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

Abstract

Spent fuel reprocessing is of great significance to the nuclear fuel cycle and the sustainable development of nuclear energy. At the same time, nuclear security radiation incidents in the spent fuel reprocessing plant are also related to national personal and property safety, which play a pivotal role. In this paper, the spent fuel reprocessing plant is divided into four plant areas: the main process area, the three-waste area, the auxiliary equipment area, and the pre-plant area, which are further subdivided into 12 evaluation units. The expert scoring method is used to score and evaluate the possibility of eight basic nuclear accident types in each area, namely radioactive dispersal device, computer nuclear security, destruction of nuclear facilities, transportation nuclear security, internal threat, potential threat, illegal transfer, and theft. According to the professional titles, length of service, education and other qualifications of experts, different weights are assigned to the experts. The scoring results are applied to the Fault Tree Analysis (FTA) of nuclear security events as the probability of basic events, so as to obtain the risk of each basic event. At the same time, the fuzzy comprehensive evaluation method and probability–mathematical statistics method are used to evaluate each evaluation unit to determine the risk of each evaluation unit and the plant area. There results show that the main process area has the highest risk degree, while the pre-plant area has the lowest risk degree, and there is a 1.5-fold relationship. This research provides theoretical and technical support for the safety management and operation of spent fuel reprocessing plants. The analysis results of this paper can be used as a reference for the proportion of nuclear security protection improvements in each plant area, so as to achieve an efficient safety protection effect. The research method in this paper can be also applicable to other similar places by providing as input the corresponding probability of occurrence to obtain the index of its risk degree, so as to reasonably allocate funds and manpower and reduce risks.

1. Introduction

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. 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 [4], computer nuclear security breaches called cyber terrorism at nuclear facilities [5], the destruction of nuclear facilities as a result of an external attack [6], transport nuclear security with a risk of radioactive material release [7], the internal threat of one of the most serious problems in the supervision of the physical protection of spent fuel reprocessing plants [8], potential threats [9], illegal transfer of nuclear materials and other radioactive sources [10], and theft [11].

The safety system theory analysis method can be adopted to analyze and evaluate the risk of the spent fuel reprocessing device [12], which has certain feasibility. Firstly, it is necessary to determine the possibility of the occurrence of each basic event. The expert scoring method [13], 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 [14], and can achieve the qualitative assessment of the occurrence probability and consequence of the identified event [15]. In terms of the risk analysis of basic events [16], 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 [17], and it has effective quantitative properties on the probability of accidents [18]. The fuzzy comprehensive evaluation method can quantify some uncertain and difficult to quantify factors, intuitively reflect the membership of evaluation indicators, and more objectively and accurately reflect the real situation [19]. It is often used to make engineering decisions on fuzzy, imprecise, and uncertain existing data and information [20], and is widely used in architecture, management, biotechnology, medical science, environmental science and other fields [21,22,23,24,25]. Weijun Li et al. [26] used the fuzzy comprehensive evaluation method to evaluate the performance of enterprises in health, safety and environment (HSE) management, and took a specific petrochemical company as an example to verify the accuracy and effectiveness of this method. This method and academic thought are also applicable to the spent fuel reprocessing plant, the subject of this study. Therefore, it is verified from the side that when the probability of basic nuclear safety events occurring in the spent fuel reprocessing plant is difficult to obtain, the fuzzy comprehensive evaluation method has significant advantages in the internal risk analysis of the spent fuel reprocessing plant, and it also ensures the accuracy and effectiveness of the results.

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 comprehensive evaluation 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.

2. Determine the Basic Event Probability

It is very difficult to obtain the basic event probability value, which can be obtained through a large number of repeated trials, observations, analysis, and inspection; the accuracy will be affected by the environment and application conditions. Especially in the special nuclear environment of the spent fuel reprocessing plant, this paper uses the expert scoring method, combined with expert weights, to obtain the occurrence probability of each basic event by the weighted average method, and uses frequency to replace the probability.

