An Evidential Reasoning-Based CREAM to Human Reliability Analysis in Maritime Accident Process

2.1. Brief Overview of the Accident Development Models

Compared with the epidemiological and systemic and functional methods, the perspective of the sequential accident development model, which views the accident as a result of a chain of events occurring in a specific order, has attracted much attention in the recent decades.2, 3, 33-35 The sequential accident development model, derived from the well-known domino theory,33 has been developed into a Swiss cheese model, and then into the HFACS method.34, 35 This perspective is widely used in maritime accident analysis; however, it is criticized for ignoring the cognitive error causes and error detection as well as recovery process.36 Consequently, as this article focuses on human reliability analysis for maritime accidents, a novel method should be developed not only considering the accident development but also the human performance.

Risk scenario is another widely used viewpoint in sequential accident development. The main principle of this approach is to divide the accident development into three states, which are initiating event, mid-states, and end states.37 In fact, both the widely used fault tree analysis38 and event tree analysis39 in maritime risk assessment are derived from this concept. This method is acknowledged to be a generic accident development model because it can be applied to different types of maritime accident analysis (e.g., collision,40 not under command ship).37 Therefore, different types of accidents can be analyzed in this model if the risk scenarios can be well defined.

Moreover, a safety-barrier-based model is the widely used accident development model for human performance assessment. This model views accidents as failures of safety barriers.33 Sklet41 thoroughly reviewed the definition, classification, and performance of the safety barrier system. Owing to its intuitive feature, safety barrier is widely used to understand the function of human activities in accident development. Rathnayaka et al.42 proposed a human factor barrier-based model to analyze the accident process, and this model was validated in another paper.43 Furthermore, Xue et al.44 introduced the human factor barrier-based model to analyze offshore drilling blowout accident.

2.2. Framework of the Proposed Accident Development Model

The framework of the proposed accident development model, which integrates the risk scenario analysis and safety barrier method, is shown in Fig. 1. In the proposed model, the ship departs from the normal state (NS), and will arrive at the destination safely (DS) in the ideal trajectory. In this ideal trajectory, even if sometimes the initiating event is trigged, the safety barrier system can prevent the development of this adverse event (AE). However, if some of the barriers failed, the IE will develop into the mid-states, and finally the end state. It should be noted that more than one mid-state may exist in the maritime accident process.

Another significant element of the proposed model is the safety barrier system. Since this article focuses on the reliability of human action in maritime adverse events, only human/operational barrier systems are established, including the ordinary action barrier (OA), critical situation barrier (CS), externally involved action barrier (EI), and emergent situation action barrier (ES). Therefore, the physical and technical barrier systems, which also play a crucial role in preventing the occurrence of adverse events, will be discussed in the following subsection, where the functions of each barrier are also analyzed in detail. In this barrier system, the order of the four barriers is predefined, which means the latter barrier will be trigged only if the former barrier fails. However, the latter barrier can be activated before the former barrier when preventing the development of accidents.

2.3. Safety Barrier System in Maritime Accident Process

Apart from the four safety barriers mentioned in the former subsection, three more safety barriers should be also considered. As shown in Fig. 2, the safety barrier system is divided into two phases. The first phase includes the primary, secondary, and tertiary safety barrier, which is adapted from the railway industry.41 These three barriers cannot be ignored because the physical, human/operational, and technical barrier can prevent the adverse event before it occurs; however, once the adverse event occurs, well-trained crews should have the ability to deal with these events by themselves according to requirement on crews by the regulation of SOLAS (Convention on the Safety of Life at Sea) and STCW (International Convention on Standards of Training, Certification and Watch Keeping for Seafarers). In terms of difficulty in the process of accident development, four safety barriers are established in the second phase, as shown in Table I. Moreover, the failure patterns of each barrier in the maritime accident process, including opportunity of response missed (OM), undesired events occurred (UE), and human error in response (HE), are shown in Fig. 2. The failure patterns can be used to facilitate expert judgment under the CREAM framework, and they are not described in detail in this article.

