A Method for Identifying the Key Performance Shaping Factors to Prevent Human Errors during Oil Tanker Offloading Work

<jats:p>Oil tanker offloading is a human-related and high-risk task. A small operational error may trigger catastrophic accidents such as fire and explosion. It is recognised that more than 70% of industrial accidents are blamed for human errors, so preventing them is crucial. As human error is associated with a variety of Performance Shaping Factors (PSFs), it is meaningful to identify key PSFs for safe operations during oil tanker offloading process. However, some issues are obstacles to finding the crucial PSFs. The recording data of most PSFs are always incomplete and imperfect. Moreover, the standard for ranking PSFs should be rational. In addition, the performance of each PSF at the different stages is oil offloading is usually unstable and may change with time. As a result, this study aims to conduct a method that mainly relies on Grey Relational Analysis (GRA), the definition of “Risk” (combination of likelihood and impact), and Hierarchical Task Analysis (HTA) to find several significant PSFs to prevent human errors. GRA deals with the incomplete and imperfect data; the definition of “Risk” provides a rational basis for ranking PSFs; and HTA gives support for considering the PSFs’ changes at different stages of a task. The proposed approach is tested on a real engineering case of oil tanker offloading work at offshore terminal. The result indicates that the method can be applied to identify key PSFs, which in turn provides recommendations for human error prevention to ensure the safety both on board and at terminal.</jats:p>

section_content: Human error is a considerable challenge to safety in an oil tanker offloading process. Many published reports and academic articles have concluded that over 70% of accidents are closely associated with human errors in the marine industries and the oil and gas industries [1] [2] [3] [4]. Therefore, preventing human error is important to ensure safety during oil tanker offloading work. 

It is acknowledged that human error is associated with many Performance Shaping Factors (PSFs) [5, 6], and many publications have indicated different PSFs have different weights on a human error, so finding key PSFs and control them can help to avoid human error strategically [7, 8]. However, the way for effectively identifying key PSFs is still a challenge. 

Thus far, many techniques have been designed to evaluate the different weights of different PSFs. Among them, the Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) are two typical methods [9, 10]. Both AHP and ANP have the function to estimate the importance weights of PSFs for determining the key one during operating a task [11]. AHP is suitable if all selected PSFs are mutually exclusive, and ANP is otherwise applied [12]. These techniques have been applied widely to assess and rank the significance weight degrees of PSFs. AHP has been selected to recognise the important PSFs for human error in marine-related operations for the oil and gas industries [13] [14] [15] ; ANP has also been used to determine the weight value of each PSF for human error to ensure safety [6, 10, 16]. However, AHP and ANP may not a perfect choice. Both AHP and ANP have insufficient considerations about dynamic scenarios in a task, because they mostly treat a task as a static whole. The second limitation is consistency tests are required for AHP and ANP. When there are too many PSFs, large efforts are needed to ensure the constructed pairwise comparison matrix can pass the consistency test. The third limitation is that the historical data of PSFs are always limited and imperfect. 

In 2017, a risk-based approach was published to rank key PSFs for the operations in the main control room of nuclear power plants [17]. It provides a well-designed procedure that can assess plenty of PSFs. The definition of "Risk" is used as the standard to identify key PSFs, which makes each PSF can be evaluated reasonably from different dimensions (likelihood and impact) [17]. However, the approach is still not strong enough to provide a robust PSF ranking. As PSF data recording is insufficient, research has used questionnaires for collecting risk data, and the mean value of the collected data for each PSF is used to describe each PSF. However, only using a simple mean value to describe a PSF may not reflect the true performance, since the mean value can be dominated by unreasonable maximum data or minimum data. Another significant issue is that research also gives limited consideration to the dynamic scenarios of a task, but a task is always a dynamic process [18, 19]. Therefore, to rely only on this approach is not comprehensive enough, but it is beneficial to judge PSFs by the definition of "Risk", which can make a rational identification and ranking. 

According to the above description, it can be found that the poor recording of PSF data, and the limited consideration on dynamic scenarios in a task are two main challenges to effectively identify key PSFs for human error prevention. In addition, when there are plenty of PSFs involved, the efforts used for finding the key PSFs may large. Therefore, this study will focus on dealing with the poor quality of PSFs' data recording and to consider the dynamic scenarios in the oil tanker offloading task in a rational way. 