2.1. Construct an Expert Scoring System

In the process of analysis and research in this paper, 30 experts were invited to form an expert group, and the spent fuel pool is divided into four plant areas: the main process area, the three-waste area, the auxiliary equipment area and the pre-plant area. In order to improve the accuracy of the analysis, the evaluation unit is further subdivided, and the main process area is divided into three units: the spent fuel pool, the extraction process plant, and the tail-end conversion plant. The three-waste area is divided into four units: waste liquid purification workshop, curing workshop, discharge workshop and solid waste reconditioning workshop. The auxiliary equipment area is divided into two units: equipment room and warehouse. The pre-plant area is divided into three units, such as central control room, office, and dormitory, with a total of twelve units. At the same time, the possibility of the occurrence of eight types of basic nuclear security incidents is divided into seven levels: very small, small, slightly small, medium, somewhat large, large, and very large. Through the above settings, experts evaluate the possibility of various nuclear security incidents in each evaluation unit.

Due to the deviation in the familiarity of the experts with the spent fuel reprocessing plant and the eight types of nuclear security events, in order to ensure the accuracy of the conclusion, the experts’ qualifications such as professional title, educational background, length of service, and fit degree of work unit are given corresponding scores, and then normalized to form corresponding weights. In order to facilitate the statistical data and presentation, the experts with the same score are divided into the same group, so the 30 invited experts are divided into six groups, and the specific grouping is shown in

Table 1. Expert weight allocation table.

Serial Number/ Group	Experts	Number of People	Qualification	Length of Service	Record of Formal Schooling	Total	The Weight
1	Safety Engineer	9	5 (Senior Engineer)	5 (30 to 40 years)	5 (PhD students)	15	0.115
2	Safety Engineer	8	5 (Senior Engineer)	4 (20 to 30 years)	4 (Master’s students)	13	0.352
3	Strategic Planner	6	4 (Researcher)	3 (10 to 20 years)	5 (PhD students)	12	0.272
4	Professor	4	4 (Associate Professor)	2 (5 to 10 years)	5 (PhD students)	11	0.188
5	Safety Engineer	2	3 (Assistant Engineer)	2 (5 to 10 years)	5 (PhD students)	10	0.021
6	Safety Engineer	1	3 (Assistant Engineer)	1 (0 to 5 years)	4 (Master’s students)	8	0.052

below. Assuming that a total of n experts participate in the scoring, the total score of each expert is C, then the weight $X_{\mathfrak{i}}$ of each expert is as follows:

$$X_{\mathfrak{i}}=\frac{C_{\mathfrak{i}}}{{{\displaystyle \sum }}_{\mathfrak{i}=1}^{\mathrm{n}}{C}_i}$$

(1)

In the formula, $C_{\mathfrak{i}}$ represents the total score of the first expert.

2.2. Calculation of Probability of Occurrence of Basic Events

The radioactive dispersal device event is used here as an example. The first group of experts considers that among the 12 evaluation units, there are 3 units with a very small probability of radioactive dispersal device events, 4 units with a small probability, 3 units with a slightly small probability, and 1 unit with a somewhat large probability. In the same way, the evaluation results of the other five groups of experts can be obtained. 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. According to the principle of probability theory, the probability of occurrence is set as P, then the probability of non-occurrence is $\left(1-P\right)$. The probability of non-occurrence of the top event can be obtained by multiplying the probability of non-occurrence of each basic event, and 1 minus the probability that the top event will not occur is the probability that the radioactive dispersal device event will occur. The calculation process of the event probability of the radioactive dispersal device is shown in

Table 2. Calculation table of probability of occurrence of basic events.

The Serial Number	The Weight	Very Small	Small	Slightly Small	Medium	Somewhat Large	Large	Very Large
1	0.115	3	4	1	0	1	3	0
2	0.352	7	0	0	4	1	0	0
3	0.272	7	2	2	0	1	0	0
4	0.188	0	1	7	4	0	0	0
5	0.021	5	1	6	0	0	0	0
6	0.052	6	1	0	1	1	3	0
A total of		5.130	1.537	1.101	2.212	0.052	0.501	0
The normalized		0.455	0.136	0.098	0.196	0.070	0.045	0
1 − P		0.545	0.864	0.902	0.804	0.930	0.955	1

. The occurrence probability and normalized results of the eight basic events are shown in

Table 3. List of basic nuclear security incidents for spent fuel reprocessing plants.