2.4. Accident Scenario Analysis

In order to evaluate human reliability in response to different adverse events, scenario analysis of different accidents is carried out by defining distinctive states under the proposed framework. For the ship collision accident, according to the COLREGs (Convention on the International Regulations for Preventing Collisions at Sea), a ship collision can be divided into three stages, including collision risk, close-quarters situation, and immediate danger, which are accepted by many researchers.38, 40, 45-47 For the NUC caused collision accident, Mazaheri et al.37 proposed the developing states in the scenario analysis, where the NUC ship is utilized as a case study. The developing states of bad weather and fire/explosion are defined according to the emergency plan of the ships, which is required by SOLAS. Since the accident may develop into second-tier (ST) accidents (initiating event of another event) according to the study of Uluscu et al.,48 the flooding accident is also analyzed according to the previous works of Khaddaj-Mallat et al.49, 50 and Santos and Guedes Soares; all the above-mentioned scenarios are shown in Table II.50

3.1. Description of the Basic CREAM

3.1.3. Transformation of CPC Effects to Control Mode

Apart from the nine CPCs shown in Table III, the basic CREAM also defines the CPC levels and associated effects, which are expressed by linguistic terms. When introduced to analyze human error, it is easy to define the CPC levels by using the linguistic terms based on CREAM, which means the associated effects of each CPC can also be easily obtained.

Moreover, the basic CREAM also provides a mapping method to establish relationship between the CPC effects and the control modes, which is shown in Fig. 3. By introducing Fig. 3, the combined scores, which consist of positive and negative scores, can be transformed to the corresponding control mode. Specifically, the transformation of CPC scores to control mode is defined as follows. First, by counting the number of times in terms of the CPC effects, the CPCs scores of positive performance reliability, negative performance reliability, and neutral performance reliability can be derived, respectively. Second, the neutral performance reliability is not considered since it has no significant effects on human performance reliability. Finally, one of the four control modes is selected in accordance with the CPCs combined score.

3.2. Development of the New CREAM

The evidential reasoning-based CREAM is established as follows. First, the effects of the CPCs are defined as the referral attributes and the nine CPCs are defined as the basic attributes. Second, the linguistic terms of the nine CPCs are assessed with belief degree, and both the qualitative and quantitative assessments are transformed to the referral attribute by using the rule- and utility-based transformation technique.51 Third, the effects of the nine CPCs are synthesized using the evidential reasoning combination rules.52 Finally, the CII, which is expressed by belief degree after introducing the evidential reasoning method, is used for estimating the HEP.

The comparison between the proposed CREAM and existing CREAM is summarized and shown in Table V. In fact, the CREAM models from the literature review can be divided into two categories in terms of their modeling process. One category is to obtain first the CII of nine CPCs, then to estimate the HEP (basic CREAM17 and extended CREAM).14 Another category is to obtain first the relationship between each CPC and control mode by using reasoning rules, then to synthesize the nine CPCs by assigning their associated weights (fuzzy CREAM,10 Bayesian based CREAM,26 and Yang's CREAM).16

The detailed comparison is analyzed as follows. First, the proposed CREAM utilizes the belief degree to describe effects (linguistic variables) of each CPC, while all the existing methods use 100% certainty to describe the effects. However, in practice, it is very hard to use 100% certainty to describe the CPC effects. For example, when describing the “adequacy of organization” shown in Table III, it is very hard to use only one linguistic variable (such as negative) to describe the effect, while a combination of the linguistic variables (such as “negative” with belief degree of 30%, “neutral” with belief degree of 20%, and “positive” with belief degree of 50%) is more appropriate. Second, the incomplete information (uncertainty) of the effects can be taken into consideration both in the description of the CPC effects and synthesis of the CPC effects, while the basic CREAM ignores both of these in the description and synthesis. The fuzzy CREAM ignores the incomplete information in synthesis though this is acceptable and will be discussed in Subsection 3.2.4., while Yang's CREAM16 considers the incomplete information of the control mode rather than the CPC effects. Third, the synthesis of CPC effects is different. The proposed method utilizes evidential reasoning while the fuzzy and Yang's CREAMs transform the synthesis of CPC effects to the synthesis of control modes. Fourth, the relationship between CPC and control mode is different. The proposed and basic CREAMs use CII while the fuzzy and Yang's CREAMs use IF-THEN rules.

3.2.1. Define the CPC Levels and Effects

In the human reliability analysis using basic CREAM, the experts are required to make assessment in terms of linguistic terms of the CPCs shown in Table III. However, it is very hard to only use one linguistic term with 100% certainty to quantify human performance when assessing the CPC levels, whereas it will be much easier by using multiple linguistic terms with belief degrees.