As the recording of PSF's data is always incomplete and imperfect, grey theory should be an option for our research. Proposed by Deng, this theory is specifically designed for a system with incomplete and imperfect information [20], and many grey theory-based methods have been developed [21]. Among them, Grey Relational Analysis (GRA) is a typical one which has been applied to identify safety-and risk-related key factors [22]. This method is based on the similarity of geometric shape formed by all grey data of each contributing factor, so the influence from each datapoint can be easily included without extra efforts, such as through a consistency test. Thus far, GRA has been combined with Failure Mode and Effects Analysis (FMEA) to find the important failure modes among plenty of failure modes of tanker equipment, medical devices, and steam turbine system in power plants from the aspects of occurrence, severity, and detection [23] [24] [25] [26] [27]. Moreover, GRA has also been used to identify the key factors that can impact the safety decisions while manoeuvring an autonomous ship [28]. In addition, many data analysis techniques, such as fuzzy logic and Dempster-Shafer theory, have been integrated with GRA [23, 24, 29, 30]. Learning from the combination of GRA with FMEA and concerning this study, we can combine GRA with the definition of "Risk" to perform a grey and risk-based method for rationally finding key PSFs to prevent human errors. Six experienced domain experts are invited for collecting risk-based grey data to support the GRA practice. In order to consider the impacts caused by the differences among the six experts, AHP is used to determine their importance weights. It should be noted that we have enough information about each expert for applying AHP. 

As studies have indicated that a task is always performed dynamically in its different stages, the different performance of each PSF at different stages of a task must be considered. To obtain an effective result that can truly reflect the oil tanker offloading work, HTA should be adopted. It can effectively decompose a task into several Sub-tasks (STs) [31]. In this study, each PSF is considered and assessed in each ST, and with HTA, the changes of each PSF in the task operation process can be analysed for human error prevention. 

Based on the description above, this study aims to integrate HTA, AHP, GRA, and the definition of "Risk" together for effectively identifying key PSFs to strategically prevent human error. In the proposed method, HTA is conducted for considering the dynamics scenarios (the changes of each PSF during operating oil tanker offloading work); AHP is used to estimate the importance value of each invited expert; and the combination of GRA and the definition of "Risk" is used to deal with the imperfect and incomplete recording of PSFs' data for identifying some key PSFs. Namely, through the proposed method, this study can consider the dynamic scenarios and each expert's importance weight; moreover, this proposed method can simultaneously take plenty of PSFs' performance at different task stages into consideration; furthermore, it can deal with the incomplete and imperfect data of PSFs and to identify some important PSFs in a grey and risk-based rational way. Those together form the main contributions of this research. 

The remainder of this article is arranged as follows. Section 2 presents the methodologies used in this study and the steps of using the proposed approach for this study. Section 3 validates the proposed approach through a case study of an oil tanker offloading operation. Our research is compared and discussed in Section 4, and Section 5 relates our conclusions, limitations, and future work.
section_name: Introduction

section_content: According to the above description, three main approaches (HTA, AHP, and GRA) are selected to determine the significant PSFs for human error prevention during an oil offloading process. The details of the three methods are illustrated in following parts. Moreover, as oil tanker offloading tasks are related to the oil and gas industries, all of the nine PSFs involved in the Petro-HRA (Human Reliability Analysis) method are selected for analysis in this study, shown in Table 1.
section_name: Methodologies

section_content: HTA is one of the most famous techniques for task analysis. It is initially designed to describe and analyse operations in the chemical industries and the energy industries [35], and it has been expanded to many other industries [36]. The method has four steps. The first is to define the main task and its main goal. The second step is to decide the sub-goals of the main task. The third is to decide the STs within the main task and to match each ST to each sub-goal. The final step is to connect the STs to complete an entire HTA application. The procedure of HTA can be also found in Figure 1.
section_name: HTA Technique

section_content: AHP is a well-known technique for multicriteria decision-making. It starts with a pairwise comparison matrix to compare each alternative, and then, based on this pairwise comparison matrix, it collects the weight value of each alternative. The detailed procedures of the AHP method are presented as follows. In order to fill the required pairwise comparison matrix, Professor Thomas Saaty (the designer of AHP) provided a scale to describe the relative importance, shown in Table 2. Extreme importance (1, 3), (3, 5), (5, 7), (7, 9) Intermediate values between two adjacent judgments 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9

