1 Introduction

For years, human errors and individual component failure were considered the basic reasons for many accidents [1, 15, 21,22,23,24]. It has been lately argued that human error was a causal factor in the occurrence of many serious accidents in the railway system, both in the UK [2] and across Europe [3].

Many organizations are looking forward to reduce human errors to increase efficiency. For example, a petrochemical unit is one of the places that has the potentiality prone to accidents. In other words, in these places human mistakes impose at great costs to the organization and hence reduce efficiency.

In this regard in the recent years a large number of articles have been published which aimed to reduced human errors and consequently increase organizational efficiency. Madigan et al. [4] examined the relationship between active and latent factors and found a solution for these types of incidents by using human factor analysis and classification system (HFACS) to examine rail industry incident reports.

As mentioned earlier, human error and safety management are the subjects which many organizations face and in this regard, several methods and approaches have been suggested which aim to increase organizations, ability regarding them. In another study, Azadeh and Zarrin [5] have evaluated the efficiency and effectiveness of a large petrochemical plant’s staff by considering three concepts namely Resilience Engineering (RE), motivational factors in the work environment and Health, Safety Environment and Ergonomics (HSEE).

Malgorzata Pecillo [6] checked out whether the resilience engineering concept is related to the implementation of occupational safety and health management systems (OSH MSs) and to safety levels in Polish enterprises of different sizes and activities. In the literature, two concepts and approaches namely Resilience Engineering and Integrated Resilience Engineering have been proposed to reduce accidents and increase efficiency.

If we were to break down Resilience Engineering from the engineering point of view, that would be the practice of identifying and detecting the instabilities, variations, interferences or any sort of surprises and actually try to change, revise or tackle the identified issues [7]. During the recent years, a strong interest has been shown in organizational resilience in both theory and application [8].

Nowadays the resilience engineering approach appears to be a practical idea, considering the fact that it can extensively increase the safety in complex systems since it has the ability to incorporate both safety and performance together in a functional way without causing any conflict in terms of performance and safety [9].

Resilience engineering is the ability of organizations for unforeseen events and adapts to the potential for accidents [10]. In fact, RE either improves safety of systems in the process industry or as a new method can control incidents and limit their outcome [11].

Azade and Zarrin [5] showed that five factors from Resilience Engineering, two from Health, Safety, Environment and Ergonomics (HSEE) and three factors from work motivational factors (WMFs) have significant positive effects on effectiveness. Assessment and studies over Resiliency factors (RFs) in an unpredictable environment shows that this approach has significant impacts on the management of enterprises.

Resilience engineering and macro-ergonomic focus on reducing risks and increasing efficiency within organizations. In this paper ten factors that were selected from both the fields of resilience engineering and macro-ergonomics were introduced and the relationship between them analyzed.

The purpose of this analysis is to identify the mutual influence of factors among each other as well as to determine the degree of this effect. All this analysis has been performed by a Bayesian Network modeling approach. Accordingly, the aim of this paper is to analyze the sensitivity between the factors that are selected from the fields of resilience engineering and macro-ergonomic. In other words, the aim of this work is to investigate the achievable level efficiency by considering resilience engineering and macro-ergonomics.

The paper has been organized as follows. Section 2 presents the methodology and result of the work is discussed in Sect. 3. The paper is finally concluded in Sect. 4.

2 Methodology

This study aims to find the relationship and also the level of importance of ORE and ME indicators on organizational regulations effectiveness (OREF). The six resilience engineering factors are as follows: teamwork, preparedness, flexibility, fault- tolerance, redundancy and self-organization and the three factors selected from macro-ergonomics are: redesign, DM speed ability and finally information flow. In this study, these nine factors are systematically analyzed and evaluated through a Bayesian network model. The effect of these factors on each other as well as OREF are investigated. Results and Sensitivity analysis are finally represented in the next section. The Bayesian network modelling in our study includes the five following step (Fig. 1).

Fig. 1.
figure 1

Flow chart for Bayesian network construction by considering ten factors selected from resilience engineering and macro-ergonomic.

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2.1 Bayesian Networks

Bayesian networks (BNs) are useful tools for demonstrating the causal relationships and interdependence between a number of factors [12, 13]. BNs are a well-established graphical formalism for the demonstration of conditional probabilistic relationships among indecisive variables [14]. Since BNs are based on experts’ knowledge they are a very powerful tools which can be utilized in many different fields for the sake of modeling. Especially the causal interrelationships among some variables can be easily modeled using BNs [12, 13]. Moreover, BNs are a graphical structure that can consider and analyze a large number of variables in state of uncertainty. Nodes in a BNs represent variables that may be either connected together directly by an arc or connected indirectly.