Suppose there are N distinctive grades that provide a set of standards for evaluating the CPC levels. The distinctive grades can be written as Equation 1:

(1)

where is the nth distinctive grades.

Then, the assessment on the jth CPC by using linguistic terms, expressed by , can be expressed as Equation 2:

(2)

where is the associated belief degree of the nth distinctive levels, and . It is assumed that the assessment is incomplete when , while the incomplete information is uncertainty and can be expressed by . The incomplete assessment is always caused by time pressure, partial knowledge, or ignorance.

Accordingly, the assessment on the effects can also be written as Equation 3:

(3)

where is the assessment on the CPC by using the effects. is the distinctive grade used for assessing the CPC effects, specifically, means the negative reliability performance, means the neutral reliability performance, means the positive reliability performance, and is the uncertainty of the effects. is the belief degree belonging to the associated effects. The relationship between and can be established by using the transformation matrix, and it can be written as Equation 4:

(4)

where is the transformation matrix and shown in Equation 5. The transformation matrix can be established according to the mapping relationship between CPC levels and CPC effects.

(5)

3.2.2. Transform the Assessment on CPCs Levels with Crisp Values

Before transforming the assessment on the CPC levels to the CPC effects, the assessment on the CPC levels should be transformed. Marseguerra et al.10 proposed a [0, 100] rating range to estimate the CPC effects, which is also used to assess the CPC levels in Ref. 20. It should be mentioned that the fuzzy rules cannot be directly transformed to the effects owing to both probability and fuzzy uncertainties.53 Similarly, a rule- and utility-based method51 is introduced to transform the assessment on the CPC levels. In the rule- and utility-based transformation process, the memberships, which equal to 1 and 0, are assigned the same numerical values as in Ref. 20; therefore, the transformation of CPC effects can be easily established.

However, as this article focuses on human reliability analysis from the prospective viewpoint, some quantitative assessments of CPCs are hard to make with crisp values, for example, the CPC “crew collaboration quality.” Hence, the qualitative assessment should be used in this assessment. Similarly, this quantitative assessment can also be transformed by using the rule- and utility-based method.51

The transformation of the quantitative assessment can be carried out as follows. Suppose the crisp value of estimation on the CPC levels is represented as . The numerical estimation on the CPC levels can be transformed in terms of the proportions to the associated grade:

(6)

3.2.3. Obtain the Weights of Nine CPCs

One of the shortcomings of the basic CREAM is that it did not consider the importance of the nine CPCs.16 There are many methods to obtain the weights of different attributes, like Delphi and pairwise. The most widely used method is the analytic hierarchy process (AHP) proposed by Satty54 in 1977. The process of using AHP can be divided into three steps. First, establish a hierarchical structure of the nine CPCs; in this study, the nine CPCs are constructed in the same level. Second, obtain the pairwise comparison matrix to indicate the relative importance of the nine CPCs, which is carried out by expert judgments. Generally, a nine-rank scale is used in the comparison between the two CPCs. Third, calculate the weights of the nine CPCs by the following equation:

(7)

where A is the comparison matrix between the nine CPCs. is the largest eigenvalue of comparison matrix, and is the associated eigenvector of .

The consistency index () is used to examine the consistency of the expert judgments, which is defined as Equation 8:

(8)

Afterwards, the consistency ratio (CR) is constructed by dividing the random consistency index (), which is derived by using Monte Carlo simulation.54 The value of is related to the dimension of comparison matrix; in this study, the is a predefined number (i.e., equal to 1.46) since there are nine CPCs:

(9)

If , the comparison matrix is assumed to be inconsistent and the experts are required to make adjustment on their judgments until the comparison matrix can meet the requirement on CR.

3.2.4. Synthesize the CPC Effects Using Evidential Reasoning

After obtaining the weights of the CPCs, the assessment on the effects can be integrated by using the evidential reasoning method. The evidential reasoning method was proposed by Yang and Xu,52 and it is widely used in maritime transportation.16, 55, 56 The merit of using the evidential reasoning method is that it can integrate the CPCs by its own algorithm, while the other methods (e.g., fuzzy logic) have to establish a large number of reasoning rules. Moreover, it can deal with incomplete information.

