When a disaster occurs, it is necessary to immediately provide relief plans. Many decisions must be made in very short time, which may have a relevant impact on the consequences of the disaster. For an efficient and smart exploitation of available resources, it is necessary to mitigate damages. Many applications of operations research methods to disaster response optimization may be found in the literature. Barbarosoglu G, Arda Y. [14] proposed a two-stage stochastic programming model for transportation planning in a disaster, while a multi-objective model for quick response to emergencies in logistics distribution has been proposed by Liu and Zhao [15]. In Ref. [16], the authors proposed a mixed-integer programming model for facility location in humanitarian relief. Ozdamar and Yi [17] dealt with vehicle dispatch plan for relief and evacuation. Other papers presented studies related to relief operations in a specific type of disaster, such as in Ref. [18], where a decision support system, specific for emergency response in the case of nuclear accident, has been presented, and in Ref. [19], the authors proposed an optimization model for allocating emergency resources after an earthquake. Similar issues may be found in ambulance allocation dispatching, where a limited fleet of ambulances must be allocated to realtime requests. A complete review on this subject may be found in Ref. [20].

We deal with buses allocation for mass evacuation. In detail, considering a case in which, due to toxic gas dispersion, all the population located in a risk area surrounding the emergency site must be evacuated. This area is sub-divided into zones, for each one of which the number of people to be evacuated is known. We consider a set of depots where buses are located, for each one of which, we suppose to know the number of available vehicles of identical capacity (in terms of the number of people which can be carried), and the delay with which the vehicles will be available at that depot. A delay equal to 0 means that vehicles are always located at the depot and that they are immediately available. We consider a set of potential evacuation areas with different capacities. For operational reasons, people from the same zone must be evacuated in the same evacuation point located within the area [21–23].

The goal is to minimize the averaged evacuation time. In particular, for evacuation time of a zone, we intend the time within which all the people from that zone are evacuated.

Before proceeding with the mathematical formulation, we define the parameters, sets and variables of the model.

Model parameters:

#### Model sets:

Involved variables:

The mathematical model for buses allocation for mass evacuation can be formulated as follows:

$$\min \sum\_{i \text{ in } I} \frac{T\_i}{|I|} \tag{1}$$

s.t.

$$\sum\_{\vec{i}\in\vec{k}\text{ in }K} Y\_{i\vec{k}} \ge 1 \qquad \forall i \in I \tag{2}$$

$$\sum\_{i \neq j \in I} \mathbf{Z}\_{ij} = 1 \qquad \forall i \in I \tag{3}$$

A Bus Allocation Model for Major Industrial Disasters http://dx.doi.org/10.5772/intechopen.68808 91

$$\sum\_{i \text{ in } I} q\_i Z\_{ij} \le \mathbf{C}\_{\flat} \forall j \in I \tag{4}$$

$$\forall V\_{ik} \le R\_k \mathcal{Y}\_{ik} \forall i \in I \; \forall k \in K \tag{5}$$

$$\sum\_{i \text{ in } l} V\_{ik} \le \mathcal{R}\_k \forall k \in K \tag{6}$$

$$\sum\_{k \text{ in } K} c \ast V\_{ik} \ge q\_i \forall i \in I \tag{7}$$

$$\left(\sum\_{k\text{ in }K} V\_{ik} - 1\right) \* c \le q\_i \forall i \in I \tag{8}$$

$$A\_i \succeq \left(\sum\_{k \text{ in } K} \tau\_{ik} + \left. p\_k \right|\right) Y\_{ik} \,\forall i \in I \tag{9}$$

$$T\_i = \sum\_{j \text{ in } \mathbb{J}} t\_{ij} \, Z\_{ij} + \, \ A\_i \, \forall \mathbf{i} \in I \tag{10}$$

$$Y\_{ik} \in \{0, 1\} \quad \forall i \in I \; \forall k \in K \tag{11}$$

$$Z\_{\forall} \in \{0, 1\} \quad \forall i \in I \; \forall j \in J \tag{12}$$

$$V\_{ik} \in \mathbb{Z}^+ \quad \forall \mathbf{i} \in \mathbf{I} \; \forall \mathbf{k} \in \mathbf{K} \tag{13}$$

The objective function is to minimize the averaged evacuation time, expressed in Eq. (1). Constraint Eq. (2) imposes that each zone must be served by at least one depot, while constraint Eq. (3) ensures that all the population of a zone must be evacuated to the same evacuation point. Evacuation areas' capacity restriction is satisfied by constraint Eq. (4). Constraint Eq. (5) imposes that a zone may be evacuated by vehicles located at a depot only if it is served by that depot. The number of vehicles used, for each depot, must be lower than the number of available vehicles at that depot, as stated in constraint Eq. (6). Constraints Eqs. (7) and (8) ensure that the number of vehicles used to evacuate a zone is the minimum necessary. For each zone, the arrival time of the last bus is computed by constraint Eq. (9), while the evacuation time is computed by constraint Eq. (10). In fact, the evacuation time of a zone, defined as the arrival time of the last bus, evacuating people from that zone, to the evacuation area, can be computed as the sum of the arrival time of the last bus to the zone plus the travel time between the zone and the evacuation area. Finally, constraints Eqs. (11)–(13) specify the domain of the variables.

It is also interesting to analyse how the solution changes if instead of minimizing the averaged evacuation time, we would minimize the largest evacuation time, defined as the time necessary to evacuate all the zones. In this case, the new objective function results:

$$\min\_{i \text{ in } l} \sum\_{i} W\_{i} \tag{14}$$

subject to constraints Eqs. (2)–(13) and the following additional constraints:

Before proceeding with the mathematical formulation, we define the parameters, sets and

• Yik: binary variable taking value equal to 1 if zone i is evacuated by bus located at depot k

• Zij: binary variable taking value equal to 1 if zone i is evacuated to evacuation area j and

• Yik: number of vehicles starting from depot k and used to evacuate zone i

X k in K

X j in J

• Ai: time within which all vehicles that have been assigned to zone i reach the zone

The mathematical model for buses allocation for mass evacuation can be formulated as follows:

minX i in I Ti

jIj ð1Þ

Yik ≥ 1 ∀i∈ I ð2Þ

Zij ¼ 1 ∀i∈I ð3Þ

variables of the model.

• c: vehicles' capacity

• qi: number of people to be evacuated from zone i

• pk: delay with which the vehicles are available at depot k

90 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

• tij: travel time between zone i and evacuation area j

• τik: travel time between depot k and zone i • Rk: number of vehicles available at depot k

• Cj: capacity of evacuation area j

• I: set of zones to be evacuated

• J: set of evacuation areas

• K: set of depots

Involved variables:

and 0 otherwise

• Ti: evacuation time for zone i

0 otherwise

s.t.

Model parameters:

Model sets:

$$\forall W \succeq T\_i \quad \forall i \in I \tag{15}$$

$$W \in Z^{+} \tag{16}$$

#### 3. Data description

The company is located in Italy and it is the European leading company in the main sector of waste oils regeneration. More than 150 people work for the company. The working activities take place 365 days a year, 24 hours a day, in the two production plants: one in the North of Italy and the other one near Rome.

#### 3.1. Data providing information on the population to be evacuated

The risk area within a radius of 3 km from the emergency site has been divided in 23 potential evacuation zones. For each one, the following information has been defined:

Table 1. List of zones and number of inhabitants to be evacuated.

Table 2. Zones and number of inhabitants to be evacuated.

W ≥ Ti ∀i∈ I ð15Þ

W ∈ Zþ ð16Þ

) and the population

The company is located in Italy and it is the European leading company in the main sector of waste oils regeneration. More than 150 people work for the company. The working activities take place 365 days a year, 24 hours a day, in the two production plants: one in the North of

The risk area within a radius of 3 km from the emergency site has been divided in 23 potential

• The number of people to be evacuated: For each zone, the number of people to be

) (Table 1). • Collection points' location: For operational reasons, people from the same zone must be evacuated in a specific collection point, identified by its geographical coordinates.

• Distance: Distances between collection points and depots (D) and between collection

Zones Inhabitants Zones Inhabitants

Zone 1 725 Zone 13 626 Zone 2 422 Zone 14 447 Zone 3 367 Zone 15 775 Zone 4 367 Zone 16 338 Zone 5 442 Zone 17 318 Zone 6 362 Zone 18 218 Zone 7 467 Zone 19 328 Zone 8 343 Zone 20 288 Zone 9 660 Zone 21 745 Zone 10 943 Zone 22 367 Zone 11 278 Zone 23 357

3.1. Data providing information on the population to be evacuated

92 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

evacuation zones. For each one, the following information has been defined:

evacuated has been calculated considering the total zone size (km2

points and evacuation areas (EAs) have been computed (Table 2).

3. Data description

Italy and the other one near Rome.