Event Number	The Name of the Event	Probability of Occurrence	Normalized Results
X1	Radioactive dispersal device	0.697	0.12
X2	Computer nuclear security	0.706	0.13
X3	Destruction of nuclear facilities	0.690	0.12
X4	Transportation nuclear security	0.707	0.13
X5	Internal threat	0.702	0.12
X6	Potential threat	0.687	0.12
X7	Illegal transfer	0.721	0.13
X8	Theft	0.709	0.13

.

3. 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. 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 = $\varnothing \left(X\right), \varnothing \left(X\right)$ 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 $\phi \left({\rm X}\right)$ 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 $\phi \left({\rm X}\right)$ status value is 1; if the state values of X₃ and X₈ are 1 at the same time, the $\phi \left({\rm X}\right)$ state value is 1;if the state values of X₄ and X₇ are 1 at the same time, the $\phi \left({\rm X}\right)$ 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 (2)–(4) for the formula [27] of structural importance $\mathrm{I}\mathsf{\phi }\left(X_{\mathfrak{i}}\right)$, probability importance $\mathrm{I}\mathrm{g}\left(X_{\mathfrak{i}}\right)$ and critical importance ${\mathrm{I}}_{\mathsf{\delta }}\left(X_{\mathfrak{i}}\right)$.

$${\mathrm{I}}_{\mathsf{\phi }}\left(X_{\mathfrak{i}}\right)=\frac{1}{2^{\mathrm{n}-1}}{\displaystyle \sum }_1^{2^{\mathrm{n}-1}}\left[\mathsf{\phi }\left(1_{\mathfrak{i}}, \mathrm{X}\right)-\mathsf{\phi }\left(0_{\mathfrak{i}}, \mathrm{X}\right)\right]$$

(2)

$${\mathrm{I}}_{\mathrm{g}}\left(X_{\mathfrak{i}}\right)=\frac{\partial \mathrm{Q}}{\partial {\mathrm{q}}_{X_{\mathfrak{i}}}}$$

(3)

$${\mathrm{I}}_{\mathsf{\delta }}\left(X_{\mathfrak{i}}\right)=\frac{\raisebox{1ex}{$\partial \mathrm{Q}$}\!\left/ \!\raisebox{-1ex}{$\partial {\mathrm{q}}_{X_{\mathfrak{i}}}$}\right.}{\raisebox{1ex}{$\mathrm{Q}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{q}}_{X_{\mathfrak{i}}}$}\right.}$$

(4)

Among them, $X_{\mathfrak{i}}$ 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:

$$\mathrm{I}\mathsf{\phi }\left({\mathrm{X}}_1\right)=\mathrm{I}\mathsf{\phi }\left({\mathrm{X}}_2\right)=\mathrm{I}\mathsf{\phi }\left({\mathrm{X}}_5\right)=\mathrm{I}\mathsf{\phi }\left({\mathrm{X}}_6\right)=\mathrm{I}\mathsf{\phi }\left({\mathrm{X}}_3\right)=\mathrm{I}\mathsf{\phi }\left({\mathrm{X}}_7\right)>\mathrm{I}\mathsf{\phi }\left({\mathrm{X}}_4\right)=\mathrm{I}\mathsf{\phi }\left({\mathrm{X}}_8\right)$$

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:

$${\mathrm{I}}_{\mathsf{\delta }}\left({\mathrm{X}}_2\right)>{\mathrm{I}}_{\mathsf{\delta }}\left({\mathrm{X}}_1\right)={\mathrm{I}}_{\mathsf{\delta }}\left({\mathrm{X}}_5\right)={\mathrm{I}}_{\mathsf{\delta }}\left({\mathrm{X}}_6\right)>{\mathrm{I}}_{\mathsf{\delta }}\left({\mathrm{X}}_7\right)>{\mathrm{I}}_{\mathsf{\delta }}\left({\mathrm{X}}_3\right)>{\mathrm{I}}_{\mathsf{\delta }}\left({\mathrm{X}}_4\right)>{\mathrm{I}}_{\mathsf{\delta }}\left({\mathrm{X}}_8\right)$$

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 is minimal, but it may happen.