The process of integrating the CPCs is as follows. First, the assessments on the CPC effects are assigned the associated weights, which is represented as . Moreover, the unassigned belief degrees () are divided into two parts, which are and , and their relationship is in accordance with the equation :

(10)

(11)

(12)

Second, the integration of the CPC effects is carried out by using the evidential reasoning algorithm. Suppose that is the integrated results of the first kth CPC effects, and is the unassigned belief degree. It can be easily obtained that and . The nine CPC effects are recursively integrated by using the following equations:

(13)

(14)

(15)

(16)

Finally, the unassigned belief degree caused by weights is reassigned to distinctive grades (CPC effects) proportionately:

(17)

(18)

Therefore, the integrated results of the effects can be obtained, which is shown in:

(19)

3.2.5. Estimate the HEP

Similarly with the CII proposed by He et al.,14 this article also uses the integrated negative reliability performance minus the integrated positive reliability performance as the CII. However, as uncertainty exists in this human reliability analysis, a simple method that considers the uncertainty is proposed to calculate the CII:

(20)

(21)

(22)

In these equations, the neutral effects are not considered because the neutral effects are not significant for estimation of the HEP; for example, both the basic and extended CREAM14 assigned the value of zero to this effect. Although some researchers26 suggested that the neutral effects should be assigned equally to the positive and negative effects, the result of CII will not be changed if this viewpoint is adopted.

It should be mentioned that PII, which is proposed by He et al.14 to quantify the CPC effects, seems to be better than CII, but this method cannot achieve a continuous HEP in assigning the predefined values to the effects, and essentially, PII is a special case of the evidential reasoning.

The highest value of HEP is reached when the positive reliability performance reaches the minimum and the negative reliability performance reaches the maximum. On the contrary, the lowest value of HEP is reached when the positive reliability performance reaches the maximum and the negative reliability performance reaches the minimum. Therefore, the following equations can be constructed, as proposed by Sun:15

(23)

(24)

It can be found from Table IV that the and . Then, by employing these values in Equations 23 and 24, the following equation can be achieved:

(25)

Table IV. Control Modes and HEP Interval17

	Reliability Interval
Control Mode	(probability of action failure)
Strategic
Tactical
Opportunistic
Scrambled

Last, the HEP can be assessed by using Equation 26; owing to the sequential character of a maritime accident process, the HEP of each barrier is indicated by .

(26)

By comparing Equation 26 with the HEP estimation equation proposed by Sun,15 it can be found that the proposed CREAM cannot only accurately express the CPC levels by introducing the belief degree, but also makes the result of the HEP continuous without any transformation, which can estimate the HEP with better accuracy. It should be mentioned that as the CII has three values in Equations 20–22, there also three corresponding , which can be represented by ,, and , respectively.

3.3. Validation of the Proposed CREAM

The proposed CREAM is validated by using the same numerical example as in Yang et al.;16 however, only the HEP method using the former four steps is used as this is a numerical example, which means this example did not consider the HEP with subbarriers.

The assessments of the effects used here are the same as in Table IV of Ref. 16 and the weights are also the same as those shown in Table V of Ref. 16 . The integrated results can be obtained by using the evidential reasoning method:

Then, the CII can be obtained by using Equation 21:

Last, the HEP is calculated as follows:

The result of the proposed CREAM in this article is , between the value of basic CREAM () and modified CREAM proposed by Yang et al.16 (). It is reasonable since the control modes in this numerical example are the same and deduced to be “tactical” by all three methods. However, a small fluctuation is caused by the importance of CPCs, which is explained in detail by Yang et al.16 The merit of the proposed method is that it does not need to establish a lot of reasoning rules and the calculation process is simpler than the modified CREAM proposed by Yang et al.16

4.1. Description of the Numerical Example

In this section, a numerical example is used to validate the proposed evidential reasoning CREAM approach in a maritime accident process. The detailed information of this accident in the different stages is described as follows.

This numerical example is adapted from the Motor Vessel Haoping, which departed from Yingkou Port at 17:00, and was sailing to Jiangyin Port on 25 June 2008. The ship's particulars are as follows: dead weight tonnage (DWT): 5072; ship length: 99.8 m; load draught: 5.65 m. The ship is manned with qualified, certificated, and medically fit seafarers in accordance with minimum safety manning documents. Furthermore, the cargo is also in good condition after self-check. From the weather forecast, the wind conditions will not be exceeding Beaufort 5 condition, which can meet the requirements on the resistance of the wind for this ship. The route is close to the coast, which means the rescue team can arrive within one hour.