Zone 12 536

Table 1. List of zones and number of inhabitants to be evacuated.

density of the zone (inhabitants/km2

Table 3. List of evacuation areas capacity.

#### 3.2. Data providing information on the evacuation area

A set of nine evacuation areas has been identified for each one of which the following information has been collected:

#### 4. The case study

In this scenario, we consider a toxic gas dispersion due to which the population within a radius of 3 km from the company must be evacuated.

We defined 23 zones to be evacuated and for each one we supposed to know the number of people to be evacuated.

We consider a homogeneous fleet of 170 vehicles located in three depots. 20 of them are located at Depot 1 and are supposed to be immediately available while the other buses are supposed to be around the city and 50 of them can be available in 20 minutes at each depot (1, 2 and 3). We have defined nine available evacuation areas, each one of them is known with the maximum capacity.

Each zone can be served by buses coming from different depots but, for operational reasons, all the people from the zone must be evacuated to the same evacuation area. Distances between depots and zones and between zones and evacuation areas have been computed with Google Maps. Travel times have been computed considering a travel time equal to 10 Km/h, compatible with a congested urban traffic. We have carried out four tests. In Tests 1 and 2, we have tried to minimize the average evacuation time, while in Tests 3 and 4, we aimed to minimize the total evacuation time, i.e. the time within which all the population is evacuated. Furthermore, Tests 1 and 3 consider all evacuation areas available, while in Tests 2 and 4, evacuation areas 4 and 9 are not available.

Tests outlines are described in Table 4.

Table 4. Tests outlines.

In Tables 5 and 6, we report, for each zone, the area to which it has been evacuated, the evacuation time (expressed in minutes), other than averaged and maximum evacuation time.

3.2. Data providing information on the evacuation area

of 3 km from the company must be evacuated.

evacuation areas 4 and 9 are not available.

Test Evacuation areas Minimize All Avg Time No. 4 and 9 Avg Time All Max Time No. 4 and 9 Max Time

Tests outlines are described in Table 4.

Table 4. Tests outlines.

number of persons that the area can accommodate (Table 3).

94 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

mation has been collected:

4. The case study

people to be evacuated.

capacity.

A set of nine evacuation areas has been identified for each one of which the following infor-

• Capacity: For each area, it is specified the maximum capacity intended as the maximum

In this scenario, we consider a toxic gas dispersion due to which the population within a radius

We defined 23 zones to be evacuated and for each one we supposed to know the number of

We consider a homogeneous fleet of 170 vehicles located in three depots. 20 of them are located at Depot 1 and are supposed to be immediately available while the other buses are supposed to be around the city and 50 of them can be available in 20 minutes at each depot (1, 2 and 3). We have defined nine available evacuation areas, each one of them is known with the maximum

Each zone can be served by buses coming from different depots but, for operational reasons, all the people from the zone must be evacuated to the same evacuation area. Distances between depots and zones and between zones and evacuation areas have been computed with Google Maps. Travel times have been computed considering a travel time equal to 10 Km/h, compatible with a congested urban traffic. We have carried out four tests. In Tests 1 and 2, we have tried to minimize the average evacuation time, while in Tests 3 and 4, we aimed to minimize the total evacuation time, i.e. the time within which all the population is evacuated. Furthermore, Tests 1 and 3 consider all evacuation areas available, while in Tests 2 and 4,

• Location: The location of each area is provided in terms of geographical coordinates.

In Tables 7 and 8, we report the vehicle dispatching resume. In detail, for each zone, we report the number of buses started from each depot to evacuate that zone. Depot 1\* concerns vehicles starting from Depot 1 but available after 20 minutes.

Table 5. Evacuations area assignment and evacuation time for Tests 1 and 2.

Table 6. Evacuations area assignment and evacuation time for Tests 1 and 2.

Comparing results obtained in Tests 1 and 2, we can observe that if two evacuation areas are not available anymore (Test 2), the average evacuation time only increases by 2 minutes (from 75 to 77), which shows the robustness of the system. The same behaviour can be noted in Tests 3 and 4. In this case, even if evacuation areas 4 and 9 are not available, the optimal maximum evacuation time is the same as in the case in which all the evacuation areas are available, and the increment of average evacuation time is very little.

Table 7. Vehicles dispatching for Tests 1 and 2.

Comparing results obtained in Tests 1 and 2, we can observe that if two evacuation areas are not available anymore (Test 2), the average evacuation time only increases by 2 minutes (from 75 to 77), which shows the robustness of the system. The same behaviour can be noted in Tests 3 and 4. In this case, even if evacuation areas 4 and 9 are not available, the optimal maximum evacuation time is the same as in the case in which all the evacuation areas are available, and the increment of average evacuation time is very

Table 6. Evacuations area assignment and evacuation time for Tests 1 and 2.

Avg Time 82 Avg Time 84 Max Time 95 Max Time 95

Test 3 Test 4

96 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

Zone Evacuation area Time Zone Evacuation area Time 6 94 1 6 94 7 92 2 5 73 5 95 3 5 95 8 81 4 6 81 6 77 5 6 77 6 93 6 6 93 6 79 7 6 79 6 90 8 6 91 4 79 9 7 83 5 75 10 8 89 5 77 11 2 85 6 73 12 6 73 1 89 13 6 86 6 63 14 6 94 9 86 15 5 71 6 68 16 3 84 6 78 17 5 94 5 93 18 5 77 5 93 19 6 71 6 81 20 3 84 5 76 21 7 94 8 80 22 5 69 6 71 23 6 92

little.

Comparing Tests 1 and 3, we can observe that, trying to minimize the maximum evacuation time or the average one, we obtain sensibly different solutions but values obtained for both criteria are comparable.

The same behaviour can be noted in Tests 2 and 4.

For what concerns vehicle dispatching, we can observe that in Tests 1 and 2, the optimal vehicle assignment is the same, while in Tests 3 and 4, we obtain a different vehicle assignment. This fact depends on the different objective functions. In fact, when we aim to minimize the maximum evacuation time, there are many feasible vehicle assignment configuration, which may yield to the same objective function value.

Table 8. Vehicles dispatching for Tests 3 and 4.

#### 5. Concluding remarks

The state of the art underlines that in the event of a major disaster there is a strong need for decision support tools that give solutions to the allocation problem in a short time interval. From a transport/logistics point of view, the most important decisions that should be made by emergency vehicle managers during a disaster response phase are related to the location and allocation of the emergency vehicles.

A mixed-integer programming model for buses allocation has been calibrated to determine the optimal number and allocation of buses, which must be involved in order to evacuate all the population located in a defined risk area around the emergency site and the optimal location for evacuation areas.

Four different scenarios have been calibrated: in two of them, the average total travel time of buses has been minimized, while in the other two the maximum total travel time of buses has been minimized.

Comparing the scenarios with all zones, the obtained results are different but values obtained for both criteria are comparable; the same aspects have been noted comparing the scenarios without areas No. 4 and No. 9.

Regarding further evolution of the research, interesting developments can be followed expanding and integrating the results of bus allocation model with a route choice model and a route assignment model.

#### Author details

Paolo Fadda1 , Gianfranco Fancello1 \*, Simona Mancini2 and Claudia Pani3

#### References

5. Concluding remarks

allocation of the emergency vehicles.

Table 8. Vehicles dispatching for Tests 3 and 4.

The state of the art underlines that in the event of a major disaster there is a strong need for decision support tools that give solutions to the allocation problem in a short time interval. From a transport/logistics point of view, the most important decisions that should be made by emergency vehicle managers during a disaster response phase are related to the location and

Test 3 Test 4

98 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

1 0 0 11 0 1 0 0 11 0 27 0 0 0 27 0 0 0 30 0 6 0 30 0 6 0 46 0 0 0 46 0 0 0 57 0 0 0 57 0 0 0 60 6 0 0 60 6 0 0 70 7 0 0 70 7 0 0 80 0 0 5 80 0 5 0 9 0 0 10 0 9 0 0 10 0 10 0 0 14 0 10 0 0 0 14 110 0 4 0 110 0 4 0 120 8 0 0 120 8 0 0 130 9 0 0 130 0 0 9 140 7 0 0 140 0 7 0 15 0 0 0 12 15 0 12 0 0 160 5 0 0 160 5 0 0 170 5 0 0 170 0 0 5 180 0 4 0 180 0 0 4 190 0 0 5 190 5 0 0 200 0 0 5 200 5 0 0 21 0 0 0 11 21 0 0 0 11 220 0 0 6 220 0 0 6 230 0 0 6 230 0 6 0

Zone Depot 1 Depot 1\* Depot 2 Depot 3 Zone Depot 1 Depot 1\* Depot 2 Depot 3

A mixed-integer programming model for buses allocation has been calibrated to determine the optimal number and allocation of buses, which must be involved in order to evacuate all the