The inverse meaning of 2, 3, 4, 5, 6, 7, 8, and 9

Then, with Table 2, the pairwise comparison matrix can be formed, and Equation (1) presents its general expression:

where A is the required comparison matrix; in this matrix, the value 1 (equal importance) means an alternative compared with itself, element a ij (1 ≤ i ≤ n, 1 ≤ j ≤ n, i = j) in this matrix represents the importance value when one alternative i compared with another alternative j, while n means the total number of alternatives. With the matrix, the initial weight of each alternative can be determined through Equation (2):

where W i is the initial weight value of the ith alternative and a kj is the kth element in the jth column of matrix A. The remaining procedures of the AHP are to prove the comparison matrix and those collected initial weight data can pass a consistency test. This test starts with finding the Consistency Index (CI) value. Equation (3) shows how to find the CI value:

where n is the order of the matrix A, which equals to the number of alternatives, and λ max is the maximum eigenvalue of the matrix A, which can be found from Equation ( 4 ):

where E is the identity matrix and W is the matrix composed of each initial weight data collected from Equation ( 2 ) and can be expressed as

With the CI value, a Consistency Ratio (CR) is required for a consistency test. The way to find CR is expressed as Equation ( 5 ):

where RI represents the Random Index obtained from Table 3. When CR is less than 0. 1, the consistency test is acceptable. The procedure of AHP is also presented in Figure 2.
section_name: AHP Technique

section_content: GRA is a powerful technique to evaluate a system with imperfect and grey information [20, 21]. GRA generates the grey relational degree for assessing the relationship between the reference sequence and other comparative sequences. The procedures of the GRA application are presented below. 

The first step is grey data collection. For this research, several data series must be collected to form a grey matrix, which is expressed as Equation ( 6 ):

where X 1 through X m are the data series formed by the collected grey data and X m (s) represents the grey data in for the sth criterion in the mth data series. Because the grey data may have different units and criteria, we use a Likert-type scale from 0 to 5 to ensure comparability. The second step is to identify the reference series from the grey matrix. The determination of reference series depends on the research objective. For instance, if the objective is to analyse the grey relation between the best performance and other performance, then the best performance value for each criterion is selected to form the reference series, and vice versa. This study is to identify the risk-based grey relation degree, and the higher the risk-related value, the higher the level of importance, so the maximum risk-related value for each criterion is selected to build the reference series. Equation ( 7 ) displays the expression of it:

where X O means the reference series and

are the maximum value in the first, the second, • • •, and the sth criterion. The third step is to calculate the absolute differences between the reference series and other comparative series. Equation ( 8 ) presents the passage for obtaining the required absolute different values:

where ∆ od (h) is the absolute difference between X o (h), which is the hth element in the reference series, and X d (h), which is the hth element in the dth comparative series. 

In the fourth step, the grey relation coefficient can be collected through Equation ( 9 ) below:

where r d h is the grey relation coefficient between the hth element in the reference series and that in the dth comparative series. The term min 1≤d≤m min 1≤h≤s ∆ od (h) means the minimum value of each ∆ od (h). The max 1≤d≤m max 1≤h≤s ∆ od (h) is the maximum data of each ∆ od (h). δ ∈ [0, 1] is the identifier, and this parameter is to make the difference of grey relation coefficient for each element can be clearly identified. However, there is no certain conclusion about the value of δ, the designer of GRA and most applications suggest taking 0. 5 as the value for δ [20, [23] [24] [25] [26] [27] [28] [29] [30], so this study also takes 0. 5 as the value for δ. When the grey matrix M G is determined, the term min 1≤d≤m min 1≤h≤s ∆ od (h) and max 1≤d≤m max 1≤h≤s ∆ od (h) are two certain values, and the identifier δ is 0. 5, so in this equation, the variable is ∆ od (h). 