After passing the waypoint of Chengshantou Water Area, the ship turns to the north–south transportation route, which connects the Chengshantou Water Area and Shanghai traffic separation scheme. In this waterway area, each ship navigates in its corresponding route, which means a two-way traffic flow is established though there are no mandatory rules. It should be mentioned that there is no anchorage on this passage route because the waterway area is far from the coast. Later, this ship received the updated weather forecast that the wind scale would be Beaufort 7–8 within one day, and the expected wave heights would be 5 m, which would exceed the designed ability (1.5 m).

Four hours later, the ship yaws in the waves, and the captain alters the course to 145 degrees; meanwhile, the ship speed is reduced from 9 knots to 6.7 knots due to sailing against the wind. One hour later, the ship speed is reduced to 4 knots, and the ship yaws sharply. At this time the chief officer suggests sailing to the anchorage; however, considering that the ship is far from the anchorage, the captain decides to continue the voyage.

Ten hours later, the chief officer finds green water on deck, which makes the ship lean to the port side. In order to fix this problem, the chief officer asks the boatswain to measure the lean, and simultaneously he tells the engine room to fill ballast tanks. Five minutes later, the engine room tells the officer that the ballast water has little effects to prevent the ship leaning, and the ship has leaned around 15 degrees in the past 15 minutes. The ship sends a distress signal to the search and rescue center through the Global Maritime Distress and Safety System, and also to the nearby ships through very high frequency (VHF).

However, the rescue team cannot arrive immediately as the ship is far away from the coast. Moreover, it is hard to prevent the ship capsizing by itself half an hour later and the captain has no choice but to command to abandon ship immediately.

4.2. Identification of the Safety Barriers Using the Accident Development Model

Traditionally, the HEP estimation is carried out in a short period. This is generally acceptable when it is applied to estimate the HEP in fulfilling a task with complex conditions. By adopting this method, the tasks with a large likelihood of human error can be selected for more training than the normal tasks so as to enhance human reliability. For example, Yang et al.16 utilized the modified CREAM to estimate the HEP in a specific task for marine engineering. However, the development of maritime accidents is always time dependent, and the crews have to fulfill many tasks in the accident development. Take this case study, for example; if the HEP in the emergent situation is very high but the HEP in normal situation is very low, this should be assumed to have high likelihood of human error. This is because the crews should have the ability to overcome the problems in the whole route, which is also the requirement of ship seaworthiness.

Therefore, in order to make a comprehensive estimation of the HEP, time dependency should be considered in the maritime accident process. As the safety barriers are assumed to be key components in accident development, the four safety barriers should be first identified by using the scenario- and barrier-based accident development model proposed in Section 2.. It should be mentioned that as the HEP is carried out from the prospective way, the scenario of maritime accidents should be anticipated in this process. However, this article uses the real accident development process for simplification, and the four safety barriers are identified from this real accident development process described in the former subsection.

From the description of the numerical example, this accident can be divided into four stages in terms of the scenario description of bad weather in Table VII. The first stage is that the ship sails from the departure port to the waypoint of Chengshantou Water Area because this waterway area is close to the coast and the navigational environment is simple; hence, the safety barrier in this stage can be assumed to be an ordinary action barrier. The second stage is that the ship sails in a harsh navigational environment, and owing to the harsh navigational environment, this task requires the crews to be well trained and the safety barrier can be assumed to be a critical situation barrier. The third stage is that the ship tries to take effective measures to prevent capsizing, including taking measures by itself and requesting assistance from the search and rescue center, which is the third barrier in the barrier system. The fourth stage is the captain commands to abandon the ship, and the safety barrier is the emergent situation barrier.

Table VI. Calculating the HEP of Maritime Accident with a Set of Subbarriers

Logic Relation between Subbarriers	Dependence between Subbarriers	HEP of the Barrier
Parallel subtasks	High dependence
	Independent/low dependence
Sequential subtasks	High dependence
	Independent/low dependence

4.3. Assessment on the Safety Barriers in the Developing Stages

The qualitative assessment on the CPCs is shown in Table VIII, and the explanation of the assessment is as follows.