[19] Fiedrich F, Gehbauer F, Rickers U. Optimized resource allocation for emergency response after earthquake disasters. Safety Science. 2000;35(1):41–57

[6] Yang Y, Zhao H. Responsive bus bridging service planning under Urban Rail Transit Line Emergency. In: 3rd International Conference on Vehicle, Mechanical and Electrical Engineering (ICVMEE 2016). 2016. July 30-31, 2016. Wuhan, China. ISBN: 978-1-60595-370-0

100 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

[7] Zheng H. Optimization of bus routing strategies for evacuation. Journal of Advanced

[8] Oran A, Tan KC, Ooi BH, Sim M, Jaillet P. Location and routing models for emergency response plans with priorities. In: Aschenbruck N, Martini P, Meier M, Tölle J, editors. Future Security. Communications in Computer and Information Science. Vol. 318. Berlin,

[9] Muaafa M, Concho AL, Ramirez-Marquez JE. Emergency resource allocation for disaster response: An evolutionary approach. In: Conference Paper – PSAM 2014 "Probabilistic Safety Assessment and Management", Honolulu, Hawaii. Vol. 40. June 2014. http://

[10] Wang Y, Yan X, Zhou Y, Zhang W. A feeder-bus dispatch planning model for emergency evacuation in urban rail transit corridors. PLoS One. 2016;11(9):e0161644. DOI: 10.1371/

[11] Meinzer N, Storandt S. Decision Support in Emergency Medical Systems: New Strategies for Dynamic Ambulance Allocation. Albert-Ludwigs-University; 2014. Association for

[12] De la Torre LE, Dolinskaya IS, Smilowitz KR. Disaster relief routing: Integrating research

[13] Pedraza-Martinez AJ, van Wassenhove LN. Transportation and vehicle fleet management in humanitarian logistics: Challenges for future research. EURO Journal on Transporta-

[14] Barbarosoglu G, Arda Y. A two-stage stochastic programming framework for transportation planning in disaster response. Journal of the Operational Research Society. 2004;55

[15] Liu M, Zhao L. A composite weighted multi-objective optimal approach for emergency logistics distribution. In: IEEE International Conference on Industrial Engineering and Engineering Management; 2-5 December 2007, Singapore. IEEE; 2007. pp. 968–972 [16] Balcik B, Beamon BM. Facility location in humanitarian relief. International Journal of

[17] Ozdamar L, Yi W. Greedy neighborhood search for disaster relief and evacuation logis-

[18] French S. Multi-attribute decision support in the event of a nuclear accident. Journal of

the Advancement of Artificial Intelligence (www.aaai.org)

tion and Logistics. 2012;1(1-2):185–196

Logistics. 2008;11(2):101–121

tics. Intelligent Systems. 2008;23(1):14–23

Multi-Criteria Decision Analysis. 1996;5(1):39–57

and practice. Socio-Economic Planning Sciences. 2012;46(1):88–97

Transportation. 2014;48:734–749

Heidelberg: Springer; 2012

techno-info.com/

(1):43–53

journal.pone.0161644

## **An Experimental Study on Developing a Cognitive Model for Human Reliability Analysis**

Domenico Falcone, Fabio De Felice, Antonella Petrillo and Alessandro Silvestri

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69230

#### Abstract

Serious incidents that occur inside or caused by industrial plants represent a very critical issue. In this context, the human reliability analysis (HRA) is an important tool to assess human factors that influence human behaviour in disasters scenario. In fact, the reliability assessment of interaction between human-machine systems is an important factor that affects the overall performance and safety in industrial plants. However, even though HRA techniques have been available for decades, there is not a universal method/procedure to reduce human errors that affect human performance. This study aims to design a novel approach to investigate the relationship between human reliability and operator performance considering the dependence on the available time to make decisions.

Keywords: disaster management, human reliability analysis, cognitive model, PSFs

#### 1. Introduction

The increasing complexity of industrial systems requires the adoption of adequate approaches to manage emergency situations in case of accidents and disasters. In this context, the analysis of human reliability represents a crucial task [1]. In fact, the human factor is a predominant element in the study of accidents/disasters, not only in probability level, but also in terms of severity of the expected effects [2]. HRA is a set of techniques which describes the conditions of the operator during the work, taking into account errors and unsafe actions [3]. In other words, HRA aims to describe the physical and environmental conditions in which operators shall carry out their tasks, considering errors, skills, experience and ability [4]. The importance of the topic is the reason as we conducted a research on Scopus database, the largest abstract and citation database of peer-reviewed literature. Search string used in the literature survey was

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

'human reliability analysis'. String was defined according to the standards of Scopus database. Only articles in which the string 'human reliability analysis' was found in key words were analysed. The analysis on Scopus pointed out that from 1964 (first year in which the first article appeared) until February 2017 (period of survey) a set of 40,958 documents have been published divided in 32,865 articles, 3671 conference papers and the remaining part on books, editorials, letters, etc. Result showed that the scientific production on this topic is very wide and covers many scientific areas (engineering, medicine, social science, etc.). Furthermore, it is interesting to note that most of the publications (13,842) have been published in the USA. Of course, since the research was very general, it is evident that the large amount of documents found does not allow to have a specific analysis regarding our specific scientific interest. Thus, considering our specific field of interest, we refined our search applying a preliminary filter. Search string used was 'human reliability analysis AND industrial plant'. Only articles in which the string 'human reliability analysis AND industrial plant' was found in key words were analysed. In this case, only 46 documents were found from 1984 to 2017. It means that on average two articles per year have been published. Similarly, we conducted a deeper analysis applying a second filter. Search string used was 'human reliability analysis AND industrial plant AND cognitive model". Firstly, considering the three criteria: (1) article title, (2) abstract and (3) key words), only six articles were found. While taking into account the criterion 'keywords', only four articles were found.

Among the documents found, we selected some of them. An interesting point of view is analysed by Massaiu [5]. In his paper, a new approach is proposed to address the weaknesses of the HRA method or in other words the lack of empirical support of HRA method. In detail, a test of the ability to identify regularities among environmental conditions (procedures), crew expertise (teamwork) and crew behaviours were investigated. Liu et al. [6] apply the cognitive reliability and error analysis method (CREAM) to calculate the failure probability of human cognitive activities for mine hoisting operation. Cheng and Hwang [7] outline the human error identification (HEI) techniques that currently exist to assess latent human errors on the chemical cylinder change task.

Literature review shows that the human reliability analysis is an issue of growing importance in the scientific world. But, there are some limits. The major limit of HRA is related to the uncertainty which does not allow full use of the reliability analysis [8]. Furthermore, several human reliability models follow a static approach, in which human errors are described as omission/commission errors [9]. Really, in our opinion, it is essential to consider the physical and cognitive environment depending on the time in which human errors develop. This consideration led us to the development of an integrated reliability model which takes into account the dynamic influence of operators. Thus, our study aims to propose a novel approach to investigate the relationship between performance shaping factors (PSFs) and operator performances. In HRA, PSFs encompassed the various factors that affect human performance. PSFs can increase or decrease the probability of human error [10, 11]. Our research aims to develop a multi-dimensional and structural model in order to apply it in different types of activities and in different disaster scenarios to avoid potential operational errors. The model takes into account technical and environmental factors that can influence the decisions and the actions of operators. The model combines the cognitive aspects of operational analysis, the mathematical approach and the probabilistic quantification of the error. A real case study concerning the adoption of best practices for a petrochemical plant's control room during an emergency situation is presented. The rest of the chapter is organized as follows: in Section 2, experimental design is analysed; in Section 3, a detailed model in a real case study is presented; in this section the main results of the model are discussed and finally, in Section 4, conclusion and future development are summarized.

