taken as an example. Experts believe that 67.6% of the probability of the event is "very small", 30.3% is "small", and 2.1% is "slightly small".

After analysis and calculation, the probability distribution of eight types of basic events in each evaluation unit is obtained. See Table 5 for details.

Point 26: (229-234) "s" for "results"; no comments are following after the figures?

Response 26: We have made corresponding modifications and supplemented the corresponding conclusions. As follows:

(267-274) Taking the spent fuel pool as an example, this evaluation unit has a 67.6% probability of occurrence of radioactive dispenser events with a "very small" probability, a 46.1% probability of occurrence of computer nuclear security events with a "slightly small" probability, a 54.1% probability of occurrence of nuclear facility damage events with a "medium" probability, and a 35.2% probability of occurrence of transportation nuclear security events with a "medium" probability, there is also a 54.1% probability that internal threats will occur with a "medium" probability and a 64.5% probability that potential threats, illegal transfers, and theft will occur with a "very small" probability.

Point 27: (253) What is B, A, R in B = A*R? you need to describe this, and also to give comment why is important so have in text "evaluation unit" with numbers?

Response 27: (296-297) B represents the result of the evaluation set, A represents the weight set, and R represents the evaluation matrix.

The main purpose of this paper is to analyze the risk of each plant area of the spent fuel reprocessing plant, where each plant area is composed of multiple evaluation units, and the evaluation units are subsets of the plant area, so the evaluation units are important.

Point 28: (281-285) long and unclear sentence, please rephrase.

Response 28: Thanks for your guidance, we have revised the description of this paragraph as follows:

(328-332) Among them, the tail-end conversion plant is the most dangerous, which has a significant impact on the overall safety of the spent fuel reprocessing plant. Therefore, more attention should be paid to the tail-end conversion plant in the daily safety inspection and emergency drill of the spent fuel reprocessing plant, and emergency plans for various accidents should be made to prevent accidents.

Point 29: (301) consider adding "..., and the probability";

Response 29: We have made modifications as required, and the modified contents are as follows:

The probability of occurrence of basic events is difficult to obtain and the accuracy is low.

Point 30: why do you use term "accurate probability" since you haven't performed any comparison with alternative (similar) approaches, i.e. how can you be sure in your numbers?

Response 30: We are apologizing that our statement here is not accurate enough. Due to the particularity of the spent fuel reprocessing plant, the probability of nuclear security incidents is fuzzy. At the same time, the conclusion we want to obtain is not a precise probability, but a system that can analyze the risk of each plant in the spent fuel reprocessing plant. According to this conclusion, we can reasonably allocate the protective forces of plants with different hazard levels, so as to achieve the effect of saving resources. Therefore, the use of "accurate probability" here is not rigorous. Thank you very much for your professional comments, and we have decided to delete this word.

Point 31: (316-317) copy-paste error sentence ...

Response 31: We have revised this sentence as required. As following:

(364-365) The method of adding and taking the average value shows that the main process area is the most dangerous.

Thanks again for your suggestion. It is very important. Because of your suggestion, we found the shortcomings in our current work. We will improve our scientific research level according to your suggestions and guidance in the future work and make more achievements.

Author Response File: Author Response.pdf

Reviewer 4 Report

1)citation must be done at all reference paper.

2)peculiar sever accidents such as criticality, explosion, fire, abnormal release of radioactive, leakage, unexpected exposure, etc, must be taken into the account in the risk analysis of spent fuel reprocessing plant.

Author Response

Response to Reviewer 4 Comments

Point 1: Citation must be done at all reference paper.

Response 1: We are apologizing for the mistakes in our work, resulting in too few references. Now all the references have been revised and quoted in the introduction. The references in the introduction are as follows:

Based on eight types of basic nuclear security incidents, this paper uses the expert scoring method to quantify qualitative information in the form of frequency instead of probability. The fault tree model of nuclear security radiation events in the spent fuel re-processing plant has been established, and the importance of each basic event has been determined. Using the method of fuzzy decision and probability-mathematical statistics, the risk of each plant in the spent fuel reprocessing plant has been studied, and the relationship between the risk degree gap among them has been obtained. The research meth-od of this paper can be input real numbers or probabilities on different events, which many lead to accidental situations, so it can be used as a guideline (one of them) on how to distribute money and manpower in nuclear installations to mitigate risk.

Point 2: peculiar sever accidents such as criticality, explosion, fire, abnormal release of radioactive, leakage, unexpected exposure, etc. must be taken into the account in the risk analysis of spent fuel reprocessing plant.

Response 2: I'm apologizing that due to our mistakes, the introduction was not clearly described, which led to your misunderstanding. This paper focuses on the risk analysis and evaluation of "nuclear security" radiation events in spent fuel reprocessing plants, and discusses the importance of eight basic nuclear security events, such as radioactive dispersal device and computer nuclear security. We are deeply sorry for this mistake, so we have completely revised the introduction of the article, especially emphasizing the difference between "nuclear safety" and "nuclear security". Nuclear security is defined as the prevention and detection of, and response to, theft, sabotage, unauthorized access, illegal transfer, or other malicious acts involving nuclear material, other radioactive substances, or their associated facilities. The definition of nuclear safety is different, which is the achievement of proper operating conditions, prevention of accidents or mitigation of accident consequences, resulting in protection of workers, the public and the environment from undue radiation hazards. A key difference between nuclear safety and security is intentionality. Accidents related to nuclear safety are unintentional, whereas nuclear security incidents are clearly intentional and undertaken with a specific motive.

Criticality, explosion, fire, abnormal release of radioactive, leakage, unexpected exposure, etc. are specific events. What we need to discuss are several types of accidents that threaten the spent fuel reprocessing plant. Criticality, explosion, fire, abnormal release of radioactive, leakage, unexpected exposure, etc have been included in the eight categories of basic nuclear security accidents we studied.

Thank you for your professional and insightful comments. We hope our modifications and responses can satisfy you and meet the publication requirements!

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The revised paper is greatly improved and more thoroughly explains the proposed risk methodology in a more logical and complete way than the original version of the manuscript. The authors have addressed all the raised questions in a satisfactory way, so I would recommend this revised version to be accepted by the Journal in the present form.

Author Response

Response to Reviewer 3 Comments

Point: The revised paper is greatly improved and more thoroughly explains the proposed risk methodology in a more logical and complete way than the original version of the manuscript. The authors have addressed all the raised questions in a satisfactory way, so I would recommend this revised version to be accepted by the Journal in the present form.

Response: Thank you very much for your recognition of the revised paper. Because of your constructive suggestions, this article can be more complete and logical. As the supporters of this article, we are very moved by your suggestions and express our heartfelt thanks to you! At the same time, we also combined the suggestions of the editor to further optimize and improve the article from different angles.

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Risk Analysis and Evaluation of Nuclear Security Radiation Events in Spent Fuel Reprocessing Plants

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