The fifth step is to determine the grey relationship degree. Equation (10) provides the way to find this degree:

where G d is the grey relational degree of the dth comparative series to the reference series. W h means the importance weight of the hth criterion and can be determined by AHP. As this study is risk-based, the grey relational degrees with respect to likelihood and impact are individually calculated. Then, through the product rule, the grey degree of likelihood and that of the impact is combined to determine the final risk-based grey relational degree. Equation (11) gives the expression:

Imp. d (11) where G Con. are the grey relational degree of the dth comparative series with respect to likelihood and impact, respectively. For this study, the procedure of GRA plus "Risk" is illustrated in Figure 3.
section_name: GRA Plus "Risk"

section_content: Based on the description of the selected methodologies, Figure 4 illustrates the steps to connect them together for identifying key PSFs to prevent human errors in the oil tanker offloading work. Each step is briefly explained as follows. 

The first main step is to implement an HTA practise to determine the main goal, the sub-goals, and the STs of the task. The main goal is obviously to successfully offload an oil tanker. 

The second main step is to invite several experienced domain experts for collecting grey data from the aspects of likelihood and impact. The importance weight of each expert is also assessed by AHP in this step. 

The third main step is to collect the grey data and to form the grey matrices from the aspects of likelihood and impact. 

The fourth main step is to calculate the risk-based grey relational degree of each PSF by GRA with definition of "Risk" and then to determine some significant PSFs of each ST and the whole task for human error prevention.
section_name: The Procedure of This Study

section_content: An oil tanker offloading operation at the Beihai Oil Terminal is selected as a case study. This terminal is located near the South China Sea and has been owned by Sinopec (the largest petrochemical enterprise in China) since 2015. Figure 5 presents an oil tanker offloading operation at this oil terminal, and it is clear that people are highly involved, so preventing human errors is considerably important. According to the selected case, this study illustrates the approach that considers the operation process, experts' importance weights, and risk-based GRA process together to identify key PSFs for human error prevention.
section_name: Case Study

section_content: According to the procedure illustrated in Figure 4, this study starts with HTA to describe the process of the selected oil tanker offloading case. Based on our previously published research [6, 38], the whole oil tanker offloading work can be divided into four sub-goals, and each contains several STs. Table 4 presents the detailed result. Operating the transfer arms and move it towards oil port.
section_name: HTA Practice for Oil Tanker Offloading Process

section_content: Locating the oil transfer arms at their initial position, and then locking them. ST 4. 6 Finishing the relative documentation work.
section_name: ST 4.5

section_content: According to the research procedure, domain experts' judgement is required for collecting grey data of each PSF in each ST, so several certificated and experienced experts are invited for evaluating PSF. Table 5 gives the demography information of each invited expert. As each invited expert may have different importance weights in making safety-related decisions, the AHP method is adopted to estimate their weight values. According to the AHP technique illustrated in Equation (1) to Equation ( 5 ), the importance weight of each invited expert can be estimated. 

Each invited expert is familiar with oil tanker offloading work, with significant experience. The difference between each expert is their power in making decisions on safety. For instance, the chief safety inspector has a higher weight in making safety-related decision than the importance weight of the operating group leader, and the chief manager has more power in making decisions on safety. Based on that, the pairwise comparison matrix for AHP application is determined by the principal leader of the selected oil terminal. This matrix is illustrated as Equation (12). The importance scale (see Table 2 ) designed for AHP is provided by Professor Thomas Saaty, who is also the designer of AHP method. Therefore, this importance scale is used as the criterion for the top leader to determine each element in the pairwise comparison matrix. With the importance scale in Table 2, each element in the matrix is explainable. For instance, "3" in the first line and the third column means that compared with the third expert the first expert is of moderate importance:

Then, according to Equation ( 2 ), the initial importance weight of each invited expert can be estimated. Using the first expert as an example, its initial importance value is