#### 2. Experimental study: the model framework

'human reliability analysis'. String was defined according to the standards of Scopus database. Only articles in which the string 'human reliability analysis' was found in key words were analysed. The analysis on Scopus pointed out that from 1964 (first year in which the first article appeared) until February 2017 (period of survey) a set of 40,958 documents have been published divided in 32,865 articles, 3671 conference papers and the remaining part on books, editorials, letters, etc. Result showed that the scientific production on this topic is very wide and covers many scientific areas (engineering, medicine, social science, etc.). Furthermore, it is interesting to note that most of the publications (13,842) have been published in the USA. Of course, since the research was very general, it is evident that the large amount of documents found does not allow to have a specific analysis regarding our specific scientific interest. Thus, considering our specific field of interest, we refined our search applying a preliminary filter. Search string used was 'human reliability analysis AND industrial plant'. Only articles in which the string 'human reliability analysis AND industrial plant' was found in key words were analysed. In this case, only 46 documents were found from 1984 to 2017. It means that on average two articles per year have been published. Similarly, we conducted a deeper analysis applying a second filter. Search string used was 'human reliability analysis AND industrial plant AND cognitive model". Firstly, considering the three criteria: (1) article title, (2) abstract and (3) key words), only six articles were found. While taking into account the criterion 'keywords',

104 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

Among the documents found, we selected some of them. An interesting point of view is analysed by Massaiu [5]. In his paper, a new approach is proposed to address the weaknesses of the HRA method or in other words the lack of empirical support of HRA method. In detail, a test of the ability to identify regularities among environmental conditions (procedures), crew expertise (teamwork) and crew behaviours were investigated. Liu et al. [6] apply the cognitive reliability and error analysis method (CREAM) to calculate the failure probability of human cognitive activities for mine hoisting operation. Cheng and Hwang [7] outline the human error identification (HEI) techniques that currently exist to assess latent human errors on the chem-

Literature review shows that the human reliability analysis is an issue of growing importance in the scientific world. But, there are some limits. The major limit of HRA is related to the uncertainty which does not allow full use of the reliability analysis [8]. Furthermore, several human reliability models follow a static approach, in which human errors are described as omission/commission errors [9]. Really, in our opinion, it is essential to consider the physical and cognitive environment depending on the time in which human errors develop. This consideration led us to the development of an integrated reliability model which takes into account the dynamic influence of operators. Thus, our study aims to propose a novel approach to investigate the relationship between performance shaping factors (PSFs) and operator performances. In HRA, PSFs encompassed the various factors that affect human performance. PSFs can increase or decrease the probability of human error [10, 11]. Our research aims to develop a multi-dimensional and structural model in order to apply it in different types of activities and in different disaster scenarios to avoid potential operational errors. The model takes into account technical and environmental factors that can influence the decisions and the actions of operators. The model combines the cognitive aspects of operational analysis, the

only four articles were found.

ical cylinder change task.

The most influential models of operator behaviour [12, 13] assume three levels of behavioural errors: (1) automatic reactions demanding little or no attention; (2) attentive reactions when one knows how to handle in a certain, well-known situation; and (3) creative, analytical reactions when confronted with new, unknown problems without off-the-shelf solutions. The above classification is certainly helpful, but it is not sufficient to take into account the dynamism that characterized human-machine systems reliability. It is necessary to reduce human error and

Figure 1. Methodological flowchart (author's elaboration).

hence to develop the capability to find (intuitively) solutions to unexpected problems. Our model is based on the above consideration. In detail, the model framework consists in nine different steps (as shown in Figure 1): Step 1—Preliminary analysis; Step 2—Generic tasks assessment (GTTs); Step 3—Definition of the Weibull distribution function; Step 4—Choice of performance shaping factors (PSFs); Step 5—Determination PSFcomp; Step 6—Determination HEPcont; Step 7—Determination HEPcont w/d; Step 8—Rating HEPnom after the 8th hour of work and Step 9—Determination HEPtot.

The model is applied in a real case study concerning the emergency management within a petrochemical company. In detail, the model aims to investigate the adoption of best practices for company's control room in order to ensure a consistent response under demanding circumstances.

#### 3. Model development: description of a real case study

In the present section, a detailed analysis of each step is provided.

#### 3.1. Step 1: preliminary analysis

The first step aims to define actions carried out by operators. At each operations is assigned a human error probability (HEPnom), that represents the unreliability of the operator and it represents a critical point to perform a proper human reliability analysis [14]. Obviously, the probability of error is a function of the time. Therefore, increasing the working hours, it means that the likelihood of error increases. Scenario analysed concerns the management of a fire occurred in the petrochemical plant. The key element is about maintaining a state of readiness and having an awareness of the working environment. Figure 2 shows the industrial plant under the study and the control room.

During a fire emergency, it is important to set common standards and to ensure that personnel are continuously trained, assessed and re-assessed against these summaries of best practice.  Evacuation of the facility is mandatory until the signal to re-enter has been given by appropriate personnel and the alarm bells have ceased ringing. Figure 3 shows procedures that are to be followed any time a fire alarm sounds.

Figure 2. Scenario under study.

An Experimental Study on Developing a Cognitive Model for Human Reliability Analysis http://dx.doi.org/10.5772/intechopen.69230 107

Figure 3. Fire emergency protocol.

hence to develop the capability to find (intuitively) solutions to unexpected problems. Our model is based on the above consideration. In detail, the model framework consists in nine different steps (as shown in Figure 1): Step 1—Preliminary analysis; Step 2—Generic tasks assessment (GTTs); Step 3—Definition of the Weibull distribution function; Step 4—Choice of performance shaping factors (PSFs); Step 5—Determination PSFcomp; Step 6—Determination HEPcont; Step 7—Determination HEPcont w/d; Step 8—Rating HEPnom after the 8th hour of work

The model is applied in a real case study concerning the emergency management within a petrochemical company. In detail, the model aims to investigate the adoption of best practices for company's control room in order to ensure a consistent response under demanding circum-

The first step aims to define actions carried out by operators. At each operations is assigned a human error probability (HEPnom), that represents the unreliability of the operator and it represents a critical point to perform a proper human reliability analysis [14]. Obviously, the probability of error is a function of the time. Therefore, increasing the working hours, it means that the likelihood of error increases. Scenario analysed concerns the management of a fire occurred in the petrochemical plant. The key element is about maintaining a state of readiness and having an awareness of the working environment. Figure 2 shows the industrial plant

During a fire emergency, it is important to set common standards and to ensure that personnel are continuously trained, assessed and re-assessed against these summaries of best practice.  Evacuation of the facility is mandatory until the signal to re-enter has been given by appropriate personnel and the alarm bells have ceased ringing.

Figure 3 shows procedures that are to be followed any time a fire alarm sounds.

3. Model development: description of a real case study

106 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

In the present section, a detailed analysis of each step is provided.

and Step 9—Determination HEPtot.

3.1. Step 1: preliminary analysis

under the study and the control room.

Figure 2. Scenario under study.

stances.

In detail, two operators were engaged in the control room, but only one was in charge of handling emergency procedures during the fire. Operator was responsible to activate emergency procedure that includes (1) Total block of the furnaces; (2) Close all turbines; (3) Propane valve closing; (4) Locking the sequence handling propane; (5) Flow control valves closing and (6) Closure of the emergency procedure. The three main emergency conditions that may be occurred are (1) Low hazard occurring despite the emergency the decision maker has been monitoring the situation; (2) Moderate hazard to occur the decision maker emergency can take wrong decisions; and (3) High hazard, the decision maker can make a mistake with a good chance.

#### 3.2. Step 2: generic tasks assessment (GTTs)

The present step aims to define generic tasks (GTTs) or a set of generic error probabilities for different type of tasks. The tasks were defined according the scientific literature [15]. Literature proposes for each task of human unreliability a set of values defined than the 5th percentile (for the first hour of work) and at the 95th percentile (for the eighth hour of work). The reliability is maximum at the first hour of work (t = 1) and minimum at the eighth work time (t = 8), as defined in Eq. (1):

$$k = 1 - HEP\_{nom}(t) \forall t \in [1; 8] \tag{1}$$

k parameter represents the value of the operator's reliability.

In our case study, only three significant generic tasks (4, 7 and 8) were considered in order to approximate operator's activities in the control room, as shown in Table 1.

#### 3.3. Step 3: definition of the Weibull distribution function

After defining GTTs, the probability of error associated with each GTTs were defined, according to Weibull probability distribution that best describes the probability of error. In detail, the probability of error is described by the index Human Error Probability (HEP), defined according to the Weibull distribution, as follows (Eq. (2)):

$$HEP\_{\text{nom}} = 1 - e^{-a\theta} \tag{2}$$

where the parameters α and β represent respectively the scale and the shape of the curves. The above formula assumes the minimum value of reliability during the first hour of work and a maximum value at the eighth hour of work. Consequently, the probability distribution of error Eq. (2) is adapted as follows (Eq. (3)):

$$\begin{cases} HEP\_{\text{norm}}(t) = 1 - k \ast e^{-\alpha(1-t)^\beta} \,\forall \, t \in [0; \, 1] \\ HEP\_{\text{norm}}(t) = 1 - k \ast e^{-\alpha(t-1)^\beta} \,\forall \, t \in [1; \, \approx ] \end{cases} \tag{3}$$

The value of k is calculated according to the value that the curves takes for t = 1, while the parameter β = 1.5 is deducted according to the scientific literature of the human error assessment and reduction technique (HEART) model developed by Williams [16]. The value of α is determined by setting the value of the function for t = 8 for each GTTs. Starting from this function, it is possible to calculates the value of α through the inverse formulas, see Eq. (4):

$$HPP\_{\text{nom}}(t) = 1 - k \ast e^{-a(t-1)^\delta} \,\forall \, t \in [1; \infty[ \,] \tag{4}$$

Table 1. Generic tasks.

