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Figure 1. Determination of control mode based on context influence index

In general, Bayesian network is one of the data mining methods. There are three reasons highlighting the advantages of using this method. First, Bayesian network is a useful tool for incomplete data. Second, Bayesian network provides an opportunity to obtain knowledge on causal relationships. Third, Bayesian networks in combination with statistical methods can facilitate the integration of background knowledge and data ¹⁴ .

Determine the probability of Bayesian networks

The basis of Bayesiannetwork calculations is Bayes' theorem. Bayes' theorem is based on the probability of an event, based on prior knowledge on related conditions and events. Based on Bayes' theorem, the probability of the incidence of an event is dependent on the occurrence of another event.

Bayes' theorem is stated mathematically as the following equation:

(6) $$P(B\left|A\right.)=\frac{P(A\left|B\right.)P(B)}{P\left(A\right)}$$

P(A) is the likelihood of event A

P(B) is the likelihood of event B

P(A│B) is the likelihood of event B, given that event A is true

A Bayesian network model has the following four steps:

• Definition of independent and dependent variables

• Establishing relationships between variables

• Defining variable modes

• Calculating the conditional probability for each node

In this study, Fuzzy CREAM was used as an input for Bayesian network. All calculations of BN were performed using GeNIe 2.0 software.

Results

Prioritizing emergencies using Fuzzy TOPSIS method showed that fire in the chemical storage unit was the most important emergency situation; thus, human error assessment was applied for this emergency situation. CPCs were determined based on the opinions of a panel consisted of 30 experts and specialists in the field of safety and occupational health. The selected CPCs were: adequacy of organization, working conditions, adequacy of MMI and operational support, availability of procedures and plans, availability of time, adequacy of training and experience, and the quality of staff collaboration.

In addition, paired comparison of CPCs based on the AHP method was performed to determine their relative weights (Table 1). Adequacy of organization had the highest relative weight and adequacy of training and experience was ranked the second.

The data obtained on probability control modes are presented in Table 2 and . Table 3 presents the data on the probabilities of weighted control modes.

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Figure 2. Bayesian network results for the coordination task

Discussion

The aim of this study was to develop a dynamic model for human error assessment in emergency situations. Given the unpredictability of human behavior, as well as the fact that human error is a natural part of human behavior ¹¹ , one of the major challenges of industrial managers is to protect critical and vulnerable infrastructure at the time of accidents, emergencies, and crises.

The performance and response of individuals during accidents and emergencies have a very important role in reducing or increasing the risk. During an emergency, the reaction of individuals is affected by some factors such as stress, time deficiency, workload, etc. ¹¹ , all of which increase the probability of human error. On the other hand, the probability of human error in emergency situations increases with time due to increase in fatigue ³ . Under such a condition, a mistake may lead to exacerbations of circumstances and uncontrollable damages and losses. The role of human error in major disasters in the world have also confirmed, for example, we may note London Beer Flood, Seveso, Bhopal, Chernobyl, Buncefield, and Tallmansville ¹¹ .

Therefore, Human Reliability Analysis ¹⁵ in emergencies is a very important tool to reduce the consequences of human error under such conditions. In this study, CREAM was used to evaluate HRA and human error. CREAM method is one of the second-generation HRA methods widely used in various industries including petrochemicals ¹² . In this study, an applied three-step method was used to solve the weaknesses of this method. This three-step method included: determining CPC for emergency situations, determining the impact and relative weight of each CPC on the performance, and finally, the use of fuzzy and Bayesian rules to assess and reduce human error in such situations.

Human reliability is affected by individual, organizational, and environmental factors introduced in CREAM method under 9 CPCs. These CPCs are pre-defined and CPCs can be changed, increased, or decreased based on environment and working conditions. Eight modified CPCs were used for human error in tanker shipping ⁸ . Banda et al. also used 6 CPCs to evaluate human error in their study ¹³ . In this study, in order to adapt CPC in emergencies, 7 CPC was used to assess human error based on opinions of experts and specialist; accordingly, membership relationships and fuzzy sets were defined based on these 7 CPCs.

As one of the weaknesses of CREAM method, the importance of CPCs in all jobs and tasks are considered equal, while CPCs do not have the same impact on human reliability and can take different weights depending on the type of tasks and jobs ¹⁶ . It is better to weight CPCs to show their real impact on human reliability ¹⁰ . To this end, various methods such as Delphi, pair-wise, and AHP can be used ¹⁷ . In this study, AHP method and paired comparison based on expert judgment were used to determine the weight of CPCs. Another important issue in human reliability assessment is the quantification of qualitative data on working conditions (based on expert judgments), as well as the ability to evaluate quantitative and qualitative data together ⁶ . CREAM method suffers from uncertainty problem, for instance uncertainty in input data and CPCs and uncertainty in control modes ⁸ . In recent years. in order to overcome the problems of uncertainty in decision making, uncertainty of complex issues, inaccurate information, and the combination of qualitative and quantitative data, fuzzy systems have been used as an appropriate method for solving such problems. In this study, a combination of fuzzy CREAM and Bayesian method was used to solve the mentioned problems. This method is a good tool for solving traditional CREAM problems ^{4,810,12,18-21} . The utilization of BN in human error assessment provides an effective mechanism for human reliability assessment under emergency conditions ²¹ . Bayesian network model was used to develop a basic CREAM method. Bayesian network was helped to overcome the weaknesses of CREAM method via reducing uncertainties in CPCs and led to instant and precise estimation of human error probability ¹⁸ .

In this study, the comparison of the results of control mode in normal and weighted items showed that the probability distribution of these two methods is different, and CPCs should be weighed in order to better reflect the working conditions. In this study, the worst scenario was related to Tasks 3 and 5, related to coordination tasks and pre-extinguishing operations. 'Coordination' is about coordination between different responding teams such as firefighting, rescue, HSE, medical, security, and public relations teams. On the other hand, 'pre-extinguishing operations' is elated to isolation of the area, control of volume, temperature, intensity of the fire, discharge, etc.

In these tasks, due to time limitation to control the situation and prevent the occurrence of a crisis, the probability of human error is higher, also reported and confirmed by previous studies ²² . Maneuvers and training to prepare to deal with this situation as well as the effectiveness of ERP is very important in preventing human error.

Conclusion

Given the importance of identifying and controlling human error in emergencies, this study introduced and utilized an applied method to solve the weaknesses of traditional CREAM method and create a unique dynamic human error assessment method for each task. The results of this method can be used as a specific tool to manage human error in emergency. These results also can be utilized as a repeatable method for assessing human error in different industries and other critical jobs, depending to the conditions of the industry.

Acknowledgements

This study has been adapted from a research project at Hamadan University of Medical Sciences. Thereby appreciate all contributed in this research.

Conflict of interest

The authors declare that there is no conflict of interests.

Funding

This study is supported by Hamadan University of Medical Sciences, Iran (grant No. 9611037026).

Highlights

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