4. Construct a Fuzzy Comprehensive Evaluation System

The fuzzy comprehensive evaluation method includes five steps: factor set, weight set, evaluation set, single factor fuzzy evaluation and fuzzy comprehensive evaluation [26].

4.1. Construct Factor Set

The factor set refers to the set of elements that affect the evaluation in the decision-making system. The factor set U is composed of eight risk factors affecting nuclear security events in the spent fuel reprocessing plant, including the radioactive dispersal device, computer nuclear security, destruction of nuclear facilities, transportation nuclear security, internal threat, potential threat, illegal transfer, and theft.

4.2. Construct Weight Set

Since the influence degree of each factor in the factor set on the nuclear security system is different, the weight coefficient should be considered. It reflects the level of importance of each factor. The weight coefficient of each factor is obtained by the above method of the frequency instead of the probability of the expert scoring method, and the specific weight value is shown in

Table 5. Weight values of each factor.

	Factors	The Weight
U1	Radioactive dispersal device	0.12
U2	Computer nuclear security	0.13
U3	Destruction nuclear facilities	0.12
U4	Transportation nuclear security	0.13
U5	Internal threat	0.12
U6	Potential threat	0.12
U7	Illegal transfer	0.13
U8	Theft	0.13

The weight set A = {0.12 0.13 0.12 0.13 0.12 0.12 0.13 0.13}.

.

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.

4.3. Construct Evaluation Set

The four plant areas of the evaluation object spent fuel reprocessing plant are subdivided into 12 areas, which are the evaluation units for comprehensive evaluation. In order to evaluate its importance in nuclear security accidents, senior engineers, researchers, professors, and other experts from relevant nuclear industry groups, research institutes, and universities are invited to form an expert group to score and evaluate the possibility of eight types of basic nuclear security events in each region. The possibility is divided into seven levels, which are: very small, small, slightly small, medium, somewhat large, large and very large. 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 Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 for details. The abscissa in the figure is the first two digits of the first letter of eight basic events.

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.

4.4. Single Factor Fuzzy Evaluation

In the research of this paper, there are eight factors affecting nuclear security accidents, and one factor is evaluated separately to determine the membership degree of the evaluation object to the elements of the evaluation set.

Suppose the $\mathfrak{i}$ element in the factor set U is judged, and the membership degree of the $\mathfrak{j}$ element in the evaluation set V is ${\mathrm{r}}_{\mathfrak{i}\mathfrak{j}}$, then the fuzzy set can be obtained according to the evaluation result of the $\mathfrak{i}$ factor:

$$R_{\mathfrak{i}}=\{r_{\mathfrak{i}1},r_{\mathfrak{i}2},\cdots ,r_{\mathfrak{i}n}\}$$

The membership degree rows of each single-factor evaluation set are formed into a matrix, which is called the evaluation matrix:

$$\mathrm{R}=\left(\begin{array}{ccc}{\mathrm{r}}_{11}& \cdots & {\mathrm{r}}_{1\mathrm{n}}\\ ⋮& \ddots & ⋮\\ {\mathrm{r}}_{\mathrm{m}1}& \cdots & {\mathrm{r}}_{\mathrm{mn}}\end{array}\right)$$

In this paper, the spent fuel pool unit in the main process area is taken as an example for calculation. According to the above, the evaluation matrix of the spent fuel pool unit in the main process area is:

$$R_1=\left(\begin{array}{c}0.676 0.303 0.021 0 0 0 0 \\ 0.373 0.166 0.461 0 0 0 0 \\ 0 0.188 0.271 0.541 0 0 0 \\ 0.272 0.052 0.209 0.352 0.115 0 0 \\ 0.293 0.166 0 0.541 0 0 0 \\ 0.645 0.167 0 0.188 0 0 0\\ 0.645 0.167 0 0.188 0 0 0\\ 0.645 0.167 0.188 0 0 0 0\end{array}\right)$$

4.5. Fuzzy Comprehensive Evaluation

Fuzzy comprehensive evaluation refers to the comprehensive consideration of the impact of eight basic events on nuclear security radiation events in each evaluation unit, and the final evaluation results are obtained. The formula of the fuzzy comprehensive evaluation model is as follows:

B = AR

(5)

B represents the result of the evaluation set, A represents the weight set, and R represents the evaluation matrix.