α coefficient is represented by Eq. (5), as follows:

In our case study, only three significant generic tasks (4, 7 and 8) were considered in order to

After defining GTTs, the probability of error associated with each GTTs were defined, according to Weibull probability distribution that best describes the probability of error. In detail, the probability of error is described by the index Human Error Probability (HEP),

HEPnom ¼ 1 � e

HEPnomðtÞ ¼ 1 � k � e�αð1 �tÞ

HEPnomðtÞ ¼ 1 � k � e�αðt �1Þ

HEPnomðtÞ ¼ 1 � k � e

No. Generic task Limitations of

3 Complex task requiring high level of comprehension and

7 Completely familiar, well designed, highly practised, routine

8 Respond correctly to system command even when there is an augmented or automated supervisory system

skill

task

Table 1. Generic tasks.

where the parameters α and β represent respectively the scale and the shape of the curves. The above formula assumes the minimum value of reliability during the first hour of work and a maximum value at the eighth hour of work. Consequently, the probability distribution of error

The value of k is calculated according to the value that the curves takes for t = 1, while the parameter β = 1.5 is deducted according to the scientific literature of the human error assessment and reduction technique (HEART) model developed by Williams [16]. The value of α is determined by setting the value of the function for t = 8 for each GTTs. Starting from this function, it is possible to calculates the value of α through the inverse formulas, see Eq. (4):

1 Totally unfamiliar 0.35–0.97 0.65 0.03 0.1661 1.5 2 System recovery 0.14–0.42 0.86 0.58 0.0213 1.5

4 Fairly simple task performed rapidly or given scant attention 0.06–0.13 0.94 0.87 0.0042 1.5 5 Routin, highly practised 0.007–0,045 0.993 0.955 0.0021 1.5 6 Restoring a system by following the procedures of controls 0.008–0.007 0.992 0.993 �5.44E�05 1.5

�αðt�1Þ β

�αt β

β

β

∀ t ∈ ½0; 1�

∀ t ∈�1; ∞½

unreliability (%)

∀ t ∈�1; ∞½ ð4Þ

k (t = 8)

α β

k (t = 1)

0.12–0.28 0.88 0.72 0.0108 1.5

0.00008–0.009 0.9999 0.991 0.00005 1.5

0.00000–0.0009 1 0.9991 4.86E�05 1.5

ð2Þ

ð3Þ

approximate operator's activities in the control room, as shown in Table 1.

108 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

3.3. Step 3: definition of the Weibull distribution function

Eq. (2) is adapted as follows (Eq. (3)):

(

defined according to the Weibull distribution, as follows (Eq. (2)):

$$\alpha = \frac{-\ln\left[\frac{k(t=8)}{k(t=1)}\right]}{(t-1)^{\beta}}\tag{5}$$

Figure 4 shows the reliability performance according to Weibull distribution.

Table 2 shows the HEPnom values for the case study, calculated for the three different generic tasks.

#### 3.4. Step 4: choice of performance shaping factors (PSFs)

In the present step, PSFs were defined. PSFs allow to take into account all the environmental and behavioural factors that influence operator's cognitive behaviour. In particular, PSFs simulate different emergency scenarios. Analytically, PSFs increase the value of the error probability introducing external factors that could strain the 'decision maker'. PSFs and their values are deducted by standardized plant analysis risk-human reliability analysis (SPAR-H) method [17, 18]. Table 3 shows the PSFs considered.

Figure 4. Reliability performance (t = 0–8).

Table 2. HEPnom.

Table 3. Performance shaping factors.

Table 4. PSFs for the three emergency conditions.

While Table 4 shows PSFs, defined according the three emergency conditions (see Step 1).

#### 3.5. Step 5: determination PSFcomp

Defined PSFs and its multipliers, it is important to evaluate the overall PSF index (PSFcomp), as follows (Eq. (6)):

$$PSF\_{\text{comp}} = \prod\_{i=1}^{n} PSFi\tag{6}$$

PSFcomp index summarizes the weight of each influencing factor with respect to the actions/ decisions operator. Table 5 describes the values for the PSFcomp according to three emergencies levels.

#### 3.6. Step 6: determination HEPcont

The last step consists to contextualize the probability error analysis, defined as follows (Eq. (7)):

Table 5. PSFcomp.

An Experimental Study on Developing a Cognitive Model for Human Reliability Analysis http://dx.doi.org/10.5772/intechopen.69230 111

$$HEP\_{\text{cont}} = \frac{HEP\_{\text{nom}} \* PSF\_{\text{comp}}}{HEP\_{\text{nom}} \* (PSF\_{\text{comp}} - 1) + 1} \tag{7}$$

The value of HEPcont provides the level of probability of error of the decision maker, in function of influencing factors. The HEPcont value increases with the increase of time. The HEPcont is closely linked to two parameters. The first one is the time (1 ≤ t ≤ 8). The second one is the value of PSFs. In other words, HEPcont value increases with the time and increases with the increase of the 'danger' of the emergency scenario assumed. Table 6 shows HEPcont considering generic task 4 and different emergency levels.

From a graphic point of view, Figure 5 shows the trend of HEPcont the worst case scenario.

Table 6. HEPcont.

While Table 4 shows PSFs, defined according the three emergency conditions (see Step 1).

PSF Low hazard Moderate hazard High hazard

Available time 0.01 0.1 1 Stress 12 5 Complexity 12 5

PSFs PSF level Multipliers Available time Inadequate time HEP = 1

Stress/stressors Extreme 5

110 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

Complexity High complex 5

Time available > 5� time required 0.1 Time available > 50� time required 0.01

High 2 Nominal 1

Moderately complex 2 Nominal 1 Good 0.5

Defined PSFs and its multipliers, it is important to evaluate the overall PSF index (PSFcomp), as

PSFcomp index summarizes the weight of each influencing factor with respect to the actions/ decisions operator. Table 5 describes the values for the PSFcomp according to three emergencies

The last step consists to contextualize the probability error analysis, defined as follows (Eq. (7)):

PSFcomp = (PSF1 � PSF2 � PSF3) 0.01 0.4 25

i¼1 PSFi ð6Þ

Low hazard Moderate hazard High hazard

PSFcomp ¼ Yn

3.5. Step 5: determination PSFcomp

Table 4. PSFs for the three emergency conditions.

Table 3. Performance shaping factors.

3.6. Step 6: determination HEPcont

follows (Eq. (6)):

levels.

Table 5. PSFcomp.

Figure 5. HEPcont (high hazard).

#### 3.7. Step 7: determination HEPcontw/d

As stated, PSFs have been modelled starting from PSFs proposed by the SPAR-H methodology. It is worthy to note that the values attributable to each PSFs are proportional to the severity of their impact. However, this index does not take into account, any interdependencies among PSFs chosen. To cover this gap, a correlation among PSFs, developed by Boring [19], analysing 82 incidental reports in the US nuclear plants have been taken into account for our case study, as shown in Table 7.

Thus, HEP index is given by Eq. (8):

$$HEP\_{\text{Task1}}|\{PSF\_i; PSF\_j\} = HEP\_{\text{Task1}}|PSF\_i + \begin{pmatrix} 1 \ -k\_{\vec{\eta}} \end{pmatrix} \* HEP\_{\text{Task1}}|PSF\_j \tag{8}$$

where

Table 7. PSFs correlation developed by Boring.

• kij is the value of the parameter representative of the inter-dependent between two (or more) PSFs.

To quantify the influence of PSFs, the HEPcont w/d is calculated through Eq. (9):

$$HEP\_{\text{cont w/d}} = HETP\_{\text{nom}} \ast \left[ PSF\_{\text{i}} + (1 - k\_{\text{i}\dagger}) \ast PSF\_{\text{j}} \right] \tag{9}$$

Referring to our case study, HEPcont w/d is given by Eq. (10):

3.7. Step 7: determination HEPcontw/d

Thus, HEP index is given by Eq. (8):

as shown in Table 7.

For diagnosis Available

Stress/stressors 0.67\* 1

Available time 1

Experience/ training

For action

Experience/ training

Available time 1

Stress/stressors 0.50\* 1

Complexity 0.38\* 0.35\* 1

time

Complexity �0.02 0.15\* 1

Stress/ stressors

�0.03 0.06 0.21\* 1

0.31\* 0.21\* 0.32\* 1

Ergonomics/HMI 0.10\* 0.04 0.08\* 0.08\* 0.29\* 1

Fitness for duty 0.20\* 0.29\* 0.22\* 0.17\* 0.12\* 0.27\* 1

Work processes 0 0.13\* 0.16\* 0.20\* 0.35\* 0.12\* 0.15\* 1

Procedures 0.05 �0.01 0.12\* 0.08\* 1

Asterisk (\*) indicated significant correlations with p value <0.05.