In this way, other initial significance weight values can be determined, as shown in Table 6. A consistency test is required for the AHP application to validate that the comparison matrix and the initial weight values are acceptable. According to Equation (4), the maximum eigenvalue of matrix A can be calculated, then based on Equations (3) and ( 5 ), and RI value in Table 3 (RI is 1. 24, since the order of matrix A is 6 in this study), the CR result can be calculated, which is 0. 00113 (less than 0. 1). Therefore, the comparison matrix passes the consistency test, and the initial importance weight values in Table 6 are also the final weight value of each expert. The AHP procedure is conducted by the professional AHP software "Super Decisions", which is shown as Figure 6.
section_name: The Importance Weight Analysis of Each Invited Expert

section_content: Based on the research procedure, after determining the significance weight value of each expert, they need to conduct grey data collection work for the GRA process. A well-designed questionnaire is used for data collection. In this study, the definition of "Risk" is used as the standard to judge each PSF in Table 1 for the process of oil tanker offloading work. As "Risk" combines likelihood and impact, grey data collection is also from these two aspects. The likelihood describes the potential occurrence of each PSF in poor performance, and the impact expresses the consequence level when a PSF is at poor level. A "0-5 Likert-type scale" is selected for experts to estimate and evaluate each PSF. The "0-5 Likert-type scale" is widely used in social science research for collecting subjective data [17]. In this study, "0" means the lowest likelihood level or the lowest impact level, and "5" represents the highest. Different from many other published results, this study considers the PSFs' differences in each ST during the oil tanker offloading work, rather than viewing the offloading work as a whole. Therefore, the grey data collection is also for each ST in the whole task. According to the HTA result, the data (including likelihood and impact) can be determined by the six invited experts through the designed questionnaire. Figure 7 presents an example question. Using ST 1. 1 in Table 4 as an example, Tables 7 and 8 display the collected grey data of likelihood and impact, respectively, for ST 1. 1. The grey data for the rest STs can be determined in a similar way. With these data, the next section will describe the process for finding key PSFs.
section_name: Grey Data Collection from Experts

section_content: This part presents the application of the risk-based GRA method to find key PSFs for each ST and for the whole oil tanker offloading task.
section_name: Risk-Based GRA Process

section_content: Choosing ST 1. 1 as an example to illustrate the process to identify the key PSF in each ST for this study. Starting from building the grey relation matrices, each data in Tables 7 and 8 can be viewed as each element in the grey matrix of likelihood and impact. Namely, Tables 7 and 8, respectively, present the grey relation matrix of likelihood and impact for ST 1. 1. According to Equation ( 6 ), the grey relation matrices can be determined. The reference series of each grey relation matrix for ST 1. 1 can be determined by Equation (7), and they are (2. 5, 2, 0. 75, 1, 1. 25, 1) for likelihood and (3, 1. 5, 1. 5, 3, 3. 25, 3. 25) for impact. Then, based on the expert evaluation data in Tables 7 and 8, and through Equation ( 8 ), the maximum absolute difference value for likelihood data and impact data of ST 1. 1 is 2 and 3; the minimum absolute difference value for likelihood data and impact data of ST 1. 1 is 0 and 0. Afterwards, with Equation ( 9 ), the grey relation coefficient for each PSF's likelihood and impact concerning each expert's opinion in ST1. 1 can be collected. Tables 9 and 10 give the results. As discussed previously, experts have their own importance weights. Based on Equation (10) and the weight values in Table 6, the final grey relational degrees of likelihood and impact for PSF1 in ST 1. 1 are as follows: 0. 3975 × 0. 5000 + 0. 2108 × 0. 5000 + 0. 1434 × 0. 6667 + 0. 1034 × 0. 5714 + 0. 0725 × 0. 5714 + 0. 0725 × 0. 5714 ≈ 0. 5416 (likelihood); 0. 3975 × 0. 3750 + 0. 2108 × 1. 0000 + 0. 1434 × 0. 6000 + 0. 1034 × 0. 3750 + 0. 0725 × 0. 3750 + 0. 0725 × 0. 3750 ≈ 0. 5390 (impact). 