3 Case Study and Computational Results

A large energy sector unit consisting of 150 operators, was selected for this study. The first part of the required data was obtained by distributing questionnaire (Questionnaire 1) among the operators located in control rooms, who constituted the target sample. The questionnaire consisted of 80 questions, scoring of each question ranged from 1 to 20. By using the questionnaire, the basic demographic information of operators is also extracted. Standard items of the Questionnaire 1 were adopted from reliable resources [15,16,17]. The other required data that were necessary to build the Bayesian network were collected through Questionnaire 2.

3.1 Input Determination

As mentioned before, the aim of this study is to improve organizational regulations effectiveness (OREF) through concurrent modelling of organizational resilience engineering (ORE) and macro-ergonomics (ME) indicators in an organization. Six indicators namely teamwork, preparedness, fault tolerance, flexibility, redundancy and self-organization are considered as representatives of ORE. The macro-ergonomics indicators considered in this study are redesign, decision-making pace and information flow. We leverage the power of BNs to improve OREF through concurrent modelling of ORE and ME. The nine factors act as the nodes of the Bayesian network, hence in the first step they are selected and confirmed by experts to be further considered in this study.

3.2 Collecting Information by Questionnaire 1

In this step, standard questions related to the nine factors of both organizational resilience engineering (ORE) and macro-ergonomics (ME) along with organizational regulations effectiveness (OREF) were considered in designing Questionnaire 1. This questionnaire is then distributed among the operators. They can chose answers to the questions range from 1 to 20 where 1 is considered the worst score and 20 as the best score. The operators also responded to the items of the questionnaire regarding demographic information.

3.3 Testing the Reliability of Results Obtained by Questionnaire 1

Another important task before lunching BN is to test the reliability of the designed questionnaire. In this regard, Cronbach’s alpha is calculated and used to estimate the reliability of the questionnaire:

$$ Cronbach^{,} s alpha = \frac{n}{n - 1}\left( {1 - \frac{{\mathop \sum \nolimits s_{i}^{2} }}{{s_{t}^{2} }}} \right) $$
(1)

Where:

n indicates the number of questions and, \( s_{i } \) and \( s_{t} \) represent the standard deviation of the i th question and total standard deviation respectively [ 18 ].

As a rule of thumb, we required a value of 0.6 or higher for Cronbach’s alpha before using the questionnaire. Table 1 shows that the all ten factors achieve this value which allow us to use the designed questionnaire.

Table 1. Reliability of questionnaire 1 by Cronbach’s alpha
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Thus according to the value for alpha presented in Table 1, the reliability of the first questionnaire was accepted.

3.4 Collecting Experts’ Knowledge by Questionnaire 2

In this step, Questionnaire 2 has been designed for collecting experts’ knowledge to obtain information required for building the Bayesian Network.

The first step in conducting a BN analysis is to build a causal graphical model in the form of a directed acyclic graph (DAG) that represents interrelationships among all desired variables [20]. There is not a unique method in the literature to build such a network. We utilize Dempster-Shafer theory for soliciting the domain knowledge of experts. Dempster-Shafer was used by Mohammadfam et al. in the process of BN construction [20]. To this end, the Questionnaire 2 was designed and three experts with the appropriate domain knowledge of resilience engineering complete the Questionnaire 2. This questionnaire demonstrates three possible relationships between each two factors which then the experts were asked to reveal their opinions on what type of relationship they mostly think is true and should be formed between those two factors. For example, there could be three possible relationships between two variables, namely A and B. A affects B (A → B), B affects B (A ← B) or no relationship exists between A and B (A ↑ B) [20].

3.5 Bayesian Network Construction

In this step, according to the information collected in the previous section and by using the Dempster-Shafer theory the BN was constructed. The Dempster-Shafer theory is a useful method to reduce inconsistencies when information is collected from various sources [20]:

$$ m\left( a \right) = \frac{1}{1 - k} \mathop \sum \limits_{{A_{1} \mathop \cap \nolimits A_{2} \mathop \cap \nolimits A_{3} \ldots \mathop \cap \nolimits A_{n} = A}}^{n} m\left( {A_{1} } \right).m\left( {A_{2} } \right).m\left( {A_{3} } \right) \ldots ..m\left( {A_{n} } \right) $$
(2)
$$ K = \mathop \sum \limits_{{A_{1} \mathop \cap \nolimits A_{2} \mathop \cap \nolimits A_{3} \ldots \mathop \cap \nolimits A_{n} = \emptyset }}^{n} m\left( {A_{1} } \right).m\left( {A_{2} } \right).m\left( {A_{3} } \right) \ldots ..m\left( {A_{n} } \right) $$
(3)

In these equations, k represents the amount of discrepancies between the source of information and \( \left( {1 - k} \right) \) is the normalizing factor. To clarify this approach better, an example is given below:

Example:

Assuming that two experts have offered the following probability values for the three possible relationship between the two factors information flow and preparedness;

  • Expert 1 = (information flow → preparedness = 0.6, information flow ← preparedness = 0.3, information flow ↑ preparedness = 0.1).