Table 7. PSFs correlation developed by Boring.

Ergonomics/HMI 0.01 0.06 �0.05 0.20\* 0.09 1

Fitness for duty �0.03 0.03 �0.03 0.18\* 0.09 0.44\* 1

Work processes �0.06 0 0.24\* 0.55\* 0.36\* 0.15\* 0.10 1

Procedures �0.07 0.01 0.25\* 0.28\* 1

where

As stated, PSFs have been modelled starting from PSFs proposed by the SPAR-H methodology. It is worthy to note that the values attributable to each PSFs are proportional to the severity of their impact. However, this index does not take into account, any interdependencies among PSFs chosen. To cover this gap, a correlation among PSFs, developed by Boring [19], analysing 82 incidental reports in the US nuclear plants have been taken into account for our case study,

112 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

• PSFi means the value obtained by the calculation PSFcomp (with independent PSFs);

• PSFj indicates the additional PSF, which is supposed to be dependent on the previous;

Complexity Experience/ training

HEPTask1jfPSFi; PSFjg ¼ HEPTask1jPSFi þ ð1 � kijÞ � HEPTask1jPSFj ð8Þ

Procedures Ergonomics/ HMI

Fitness for duty Work processes

$$\text{HPP}\_{\text{conv}/d}(t=4) \vee \{\text{PSF}\_{\vec{\nu}} \colon \text{PSF}\_{\vec{\beta}}\} = \frac{0.0802 \ast [25 + (1 - k\_{\vec{\eta}}) \ast 3]}{0.0802 \ast [25 + (1 - k\_{\vec{\eta}}) \ast 3 - 1] + 1} \tag{10}$$

The attribution of the kij value can be assumed, considering the value of the correlation coefficients, or even based on a combination of expert judgment and data extrapolated from previous observations. The correlation between experience/training and the others PSFs is assumed moderate. In particular, a decision tree (Figure 6) is defined in order to choose the best value for kij. The final result is kij = 0.6.

Then, the value of HEPcont w/d is given by Eq. (11):

$$\left\{HEP\_{\text{conf}\_7^m}(t=4) \lor \left\{PSF\_i; PSF\_j\right\} = \frac{0.0802 \ast \left[25 + (1 - 0.6) \ast 3\right]}{0.0802 \ast \left[25 + (1 - 0.6) \ast 3 - 1\right] + 1} = 0.695\right\}\tag{11}$$

Table 8 shows the new values for PSFs and Table 9 shows the values of HEPcontw/d for the fourth generic task.

Table 8. New PSFs value.

Table 9. HEPcontw/d.

#### 3.8. Step 8: rating HEPnom after the 8th hour of work

In this step, the analysis was extended over the 8 hours of work. Figure 7 shows the reliability comprised between 0 and 16 hours of work.

For analysis after 8 hours, the only thing that changes is the k factor. For the analysis after 8 hours, we used the factor k (t = 8), while for the first 8 hours, we considered the factor k (t = 1). The remaining steps are unchanged. The use of a new factor k (t = 8) defines a raising of operator fatigue. After the 8th hour of work, there is a step on the reliability of the operator. Table 10 represents the HEPcont values for the first 16 hours of work.

#### 3.9. Step 9: determination HEPtot: discussion and results

During emergency situations, the work shifts may be longer than 8 hours of work, so the operators are subject to high stress loads. For this reason, we considered the variation of PSFs with the passage of time. To calibrate the uncertainty due to the change of time using the success likelihood index method (SLIM) [20], the worse conditions of the work of the operators, through the use of the SLIM methodology, is analysed. The operator fatigue is the first element An Experimental Study on Developing a Cognitive Model for Human Reliability Analysis http://dx.doi.org/10.5772/intechopen.69230 115

Figure 7. Reliability performance (t = 0–16).

3.8. Step 8: rating HEPnom after the 8th hour of work

Table 10 represents the HEPcont values for the first 16 hours of work.

3.9. Step 9: determination HEPtot: discussion and results

comprised between 0 and 16 hours of work.

Table 8. New PSFs value.

Table 9. HEPcontw/d.

In this step, the analysis was extended over the 8 hours of work. Figure 7 shows the reliability

PSF Low hazard Moderate hazard High hazard

Fairly simple task performed rapidly or given attention t = 1 0.0600 1.32E02 4.86E02 6.26E01

Low hazard Moderate

t = 2 0.0639 1.41E02 5.18E02 6.42E01 t = 3 0.0710 1.58E02 5.77E02 6.67E01 t = 4 0.0802 1.80E02 6.52E02 6.95E01 t = 5 0.0909 2.06E02 7.41E02 7.24E01 t = 6 0.1029 2.35E02 8.41E02 7.50E01 t = 7 0.1160 2.68E02 9.50E02 7.75E01 t = 8 0.1300 3.04E02 1.07E01 7.97E01

hazard

High hazard

Available time 0.01 0.1 1 Stress 12 5 Complexity 1 2 5 Experience/training 0.5 1 3

114 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

Generic task HEPnom (t) HEPcont w/d

For analysis after 8 hours, the only thing that changes is the k factor. For the analysis after 8 hours, we used the factor k (t = 8), while for the first 8 hours, we considered the factor k (t = 1). The remaining steps are unchanged. The use of a new factor k (t = 8) defines a raising of operator fatigue. After the 8th hour of work, there is a step on the reliability of the operator.

During emergency situations, the work shifts may be longer than 8 hours of work, so the operators are subject to high stress loads. For this reason, we considered the variation of PSFs with the passage of time. To calibrate the uncertainty due to the change of time using the success likelihood index method (SLIM) [20], the worse conditions of the work of the operators, through the use of the SLIM methodology, is analysed. The operator fatigue is the first element to consider. Fatigue is quantified using the standard sleepiness scale (SSS) [21]. The scale is represented in Table 11. The result is a score related to drowsiness.

The next step is to define the incidence of each PSFs relative to fatigue (W). The values are reported in percentage scale. The sum of the weights must give 100%. At this point, it calculates the modified SLI index using Eq. (12):

$$SLI\_{\bar{\jmath}} = \sum\_{i} R\_{\bar{\jmath}} \mathcal{W}\_{i} \tag{12}$$

Table 12 shows the SLI index calculation for generic task 4, considering the presented PSFs.

The SLI index must be transformed into HEP. It is assumed that between SLI and HEP exist the relation as follows (Eq. (13)):

$$
\log(P) = aSLI + b \tag{13}
$$

where P represents the HEP value and a and b are constants. At this point it is necessary to calibrate the value of the constants to obtain the value of HEP. To do this, a comparative comparison between the values of SLI is carried out. In the previous step, HEP index values for 1 < t < 16 have been obtained. In this step, the extreme values of that range are used, as follows:

Table 11. Stanford sleepiness scale.

Fairly simple task performed rapidly or given attention (t = 10) ∑ 4.

Table 12. SLI for the GTT 4.

Using the inverse formula, the final equation that calculates the HEP index for each task is obtained. The formula is defined according to Eq. (14):

$$
\log(HEP) = aSLI + b \tag{14}
$$

Here is a mathematical formulation that allows to define a and b:

to consider. Fatigue is quantified using the standard sleepiness scale (SSS) [21]. The scale is

The next step is to define the incidence of each PSFs relative to fatigue (W). The values are reported in percentage scale. The sum of the weights must give 100%. At this point, it calcu-

i

RijWi ð12Þ

logðPÞ ¼ aSLI þ b ð13Þ

SLIj ¼ X

Table 12 shows the SLI index calculation for generic task 4, considering the presented PSFs.

The SLI index must be transformed into HEP. It is assumed that between SLI and HEP exist the

where P represents the HEP value and a and b are constants. At this point it is necessary to calibrate the value of the constants to obtain the value of HEP. To do this, a comparative comparison between the values of SLI is carried out. In the previous step, HEP index values for 1 < t < 16 have been obtained. In this step, the extreme values of that range are used, as follows:

Degree of sleepiness Scale rating (R)

Weighting (Wk) PSFs Rating (Rk) SLI = W∙R

0.2 Available time 4 0.8 0.5 Stress 4 2 0.3 Complexity 4 1.2

Feeling active, vital, alert, or wide awake 1 Functioning at high levels, but not at peak; able to concentrate 2 Awake, but relaxed; responsive but not fully alert 3 Somewhat foggy, let down 4 Foggy; losing interest in remaining awake; slowed down 5 Sleepy, woozy, fighting sleep; prefer to lie down 6 No longer fighting sleep, sleep onset soon; having dream-like thoughts 7

represented in Table 11. The result is a score related to drowsiness.