According to Equation ( 11 ), the risk-based grey relational degree of PSF1 in ST 1. 1 can be determined as 0. 5416 × 0. 5387 ≈ 0. 2914. Then, each PSF's risk-based grey degree in ST 1. 1 can similarly be identified. Table 11 displays the results. The risk-based grey relational degree values of PSFs in other STs can be collected by the similar way to ST 1. 1. Table 12 and Figure 8 provide the results. From Table 12 and Figure 8, the most crucial PSF in each ST can be identified. PSF1 plays the dominant role in ST 1. 3 and ST 3. 1; PSF4 is the key PSF to prevent human error in ST 1. 2, ST 1. 5, and ST 4. 4; PSF5 is the most crucial one in preventing human error in ST 2. 1 and ST 4. 1; PSF7 is the most significant in ST 1. 1, ST 4. 2, ST 4. 3, ST 4. 5, and ST 4. 6; PSF8 is the priority one in ST 1. 4, ST 2. 2, and ST 3. 2. The ranking of each PSF in each ST is displayed in Table 13. Apart from the key PSFs in each ST, the significant PSF for human error prevention in the whole task is also required. Based on the data in Table 12, the next section will present the approach to identify the key PSF in the whole oil tanker offloading task.
section_name: Key PSF for Each ST

section_content: There are 15 STs connecting together to achieve the goal of successfully completing oil tanker offloading. These 15 STs are conducted step by step, so their logical relationship is in series. Figure 9 presents the HTA structure. As the STs are connected in series, the risk-based grey relational degree of each PSF in each ST can be summed to collect the degree of each PSF for the whole task. Here, PSF1 is used as an example to present the process of calculating its risk-based grey relational degree to the whole task, which is illustrated as: 0. 2919 + 0. 3177 + 0. 6610 + 0. 3858 + 0. 4404 + 0. 4122 + 0. 4563 + 0. 5674 + 0. 3940 + 0. 4616 + 0. 4235 + 0. 4343 + 0. 4657 + 0. 4481 + 0. 5230 ≈ 6. 6830

In the same way, the risk-based values for other PSFs in this oil tanker offloading task can be determined, which is displayed in Table 14. The ranking order is PSF7 > PSF8 > PSF1 > PSF4 > PSF6 > PSF5 > PSF3 > PSF9 > PSF2, so PSF7 is the top PSF in the entire oil tanker offloading work.
section_name: Key PSF for the Whole Task

section_content: If only using the definition of "Risk" and the expert's importance weight (traditional risk-based approach), the results for each ST and the whole task can also be determined, still using PSF1 in ST 1. 1 as an example. Based on the experts' importance data, the collected likelihood data, and the collected impact data in Tables 6 7 8. The likelihood data and impact data for PSF1 in ST 1. 1 are: 0. 3975 × 1. 5 + 0. 2108 × 1. 0 + 0. 1434 × 0. 25 + 0. 1034 × 0. 25 + 0. 0725 × 0. 5 + 0. 0725 × 0. 25 ≈ 0. 9231 (likelihood); 0. 3975 × 0. 5 + 0. 2108 × 1. 5 + 0. 1434 × 0. 5 + 0. 1034 × 0. 5 + 0. 0725 × 0. 75 + 0. 0725 × 0. 75 ≈ 0. 7471 (impact). 

Then, the risk value for PSF1 in ST 1. 1 is 0. 9231 × 0. 7471 ≈ 0. 6896. Through this traditional risk-based approach, the risk value of each PSF for each ST can be calculated. Table 15 gives the result. Compared to the results generated by the proposed method in this study, we can find their results are mostly same except for the key PSF in ST 1. 5, ST 4. 1, and ST 4. 5. Table 16 presents their comparison, which contains the most significant PSF in each ST and the whole task. These differences may be caused by the different analysing theory and procedure between the proposed method in this study and the tradition risk-based approach. The GRA theory is based on the geometric differences, but the tradition way uses the weighted average value. Due to the reality that PSF-related data are always insufficient and have strong characteristics of grey, we believe that the proposed method is currently a better choice for dealing with human error prevention for our study. 

It should be noticed that before this study, the leaders in the selected oil terminal knows that human error is crucial, but they have limited idea on human error prevention, and mostly, they only view training as an effective way to avoid human errors. Therefore, the staff have received frequent training on safety, even though most staff are tired of those repetitive trainings. After this research, the leaders realise that apart from some safety training work, more efforts should be paid to operators' safety attitude and supports for work and management to prevent human errors during oil tanker offloading process. Through learning the result, the management team in the selected terminal has made a strict reward and punishment policy to encourage staff to find, report, record, and correct any unsafe behaviour, to let people form a more positive attitude to safety. Through this policy, from January to April in 2022, there was no report about abnormal incidents. In addition, the working capacity in that oil terminal increased about 17. 5% compared with the data from January to April in the last year.
section_name: Comparison and Discussion

section_content: This research provides a grey and risk-based method to identify key PSFs for preventing human errors during an oil tanker offloading task. The highlights of this study are listed as follows:

1. 