In the first stage, the adequacy of organization is assumed to be efficient. The working conditions are advantageous due to the good navigational environment factors and available rescue resources. As the adequacy of MMI and operational support and crew collaboration quality is closely related to the crews, this CPC is assumed to be uncertain because sometimes these effects are negative due to human fatigue or human pressure. The availability of procedures and plans, number of simultaneous goals, available time, and adequacy of training and experience are all assumed to be positive as the crews should only carry out normal work. The time of the day is also assigned in terms of the time span of each linguistic variable.

In the second stage, the harsh navigational environment makes the working conditions difficult; moreover, the available procedures and plans are acceptable as the bad weather may have some differences from the plans. The number of simultaneous goals is also a little more than the actual capacity since the ship has to deal with the harsh environment. The available time and adequacy of training and experience are assumed to be neutral.

In the third stage, the adequacy of the organization is worse than the former two stages, but the CPC levels are assumed the same with the former two stages. It should be mentioned that the uncertainty of the available procedures and plans arises in this stage because the harsh navigational environment may be quite different from the plans. The available time is assumed to be continuously inadequate because the stage is always emergent and limited in time, and it can be seen that the crew have to abandon the ship after discovering the green water, which is an extremely short time period.

The assessment of the fourth barrier is the same as the third barrier as the third stage does not have any externally involved resources, and the captain has no choice but to abandon the ship.

4.4. Quantification of the CPCs Levels Using Numerical Values and Belief Degree

It can be seen from Table VII that some deficiencies exist by using the linguistic variables to express CPC levels. The first problem is that in the linguistic variables it is hard to quantify the small changes of the CPC levels. For example, the CPC level in the third barrier is worse than the former two barriers, but the linguistic variables are the same. Hence, it can be concluded that the CPCs cannot be accurately quantified by using these linguistic variables. Another problem is that the uncertain information cannot be taken into consideration.

The first problem is addressed by using the numerical values, which is also used in the fuzzy CREAM though with some differences. In the fuzzy CREAM, a [0, 100] rating range is used to quantify the CPC levels.10, 19, 20 This method can describe the CPC levels more precisely after defining each linguistic variables in a rating range. For example, if the range [0, 30] is used to describe the “Deficient” of the adequacy of organization, the numerical value 20 will be more deficient than 30 in modeling the CPC levels. By introducing this approach, an expert who is a professor and has done research on maritime safety for more than 30 years is invited to make assessment on the CPC levels. The precisely quantified assessment given by this expert is shown in Table VIII.

The second problem is addressed by introducing belief degree, which has been proved to be powerful in describing uncertainty.16, 56 In this case study, uncertainty is first averagely assigned to each linguistic variable since no information can be found. Take the “adequacy of man–machine interface and operational support,” for example; it is first assigned as . However, considering that the positive and negative effects will significantly influence the estimation of the HEP, the corresponding belief degrees are assumed to be uncertain. Then, the assessment can be rewritten as , and all the other CPCs with uncertain information are quantified in the similar way and the result is shown in Table IX. It should be mentioned that the belief degrees are assigned averagely because no further information can be found. For further development, expert judgments can be used in the future.

4.5. Evaluation of the Effects after Second-Round Transformation

After quantification of all the CPCs, the numerical values should be transformed to the corresponding effects. This is carried out by a second-round transformation. The first transformation is carried out by using the rule- and utility-based method, while the second-round transformation uses the corresponding transformation matrix.

As can be seen from the literature review,10, 16, 19 the numerical values are always transformed by using the membership function, which is the first step in fuzzy logic. After transformation, the numerical values can then be expressed by the memberships belonging to one or two linguistic variables. However, it is a challenge to define the membership function as so many membership functions exist; for example, Konstandinidou et al.19 introduced the triangular membership function, while Marseguerra et al.10 utilized the Gaussian membership function. As it is hard to define the membership function, a more straightforward and simple method called rule- and utility-based method is used. This method only has to calculate the geometric distance and the proportion of this distance (it can be interpreted as membership function in fuzzy logic) is assigned to the corresponding linguistic variables. Take the adequacy of organization in first barrier as an example; the assessment can be carried out by using Equation 7. Take the “adequacy of organization,” for example. As the assessment () is equal to 70, then it can be transformed as follows:

Then, the assessment can be obtained:

Moreover, the numerical values can also be automatically transformed by using the IDS software, and the result is shown in Fig. 4.