116 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

lates the modified SLI index using Eq. (12):

• HEPmin = 6,38E�04 ➔ t = 1 (low hazard) SLI = 1 • HEPmax = 9,21E�01 ➔ t = 16 (high hazard) SLI = 7

Fairly simple task performed rapidly or given attention (t = 10) ∑ 4.

relation as follows (Eq. (13)):

Table 11. Stanford sleepiness scale.

Table 12. SLI for the GTT 4.

$$\begin{cases} \log\_{10}(0.000638) = aSLI + b \\ \log\_{10}(0.921) = aSLI + b \end{cases} \begin{cases} -3.19 = a + b \\ -0.035 = a \ast 7 + b \end{cases} \begin{cases} b = -3.19 - a \\ 7a = -0.035 - b \end{cases}$$

$$\begin{cases} b = -3.19 - a \\ 7a = -0.035 + 3.19 + a \end{cases} \begin{cases} b = -3.19 - a \\ 6a = -0.035 + 3.19 \begin{cases} a = 0.52 \\ b = -3.71 \end{cases} \end{cases} \tag{15}$$

Having obtained the values a and b, the formulation for the final calculation of the index HEP becomes:

$$\begin{aligned} \log(HEP) &= 0.52 \text{SLI} - 3.71, \text{ SLI} = 4\\ \log(HEP) &= -1.63 \to HEP = 0.023 \end{aligned} \tag{16}$$

It is possible to note that the value of HEP is lower compared to the previous HEP calculated for t ranging from 1 to 16. In order to obtain a more accurate model a calibration is carried out. Figure 8 compares the HEPnom curve with the calibrated HEP curve.

HEPtot value is calculated by adding up the values HEPnom that the HEP values calculated with SLI calibration (ΔHEP). HEPtot value replaces the model EHEA the HEPnom value, as shown in Table 13.

Figure 9 shows the graph of the HEPtot. It assumes to model the increase of the HEPnom nominal value, to which are summed the corresponding ΔHEP values, starting from t = 8.

The main result of the model shows how the human reliability depends on the time and how it is important to consider operator performance beyond the canonical 8 hours.

Figure 8. HEPnom—calibrated HEP (SLI).

Table 13. HEPtot.

Figure 9. HEPnom—HEPtot.

#### 4. Conclusion

EHEA SLIM

118 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

Table 13. HEPtot.

Figure 9. HEPnom—HEPtot.

HEPnom Log10 (HEP nom) ΔHEP Log10 (HEP nom) SLI HEPtot 0.060 1.221 0.0585 1.232 1 0.118 0.063 1.194 0.0585 1.232 1 0.122 0.071 1.148 0.0585 1.232 1 0.129 0.080 1.095 0.0663 1.178 2 0.146 0.090 1.041 0.0663 1.178 2 0.157 0.102 0.987 0.0663 1.178 2 0.169 0.116 0.935 0.0751 1.124 3 0.191 0.130 0.886 0.0751 1.124 3 0.205 0.208 0.680 0.0751 1.124 3 0.283 0.222 0.652 0.0851 1.069 4 0.307 0.237 0.623 0.0851 1.069 4 0.322 0.253 0.596 0.0964 1.015 5 0.349 0.268 0.570 0.0964 1.015 5 0.365 0.284 0.545 0.1093 0.961 6 0.394 0.301 0.521 0.1093 0.961 6 0.410 0.317 0.498 0.1239 0.906 7 0.441

In general, the modelling approaches used in HRA are focused to describe sequential low-level tasks, which are not the main source of systemic errors. On the contrary, we believe that it is important to analyse in deeper human behaviour that causes errors in order to develop managerial practices that could be applied to reduce the failures that occur at the interface of human behaviour and technology. Thus, the aim of this work was to develop an innovative methodology for human reliability analysis in emergency scenarios. A hybrid model that integrates the advantages of the following methodologies: human error assessment and reduction technique (HEART), standardized plant analysis risk-human reliability analysis (SPAR-H) and Success Likelihood Index Method (SLIM) has been proposed. The key point that we have been trying to convey in this research is the analysis of all environmental and behavioural factors that influence human reliability. Results obtained from the analysis of a real case study give an empirical contribution and a theoretical contribution referring to the framework used to detect human error in risk and reliability analysis. Furthermore, the study could be a useful perspective for the entire academic community to make the community fully aware of new assumptions in human reliability analysis.

#### Acknowledgements

This research represents a result of research activity carried out with the financial support of MiuR, namely PRIN 2012 "DIEM-SSP, Disasters and Emergencies Management for Safety and Security in industrial Plants".

#### Author details

Domenico Falcone1 , Fabio De Felice1 , Antonella Petrillo2 \* and Alessandro Silvestri1

\*Address all correspondence to<EMAIL_ADDRESS>
1 University of Cassino and Southern Lazio Department of Civil and Mechanical Engineering, Cassino (FR), Italy

2 University of Napoli "Parthenope" Centro Direzionale, Napoli (NA), Italy

#### References

[1] Dhillon BS. Human Reliability, Error, and Human Factors in Power Generation. New York: Springer; 2014

[2] Jung, Won Dea; Kang, Dae Il; Kim, Jae Whan, 2005. Development of A Standard Method for Human Reliability Analysis of Nuclear Power Plants: Report of Korea Atomic Energy

[3] Hollnagel E. Cognitive Reliability and Error Analysis Method (CREAM). Amsterdam,

[4] De Felice F, Petrillo A, Zomparelli F. A hybrid model for human error probability analy-

[5] Massaiu, S., 2012. A model-based approach for the collection of Human Reliability data. Advances in Safety, Reliability and Risk Management - Proceedings of the European Safety and Reliability Conference, ESREL 2011, Troyes France 18–22 September 2011, pp.

[6] Liu, Z., Chen, L., Ren, D., 2009. Prediction analysis of human error probability for mine hoisting systems. IE and EM 2009 - Proceedings 2009 IEEE 16th International Conference on Industrial Engineering and Engineering Management, Beijing, China 21 Oct – 23 Oct

[7] Cheng C-M, Hwang S-L. Applications of integrated human error identification techniques on the chemical cylinder change task. Applied Ergonomics. 2015;47:274–284 [8] De Felice F, Falcone D, Petrillo A, Bruzzone A, Longo F. A simulation model of human decision making in emergency conditions. 28th European Modeling and Simulation

[9] Thiruvengadachari S, Khasawneh MT, Bowling SR, Jiang X. Human-machine systems reliability: In: Current Status and Research Perspective. IIE Annual Conference and

[10] Park J, Lee D, Jung W, Kim J. An experimental investigation on relationship between PSFs and operator performances in the digital main control room. Annals of Nuclear Energy.

[11] Kim JW, Jung WD. A taxonomy of performance influencing factors for human reliability analysis of emergency tasks. Journal of Loss Prevention in the Process Industries. 2003;16

[12] Rasmussen J. Outlines of a hybrid model of the process operator. In: Sheridan TB, Johannsen G, editors. Monitoring Behaviour and Supervisory Control. New York: Plenum

[13] van der Schaaf TW, Kanse L. Biases in incident reporting databases: An empirical study

[14] Di Pasquale V, Miranda S, Iannone R, Riemma S. A simulator for human error probability

analysis (SHERPA). Reliability Engineering & System Safety. 2015;139:17–32

in the chemical process industry. Safety Science. 2004;42:57–67

Research Institute, code KAERI/TR–2961/2005; (37)50. Republic of Korea

120 Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

Netherlands: Elsevier; 1998

595–603

2009, pp. 1184–1188.

Exposition; 2005

2017;101:58–68

(6):479–495

Press; 1976

sis. IFAC-PapersOnLine. 2016;49(12):1673–1678

Symposium, EMSS 2016; 2016: pp. 148–154

### *Edited by Fabio De Felice and Antonella Petrillo*

Risk management is an interdisciplinary discipline that involves several aspects. It is absolutely necessary to make sure we manage risks in order to minimize their threats and maximize their potential. This book tries to investigate the complexity that characterizes risk management. It contains original research and application chapters from different perspectives and covers different areas such as human aspects, emergency management, cognitive factors, software engineering, and marketing. The idea of the book is to expand the reader's consciousness to deal with problems regarding risk management.

Photo by valdezrl / iStock

Theory and Application on Cognitive Factors and Risk Management - New Trends and Procedures

Theory and Application on

Cognitive Factors

and Risk Management

New Trends and Procedures

*Edited by Fabio De Felice and Antonella Petrillo*


4. Final considerations

for about 50% of all topics, and then diagnosis is still present, showing little differ-

Eventually, a study of the topics and their prevalence over years was performed to see the trend of interest. A significant trend in publications could not be evinced, neither overall nor for single continent. Publication numbers by year underwent cyclic changes over the last 20 years with a peak in 2008 including 16 publications

A natural comment to the number of publication is the fact that pediatric articles, focusing on pure research, account for <1 third of overall articles about varicocele. This could be due to the fact that historically varicocele is considered as an adult pathology; thus not enough interest is found in its pediatric side. Different series of studies report a higher prevalence of varicocele in adult population than in pediatric one. However it must be taken into account the lack, in almost all countries, of pediatric screening programs for varicocele that could give a strong bias about the exact prevalence of the pathology in pediatric population. Moreover the study of varicocele related to infertility is considered more imminent in adult life, when looking for paternity that during adolescence when study of future fertility may seem premature. In fact many studies on varicocele are performed retrospectively when

ence between main topic and all mentioned topics in the publications.

the patient in adult life has not the possibility to become father (see table).

rather a different contribution to publications.

varicocele.