  • Expert 2 = (information flow → preparedness = 0.3, information flow ← preparedness = 0.5, information flow ↑ preparedness = 0.2).

In the first step, Table 2 was formed. The steps to do this have been completely explained by (Sentz and Ferson 2002); Moreover, one of the principles that need to be fulfilled in structuring a Bayesian network is to avoid the creation of any cycle.

Table 2. Calculating the integrated mass probability for each relationship between information flow and teamwork based on the opinions elicited from expert 1 and expert 2 (a = Information flow → Preparedness, b = Information flow ← Preparedness, c = Information flow ↑ Preparedness)
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According to the information represented in Table 2, the integrated mass probability for each relationship is calculated by using Eq. (2):

  • \( K \) = 0.09 + 0.03 + 0.3 + 0.05 + 0.12 + 0.06 = 0.65, \( 1 - k \) = 1−0.65 = 0.35

  • m 1−2(a) = 0.18/0.35 = 0.514

  • m 1−2(b) = 0.15/0.35 = 0.428

  • m 1−2(c) = 0.02/0.35 = 0.057

According to the results, since the amount of (\( m_{1 - 2} \left( a \right) ) \) is greater than the other two values, therefore the final relationship between these two factors based on the opinions of two experts is: a = information flow → preparedness. Which means Information flow affects Preparedness and not the other way. Consequently, according to the information collected from three experts and by using the Dempster-Shafer theory, the Bayesian network was constructed as in Fig. 2.

Fig. 2.
figure 2

The Bayesian network

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3.6 Conditional Probabilities

Once the Bayesian Network is constructed, the conditional probability distribution for each node should be calculated. In this regard, two states namely poor and good have been defined for all of ten factors. As previously mentioned, in the range of 1 to 20, 1 indicates the worst and 20 indicates the best score. If the score assigned by the experts, ranges between 1 to 12, then the state for a factor is assumed poor and if the score is in the range between 12 to 20, then the factor is in a good state. Thus the conditional probability distribution for each node in the Bayesian Network is represented in a Conditional Probability Table (CPT). In a CPT, the state of each node is dependent and conditioned to its parent nodes’ states while it is independent to other nodes. For example, the CPT for the redundancy node, with Teamwork node and Redesign node as its parents, is represented as follows (Table 3):

Table 3. CPT table for redundancy node.
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3.7 Results

In the constructed BN, there are three root nodes including teamwork, redesign and self-organization. By changing these three factors, other factors including redundancy, information flow, fault tolerance, flexibility, Preparedness, DM speed and control ability and finally organizational regulations’ effectiveness will be changed. Results of sensitivity analysis indicated that by a variation in each of the three root nodes, a significant change can be observed in other factors and finally on OREF. Moreover, based on the results, teamwork factor is more effective than redesign and self-organization. The effect of root node (teamwork, self-organization and redesign) on OREF is represented in Table 4.

Table 4. The obtained results which indicate the effect of teamwork, redesign and self-organization on organizational regulations effectiveness.
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The results that are represented in Table 4 shows the impact of three root nodes including teamwork, redesign and self-organization on OREF.

3.8 Validation

In this section, we analysis by which extend the change of teamwork, self-organizational and redesign which are root nodes in the BN affect other nodes. The results presented in the table showed that, with the increasing the 3 indicators, the other indices significantly increased, therefore, on this basis, the ORE and ME by increasing the ten indicators factors, has improved. This results are represented in Table 5. It is also obvious that OREF has been improved by 41%.

Table 5. The results of changes in factors according to suggested for improvement team work, self-organization and redesign
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The results according to Table 5 demonstrate improvement in factors after changes in three root node factors that includes: teamwork, self-organization and redesign.

4 Conclusion

This paper aimed to optimize and improve organizational regulations effectiveness (OREF) through concurrent modelling of organizational resilience engineering (ORE) and macro-ergonomics (ME) indicators in an organization. Therefor six indicators, namely, teamwork, preparedness, fault tolerance, flexibility, redundancy, self-organization and organizational regulations effectiveness are considered for ORE. The macro-ergonomic indicators are redesign, decision-making speed and information flow. The combined factors are considered and analyzed through Bayesian Network (BN). Three factors that including teamwork, self-organization and redesign were known as the factors which have the greatest impact on OREF.