The evaluation set results of each evaluation unit can be obtained as follows:

spent fuel pool B₁ = [0.130 0.130 0.130 0.130 0.115 0 0]

extraction process plant B₂ = [0.130 0.130 0.130 0.130 0.120 0.115 0]

tail-end conversion plant B₃ = [0.130 0.120 0.130 0.130 0.130 0.130 0]

waste liquid Purification Workshop B₄ = [0.130 0.130 0.130 0.120 0.120 0.120 0]

solidification workshop B₅ = [0.130 0.130 0.130 0.052 0.115 0.052 0]

discharge workshop B₆ = [0.130 0.130 0.130 0.120 0 0.120 0]

solid waste preparation workshop B₇ = [0.130 0.130 0.130 0.130 0.115 0 0]

equipment room B₈ = [0.130 0.130 0.130 0.130 0.130 0 0]

warehouse B₉ = [0.130 0.130 0.130 0.130 0.130 0 0]

centralized control room B₁₀ = [0.130 0.130 0.130 0.120 0 0 0]

office B₁₁ = [0.130 0.130 0.130 0.130 0 0 0]

dormitory B₁₂ = [0.130 0 0.130 0 0 0 0]

5. Probability and Mathematical Statistical Evaluation

The method of probability and mathematical statistics is used to process the data after fuzzy comprehensive evaluation. Taking the spent fuel pool unit as an example, 13% of the experts think that the risk is very small, 13% think the risk is small, 13% think that the risk is slightly small, 13% think the risk is medium, and 11.5% think the risk is somewhat large. According to the knowledge of probability theory, the following can be obtained:

$$1-B_1=[0.870 0.870 0.870 0.870 0.885 1 1]$$

(6)

Then, the probability P of no danger for the spent fuel pool unit is:

0.870 × 0.870 × 0.870 × 0.870 × 0.885 × 1 × 1 = 0.507

(7)

Therefore, the hazard probability of the spent fuel pool unit is: 1 − P = 1 − 0.507 = 0.493.

This method is used to calculate the risk of 12 evaluation units, and the results are shown in

Table 6. Evaluation of unit hazard calculation results.

The Evaluation Unit	Spent Fuel Pool	Extraction Process Plant	Tail-End Conversion Plant	Waste Liquid Purification Workshop	Solidification Workshop	Discharge Workshop
The calculation results	0.493	0.554	0.561	0.551	0.476	0.490
Normalized results	0.086	0.097	0.098	0.096	0.083	0.086
The Evaluation Unit	Solid Waste Preparation Workshop	Equipment Room	Warehouse	Centralized Control Room	Office	Dormitory
The calculation results	0.493	0.502	0.502	0.421	0.427	0.243
Normalized results	0.086	0.088	0.088	0.074	0.075	0.043

below.

In order to rationally allocate the protective forces in nuclear facilities, the importance of 12 evaluation units is compared and analyzed. As can be seen from the above evaluation results, there are significant differences in the hazards of the twelve evaluation units in the spent fuel reprocessing plants. 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. The dormitory area is the least dangerous, but this does not mean that the accident will not occur in the area, so it is also necessary to put in a certain amount of manpower and material resources to prevent tragedy from happening.

According to the above data, it is possible to obtain the hazard probability values of the four plant areas by adding and averaging them, and the specific results are shown in

Table 7. Calculation results of hazardous levels in the plant area.

The Factory	The Main Process Area	Three-Waste Area	Auxiliary Equipment Area	Pre-Plant Area
The calculation results	0.536	0.503	0.502	0.364
Normalized results	0.281	0.264	0.264	0.191

below.