The proposed method combines GRA process with the definition of "Risk" together to handle the incomplete and imperfect data of each PSF and to rationally rank each PSF; 2. 

This study considers the changes of each PSF in different task stages, so the dynamic scenarios are involved; 3. 

The method can deal with many PSFs without extra efforts such as consistency tests, so it is user-friendly; 4. 

The different weights of each invited expert are considered. 

Through the method proposed by this study, it can be concluded that PSF7 (Attitudes to safety, work, and management support) is the key one for the whole oil tanker offloading task. For each ST, PSF7 (Attitudes to safety, work, and management support), PSF8 (Teamwork), PSF1 (Time), PSF4 (Experience/training), and PSF5 (Procedure) should be considered, since they are ranked as the top PSFs in the corresponding STs. 

The results can be used for decision makers and safety management teams to strategically make some effective plans to prevent human errors for oil tanker offloading safety. For instance, except for the reward and punishment policy, more education and broadcasts for strengthening safety attitudes are required to increase the performance level of PSF7 (Attitudes to safety, work, and management support); crew communication skills and mutual trust among each team member should be improved to ensure a high level of PSF8 (Teamwork); more time for dealing with regular procedures and abnormal scenarios can enhance the performance of PSF1 (Time); more targeted trainings are necessary for the improvement of PSF4 (Experience/training); and some operation procedures should be optimised to make sure PSF5 (Procedure) is at good performance. 

Apart from the application in the oil tanker offloading process, the proposed method is also suitable to other human-related and safety-related applications for finding key PSFs to prevent human errors. However, this study still needs further developments. Fuzzy characteristics should be involved in the proposed method, and the dependency level of each ST should also be analysed for better calculating the total risk-based grey degree of each PSF. In the future, efforts should be made to improve on this study. 

G Likeli. d The grey relational degree of the dth series with respect to likelihood G
section_name: Conclusions

section_content: The grey relational degree of the dth series with respect to impact M G Grey matrix RI Random Index r d h Grey relation coefficient between the hth element in the reference series and that in the dth comparative series W

The matrix composed of each weight data W h

The importance weight of the hth criterion W i Initial weight value of the ith alternative X O Reference series ∆ od (h) Absolute difference between the hth element in the reference series and the hth element in the dth series

The maximum eigenvalue of the matrix A δ Identifier
section_name: Imp. d

section_name: Institutional Review Board Statement: Not applicable.

section_content: Funding: This research was funded by the Cross-Disciplinary Science Foundation from the Beijing Institute of Petrochemical Technology (grant number: BIPTCSF-003 and BIPTCSF-011 ) and the Beijing Youth Talent Promotion Project.

section_content: Informed Consent Statement: Not applicable.
section_name: Institutional Review Board Statement: Not applicable.

section_name: Acknowledgments:

section_content: Data Availability Statement: Not applicable.

section_content: The authors would like to appreciate the experts and the engineers working in the Beihai Oil Terminal for their constructive supports during the development of this work. The authors would also like to thank the editors and the anonymous reviewers for their valuable comments.
section_name: Acknowledgments:

section_name: Conflicts of Interest:

section_content: Author Contributions: Conceptualisation, R. Z. ; methodology, R. Z. ; software, R. Z. ; validation, R. Z. ; formal analysis, R. Z. and J. G. ; investigation, R. Z. ; resources, R. Z. and H. M. ; data curation, R. Z. ; writing-original draft preparation, R. Z. ; writing-review and editing, H. M., J. G. and H. T. ; visualisation, R. Z. ; supervision, R. Z. ; project administration, R. Z. ; funding acquisition, R. Z. All authors have read and agreed to the published version of the manuscript.

section_content: The authors declare no conflict of interest. The grey relational degree of the dth series to the reference series G Con. d The risk-based grey relational degree of the dth series
section_name: Conflicts of Interest:

section_name: Abbreviations