The second-round transformation is to transform all the evaluations on the CPC levels to the CPC effects. This transformation process can be carried out according to the relationship between the CPC levels and CPC effects, which is expressed by the transformation matrix shown in Equation 4. Take the first CPC, for example; the transformation matrix can be obtained from Ref. 26 as shown in Table VI:

The results of the effects of the CPCs after second-round transformation are shown in Table IX.

4.6. Acquisition of the Weights of the Nine CPCs Using the AHP Approach

As each CPC may have different influence on human reliability, the weights of the nine CPCs should be obtained in order to make comprehensive estimation of the HEP. The importance of the CPC weights has been verified by Yang et al.,16 where the HEP has been slightly changed by introducing the weights of the CPCs. In this article, the same weights of the CPCs proposed by Yang et al.16 are used. The weights of the CPCs are shown in Table X.

It should be mentioned that during this process, the consistency ratio should be less than 0.1; otherwise, the expert must be invited to reevaluate his/her judgments until the consistency ratio meets this requirement. It can be seen from Table X that the adequacy of training and experience are assumed to be the most significant attributes; this is reasonable as many efforts are made to enhance the skills of human reliability.34, 35 The second important factors are the number of simultaneous goals and available time, which are assumed to be key factors in maritime engineering because of time pressure and resource constraint. The fourth important factor is the availability of procedures and plans, which is used to instruct the crews to take effective actions. As the procedures and plans are important in maritime safety, some regular plans are required by the International Safety Management (ISM) Code, and the implementation of this code has improved maritime safety in the shipping industry.57, 58

4.7. Calculation of the HEP in the Serial System for Maritime Accidents

After obtaining the transformed result of effects and weights of the nine CPCs, the effects of the nine CPCs can be integrated by using Equations 13–19, and the result is shown in Table XI.

Then, the CII can be calculated by using Equations 20–22. Afterwards, the HEP in the four stages can be estimated, which is shown in Table XI, and the associated control modes for each barrier are also shown in Table XI. Moreover, as the four barriers are a sequential system in the accident development model, the HEP and associated control mode can be easily obtained according to Table VI.

It can be seen from Table XII that the HEP of the former two barriers is acceptable even if considering the uncertainties. However, the latter two barriers have a high probability of human error, which caused the control mode into bad conditions. This is reasonable because the crews may have not been trained for such harsh environment, and the ship condition is also unable to resist with such high sea state; moreover, the rescue resources cannot arrive within a limited time. Furthermore, the number of simultaneous goals is more than the actual capacity and the available time is continuously inadequate, which makes the failure probability of this barrier increase as these two factors play an important role in human reliability from the analysis of CPC weights.

Table XII. Control Mode for Each Barrier in Maritime Accident Process

Barriers		Control Mode		Control Mode		Control Mode
Ordinary action	0.0015	Tactical	0.0021	Tactical	0.0018	Tactical
Critical situation	0.0076	Tactical	0.0103	Opportunistic	0.0089	Tactical
Externally involved	0.0577	Opportunistic	0.1299	Scrambled	0.0938	Opportunistic
Emergent situation	0.0577	Opportunistic	0.1299	Scrambled	0.0938	Opportunistic
Max	0.0577	Opportunistic	0.1299	Scrambled	0.0938	Opportunistic

From Table XI, the control mode varies in terms of the effects being assigned. Take the emergent situation barrier, for example; the control mode is assumed to be “Opportunistic” when all the uncertainty is assigned to negative, or “Scrambled” when all the uncertainty is assigned to positive. In order to deal with this problem, the average of the HEP is adopted, and the corresponding control mode can be achieved, which is “Opportunistic” in this case. Moreover, the final HEP in this case study is to maximize all the HEP of the four barriers since the maritime accident process is a serial system, which is shown in the last row of Table XII. It can be seen from this table that the control mode for both the ordinary action barrier and the critical situation barrier are “tactical,” which means the human reliability is very good. However, considering the poor human reliability in the last two barriers, this scenario should be assumed to have poor human reliability. Therefore, this result also verifies that the human reliability analysis should be carried out in the whole maritime accident process not only considering the ordinary action but also the emergent situation.