As can be seen from the results in Table 7, the order of importance of the four plants is: main process area > three-waste area > auxiliary equipment area > pre-plant area. The results show that in the spent fuel reprocessing plant, the main process area has the highest risk. Therefore, more attention should be paid to the establishment and implementation of various preventive measures and systems. The pre-plant area has the lowest risk, but there is still the possibility of risk, which requires to be paid more attention to. At the same time, the risk of the main process area is about 1.5 times that of the pre-plant area, which also indicates that it is a more appropriate arrangement to invest 1.5 times the safety protection force of the pre-plant area in the main process area.

6. Comparative Analysis of Results

According to the risk assessment of each evaluation unit by experts, the index method is used to analyze them. The index method is to sum up and average the probability of eight types of nuclear security incidents in each plant area that are not less than “medium” by experts, and compare the results with those obtained by the above fuzzy comprehensive evaluation method, probability mathematical statistics and other methods. The risk calculation results of the assessment unit calculated according to the index method are shown in

Table 8. Risk calculation results of evaluation unit (index method).

The Evaluation Unit	Spent Fuel Pool	Extraction Process Plant	Tail-End Conversion Plant	Waste Liquid Purification Workshop	Solidification Workshop	Discharge Workshop
The calculation results	0.240	0.272	0.736	0.707	0.034	0.059
Normalized results	0.083	0.095	0.256	0.245	0.012	0.020
The Evaluation Unit	Solid Waste Preparation Workshop	Equipment Room	Warehouse	Centralized Control Room	Office	Dormitory
The calculation results	0.222	0.091	0.275	0.156	0.088	0
Normalized results	0.077	0.032	0.095	0.054	0.031	0

, and the risk level calculation results of each plant area are shown in

Table 9. Calculation results of hazardous levels in the plant area (index method).

The Factory	The Main Process Area	Three-Waste Area	Auxiliary Equipment Area	Pre-Plant Area
The calculation results	0.416	0.117	0.183	0.081
Normalized results	0.522	0.146	0.230	0.102

.

According to the above data, the extraction process plant has the highest risk, and the main process area in the four plants has the highest risk, which is the same as the conclusion obtained through fuzzy comprehensive evaluation and probability mathematical statistics. However, there is a large discrepancy between the risk degree of the three waste areas and the results obtained by the main methods used in this paper. This is mainly because the index method ignores the influence of low probability of occurrence in the calculations. Therefore, it rationales the applicability of the fuzzy comprehensive evaluation and probability mathematical statistics methods.

7. Conclusions

(1)

The probability of occurrence of basic events is difficult to obtain and the accuracy is low, the expert scoring method can be adopted to avoid the error by setting the weight corresponding to the qualifications of experts. The method of frequency instead of probability can obtain the probability of basic events.

(2)

The fuzzy comprehensive evaluation method and the combination of probabilistic-mathematical statistics are used to obtain the hazards of each evaluation unit and plant area, which provides theoretical support for nuclear safety operations and emergency prevention of spent fuel reprocessing plants.

(3)

Through the fault tree and risk analysis, it is concluded that the computer nuclear security incident is the most dangerous of the eight types of nuclear security basic events, so it is necessary to take more precautions against the occurrence of such accidents in daily operation. Through the fuzzy comprehensive evaluation and the calculation method of probabilistic-mathematical statistics, it is concluded that the tail-end transformation plant in the main process area has the highest danger, and the dormitory unit in the pre-plant area of the factory has the lowest danger. The method of adding and taking the average value shows that the main process area is the most dangerous, the pre-plant area is the least dangerous, and there is a relationship of about 1.5 times, so a considerable proportion of manpower and material resources should be invested in the work to achieve the most economical and safe preventive effect.

(4)

In this paper, the expert scoring method is used to obtain the probability of eight basic events, which will make the subjective factors stronger. In the process of establishing the model, the fuzzy comprehensive evaluation method is inevitably affected by subjective factors in terms of index selection, evaluation criteria establishment and weight determination, which has certain limitations. Therefore, our future work will mainly focus on how to correctly handle the impact of subjective and objective factors on the results, and reduce the impact of subjectivity as much as possible.