64

language [10–17].

nents, the first interest of research is surgical technique, may it be traditional surgery or videolaparoscopy technique. We can also see that in the first three majorly represented topics and figures either screening or diagnosis this reflects an attention of research to detection and treatment rather than to follow-up or prevention of infertility. Other topics were only minimally represented. It must be stated that healthcare organization of each single country may influence the topics and publications: in fact screening would not be so represented in countries with private healthcare or, on the other hand, countries with increased population density would feel less important the problem of infertility. The prevalence of varicocele according to the literature remains constant in different ethnic groups; thus, differences in publication do not reflect a difference of entity of the disease but

Concerning the major topics of the publications, in the most represented conti-

In South America the research group for the published articles is the same, and

The three most prevalent topics in North America and Asia underline an attention to study the evolution of the pathology in time even after treatment and to evaluate if the outcomes of surgical treatment meet the standards for good practice. Articles discussing endocrinology often evaluate testicular volume at diagnosis and follow catch-up growth after surgery, trying to give an indication of the best timing to prevent infertility. On the other side, the spectrum of topics in Europe reflects

Of particular interest is that there is no increasing trend during the years despite

the works represent mainly an evolution of the same study focusing on semen analysis, metabolomics, infertility pathophysiology, and endocrinology.

poor attention to prevention of infertility and follow-up after surgery.

an increase in the trend of publications about overall causes of infertility and medically assisted procreation. In fact in delivering a PubMed research, it appears that publications about MAP are more than 30 times higher than those about

We must report the fact that Asia appears abundantly below average, but a strong bias is given that the fact that many publications from China were in original

The same applies to the correlation between undescended testes and infertility if compared to the studies on cryptorchidism alone. Both associations between infertility and disease show a progressive percentage increase in the total number of studies.

about pediatric varicocele.

Male Reproductive Health

This research is intended as a warning to the countries worldwide: when talking about fertility, it is right to give a couple the chance to access medically assisted procreation; consequently, scientific studies to improve its outcomes are reasonable. International reports are therefore necessary and should foster research with increasing outcomes. More space should also be given to investigate and prevent male fertility diseases starting from the pediatric age, especially when they might impair the patient's future fertile potential [18].

All those involved in the pediatric treatment area should be stimulated to act toward this goal, and each country should bear the responsibility of promoting and financing andrological screening campaigns. At the international level, there are still few opportunities, in terms of funds and staff, for the adolescents to receive andrological counseling. This is then the bottom line: Is medically assisted procreation the cure to one or more diseases, or is it the answer to the lack of a social support network?

When talking about couple infertility, male causes account for about 35–40%, among these, varicocele figures as the first [19].

Thus collective interest, research efforts, and healthcare funding aim to study couple infertility at the time of inability of procreation, correction of varicocele in adult age, and medically assisted procreation. This choice is taken despite the increased risk of chronic irreversible damage of treating varicocele and other pediatric andrological diseases in adult age and despite the costs and risks of MAP with the additional risk of failure of medically assisted procreation.

In conclusion, the research effort and the capital invested in prevention of infertility are not balanced with respect to efforts and investments relied into medical assisted procreation.

### Conflict of interest

The authors declare no conflict of interest.

### Acronyms and abbreviations

ART Assisted reproductive technology

Male Reproductive Health


**1. Introduction**

Reproductive strategies widely affect the species distribution of vascular plants, bryophytes, and lichens. A tradeoff between dispersion and establishment abilities is the key to the success of most of the species of plants. Relying on different dispersal vectors such as wind, water, or animals, vascular plants have evolved a broad range of dispersal modes or strategies [1,2], using generative (such as spores, seeds, or fruits) and vegetative (such as fragments of stems, stolons, rhizomes, or bulbils) diaspores [3].

Lichens are symbiotic organisms in which fungi and algae and/or cyanobacteria form an intimate biological union [4] and both partners must be present for their successful reproduction and dispersal [5]. Lichen propagules (diaspores) contain cells from both partners and represent an essential evolutive solution to this problem [6]. This vegetative

**Citation:** Brunialti, G.; Giordani, P.; Ravera, S.; Frati, L. The Reproductive Strategy as an Important Trait for the Distribution of Lower-Trunk Epiphytic Lichens in Old-Growth vs. Non-Old Growth Forests. *Forests* **2021**, *12*, 27. https://doi.org/10.3390/f12 010027

Received: 11 November 2020 Accepted: 24 December 2020 Published: 28 December 2020

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).

reproduction grants a reasonable survival rate and success for the establishment of new lichen thalli [7]. Still, it is characterized by a low dispersal ability [8]. Some authors have shown that diaspores usually have a dispersal range of about 10–100 m for *Lobaria pulmonaria* [9–12], and up to 30 m for *Evernia prunastri*, *Ramalina farinacea* [13], and *Hypogymnia physodes* [14].

Sexual reproduction in lichens only involves the mycobiont partner, through spore production and propagation. To germinate and give rise to a new individual, the spore must find a compatible photosynthetic partner on a suitable substrate to colonize [4]. Sexual spores are generally smaller than vegetative structures and they are also actively discharged (except those of *Caliciales*), so they are likely to be dispersed over longer distances [6]. Further, this propagation form allows the genetic turnover of the populations, which is extremely important for adaptation to environmental changes [15]. For example, even in the hostile environments of Antarctica, Seymour et al. [6] reported that many lichens produced sexual structures, often in abundance.

In forest ecosystems, the distribution of lichen species is driven both by landscape and stand-level factors [16–19]. In this paper we focus on these latter aspects. In particular, the structural characteristics of the stand (e.g., basal area, tree height) and the availability of tree substrates suitable for lichen colonization (e.g., old trees) and of micro-habitats can be the main limiting factors conditioning the most appropriate reproductive strategies to obtain better species dispersal abilities [16–19].

So far, most studies have focused on the effect of reproductive strategies on the dispersal ability and distribution of species assemblages (see e.g., [18]) or on single forestdwelling species (see e.g., the studies on the umbrella and flagship species *Lobaria pulmonaria*; [11,12,19]). Only a few papers have explored this issue in terms of beta diversity and species turnover [20]. Furthermore, no previous study, to our knowledge, has addressed the topic comparing what happens to lichen communities in old-growth (hereafter OG) and non-old growth (NOG) forests, especially in Mediterranean oak and beech forests.

In the present study, we assess the hypothesis that the dispersal abilities for to the different reproductive strategies drive the species turnover and nestedness (beta diversity) depending on forest age and continuity. To address this question, we used the data from a study on epiphytic lichen diversity carried out in OG and NOG forest stands in a national park in Southern Italy [21,22].

The details of the study hypothesis are illustrated in Figure 1, where possible patterns of species dispersion with different reproductive strategies in OG and NOG forests are reported. We expect sexually reproducing species to be characterized by a high turnover regardless of forest type (Figure 1b,d). This hypothesis is based on the observation that spores have a potentially very high spatial range of dispersion, but, at the same time, they may encounter more difficulties than vegetative species in the formation and establishment of new thalli. These biological characteristics would lead to strong discontinuities (turnover) in the floristic compositions of the various sites. On the other hand, we hypothesize that the beta diversity of vegetative species is mainly determined by a high nestedness between sites of the same forest types and that this pattern is more evident in OG forests than in NOG ones (Figure 1a,c). This assumption is based on the fact that vegetative species are particularly favored in the colonization of contiguous sites which would tend to host a similar set of species, especially in conditions of ecological continuity such as those found in OG forests.

Additionally, we also considered the relationship between forest continuity and lichen beta diversity in terms of species rarity. Since diversity may be influenced by dispersal ability, we expect that rare species spread more easily in OG forests.

**Figure 1.** Schematic representation of the hypotheses tested in the study on the beta diversity patterns of lichen species with contrasting reproductive strategies in old-growth (OG) and non-old growth (NOG) forests. The squares represent the areas with different types of forest. We report the possible dispersion flows (arrows) of the different species (colors) between sites (circles) that determine the colonization and are the basis of the potential compositional differences: (**a**) vegetative species in OG forests; (**b**) sexual species in OG forests; (**c**) vegetative species in NOG forests; (**d**) sexual species in NOG forests.