By introducing the proposed CREAM model, the HEP of this scenario is “Opportunistic.” This result is reasonable owing to the following two reasons. First, the evidential reasoning-based CREAM has been validated in Section 3.3., where the result using evidential reasoning-based CREAM is proved to be consistent with both basic CREAM and Yang's CREAM.16 Second, the result is the same as the actual outcomes since the illustrative example uses accident data. Moreover, from historical data, more than 20 capsizing accidents have occurred in this area during the period from 2009 to 2012, owing to heavy sea and lack of anchorage and 71.4% of such accidents involve ships with length less than 100 m. This means such ships may have a large probability of human error under heavy sea especially when there is little anchorage available for emergency response. However, although the prediction of HEP is hard to validate by using historical data owing to its characteristics of unpredictability, occasionally, to further validate its human reliability, as proposed by Yang et al.,16 a maritime simulation system can be introduced to observe human reliability in the specific scenario before implementing this evidential reasoning-based CREAM in practice.

4.8. Sensitivity Analysis on the Uncertainty in HEP Estimation

In Section 4.4., uncertainty is defined as the summation of belief degrees of positive and negative CPC levels after averagely assigning the belief degree to all linguistic variables of CPC levels. This method is simple and can only be used when there is no prior information about these CPC levels. In practice, expert judgments can be used to reduce such uncertainty in human reliability analysis. In order to have a full understanding of the uncertainty propagation in this proposed method, the sensitivity analysis is carried out by changing the uncertainty in this human reliability analysis.

The sensitivity analysis is achieved as follows. First, as the emergent situation is assumed to be the worst, only the HEP of the emergent situation barrier is calculated. Second, the uncertainty changes from 0 to 1 with step 0.1 by assigning the other belief degrees to the neutral effects. The results of the sensitivity analysis are shown in Table XIII.

It can be seen from Table XIII that the minimum HEP decreases while the maximum HEP increases when the uncertainty increases, and the control mode also changes with uncertainty. Specifically, if the maximum HEP is used, the control mode for this scenario changes from “Opportunistic” to “Scrambled” when the uncertainty increases to 0.30. However, if the average HEP is used, the control mode changes from “Opportunistic” to “Scrambled” only if the uncertainty increases to a large belief degree, which is 0.70. It can be discovered that the result of human reliability analysis is slightly affected by the uncertainty. Another thing that can be deduced is that the uncertainty is reduced in the process of integration because the average HEP increases more slowly than the expected linear increase.

Table XIII. Sensitivity Analysis of the Uncertainty in Human Reliability Analysis

Uncertainty		Control Mode		Control Mode		Control Mode
0.00	0.0742	Opportunistic	0.0742	Opportunistic	0.0742	Opportunistic
0.10	0.0705	Opportunistic	0.0832	Opportunistic	0.0769	Opportunistic
0.20	0.0670	Opportunistic	0.0932	Opportunistic	0.0801	Opportunistic
0.30	0.0637	Opportunistic	0.1042	Scrambled	0.0839	Opportunistic
0.40	0.0606	Opportunistic	0.1164	Scrambled	0.0885	Opportunistic
0.50	0.0577	Opportunistic	0.1299	Scrambled	0.0938	Opportunistic
0.60	0.0549	Opportunistic	0.1447	Scrambled	0.0998	Opportunistic
0.70	0.0523	Opportunistic	0.1611	Scrambled	0.1067	Scrambled
0.80	0.0499	Opportunistic	0.1792	Scrambled	0.1145	Scrambled
0.90	0.0476	Opportunistic	0.1990	Scrambled	0.1233	Scrambled
1.00	0.0454	Opportunistic	0.2208	Scrambled	0.1331	Scrambled

In order to discover the reduced uncertainty in the process of integration by using the evidential reasoning method, the uncertainty before and after integration are calculated and shown in Table XIV, where the first column is the total uncertainties of three CPCs. It can be seen from this table that the uncertainty is reduced by approximately 94.5% after integration. The reason why so many uncertainties are reduced is because the majority of the CPCs (six CPCs) are completely known and the importance of the CPCs with uncertainty is assumed to be smaller than the others.