THE APPLICABILITY OF METHODS AND TOOLS ...

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THE APPLICABILITY OF METHODS AND TOOLS FOR ASSESSING THE CRITICALITY OF ELEMENTS OF THE ROAD INFRASTRUCTURE Jana Pupíková, Petr Rostek Abstract Today, the criticality of infrastructure elements is a frequently discussed topic, both in the security community in the Czech Republic as well as in many countries of the European Union. This article addresses the applicability of traditional methods and tools used in the risk management and specific methods and tools recommended for assessing the criticality of elements of road infrastructure. This article presents the results of the assessment of criticality as an essential property of an infrastructure element with the intent to analyze and with the use of established criteria select appropriate methods used to assess the criticality of road infrastructure. Keywords: critical infrastructure, road infrastructure, criticality of infrastructure elements, methods and tools

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INTRODUCTION

Transport infrastructure or, more precisely, road transport infrastructure is a pillar of modern society, aimed to satisfy the customers’ needs for quality, ready, rapid and safe transportation of people, goods and services. In a complex perspective, it is necessary to take the transportation (e.g. road infrastructure) and services in the territorial unit as an integrated logistics system, which includes both freight and passenger transportation. Road infrastructure (road network) consists of hubs (or “elements”) and individual connections between them. Each such element has its own importance/role or function in the assessed system (in this the road network). To express the vitality and necessity of an infrastructure element we use the term criticality. [12] According to the glossary for the SERON project (Security of Road Transport Networks) [7], criticality is defined as the quality, condition, or degree of being of the highest significance (importance), which may relate to expected economic and social impacts. The German Federal Office of Civil Protection and Disaster Relief and the Federal Office for Security in Information Technology [5] define criticality as a relative measure of the importance of infrastructure resulting from the effects of failures and interruptions of functions in the security of supplying the society with important goods and services. The ACIS method [1] defines the criticality of infrastructure as a result of the relationship between the probability and consequence (result) of an infrastructure malfunction. Criticality as a property of the infrastructure represents a potential condition of a territorial system (or the individual protected interest in it) during infrastructure outage and the influence of the outage on other infrastructures and other protected interests of the state. Criticality of an infrastructure element is expressed in a graded assessment (expression of the degree/level). Criticality defines failure or malfunctions of a particular infrastructure element in the context of a larger system and examines in particular the influences causing the severity of the impact of the outage on society, including through dependent (other) infrastructures. Criticality is linked to vulnerability. The concept of vulnerability isn’t precisely defined anywhere, but generally we can say that vulnerability is a property of the system or its components, which may weaken or limit

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the system's ability to provide the expected functionality or service in case the system is exposed to threats (incidents). [12] If we look at the concept of vulnerability in the infrastructure, or its elements or system of elements, we can speak of a set of characteristics, which may reduce or limit the ability of assessed elements of the infrastructure to meet the required functions and services due to the negative impact of adverse effects.

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PROCEDURAL STEPS OF CRITICALITY ASSESSMENT

Tasks and activities in the assessment of criticality are divided into several phases and are represented by identifying, analyzing and evaluating the criticality of an infrastructure element. 2.1 Phase 1 – Identifying the elements The first phase consists of identifying elements of the infrastructure within which the element is assessed. To assess the severity of the impact, vulnerability of the selected elements and the selection of appropriate criteria, the division of infrastructures to network infrastructures and infrastructures composed mainly of stationary elements is crucial. Then follows the identification of elements. The identification of elements is a process of creating an inventory of elements of the given system (infrastructure), under which the properties and functions of individual elements are described. [12] 2.2 Phase 2 – Analyzing criticality Criticality analysis is used to obtain input data for the evaluation of criticality. The criticality analysis takes into account the vulnerability of the elements and their importance within the infrastructure, system, sectors of society. The first procedural step of this phase is to analyze the importance of the identified elements. The importance of an infrastructure element characterizes its significance/irreplaceability for the territory, society, economy, for the system as a whole. [12] The importance of infrastructure element can be represented in several ways. In the event that the element is vital for the system under assessment, we talk about systemic importance. Systemic importance is gained especially by those infrastructure elements that due to their structural, functional and technical positions throughout the system are unique in that they are almost indispensable or their replacement would be very difficult. If the element is important due to the interdependencies between other sectors/industries of infrastructure, we are talking about the industrial or sectorial importance. If the element is important for the society, we can simply say that it has a societal importance. The next procedural step of this phase is the analysis of vulnerability of the identified elements in which the value of society vulnerability due to an outage or malfunctioning of an element is determined. The final step of this phase is to determine the extent or estimate the criticality of an infrastructure element from the analysis of vulnerability and the importance of the infrastructure element. 2.3 Phase 3 – Evaluating criticality The last phase in the process of assessing the criticality of an infrastructure element is the evaluation of criticality. The purpose of the evaluation of criticality is prioritizing an infrastructure element for which criticality must be coped with as a priority, such as elements that are necessary to reduce vulnerability and significance to the socially acceptable level.

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3

METHODS AND TOOLS FOR CRITICALITY ASSESSMENT

The aim of this chapter is to describe and assess the applicability of methods and tools generally used in risk management (traditional methods and tools) and the methods and tools used and often recommended by [11], [13], in assessing the criticality (specific methods and tools). 3.1 Traditional methods and tools In practice, risk management uses a large number of methods in different varieties, but most of these are based on just a few of the best known and most widely recognized methods from which they are not fundamentally different. Below mentioned methods have different uses depending on the size and complexity of the process, offering all sorts of results, characterized by different time requirements and costs, and requirements for staff. Index methods (Relative Ranking - RR) These methods are used for rapid process safety assessment through the use of indexes. This method is a qualitative approach to classification and comparison of critical system elements. These comparisons are based on numerical comparisons that represent the relative level of importance of each critical element in the process. [2] The advantage of these methods is that indexes can provide a good tool for the classification of critical points of the process (system). They are also useful in cases where the default system is not well known or cannot be presented. The disadvantage of these methods is that if the system is not well validated, the results may be insignificant. Moreover, these methods are unsuitable for network infrastructures and the assessment of a large number of elements generally. It is therefore appropriate to complement such a method with e.g. the network analysis method. The time required depends on the size and complexity of the system. What - If Analysis (WI) This method uses brainstorming to search for possible impacts of selected incidents or operational situations. The analysis is performed in working discussions, when all recorded questions are divided into different areas and the team is looking for answers to these questions together. [6] This analysis is a useful tool to stimulate participants to identify the important infrastructure elements. The advantage of this method is that it is relatively low time-consuming. The analysis provides a detailed understanding of the nature of the problem and the factors that increase the criticality of the system. However, the analysis requires a high level of knowledge of the system and the availability of quality information and data that are often not available. Failure Modes and Effects Analysis (FMEA) This analysis is used to identify the failure modes of components, systems or processes compared to their design intent. This method identifies possible failure modes of various parts of the system, the consequences of these failures for the system, failure mechanisms and ways to prevent these failures or mitigate their consequences.[3] This analysis is widely applicable to devices and systems, including the failure modes of human activity. It identifies the essential elements of the system, the causes of their failures and their consequences for the system. FMEA may be easily updated after the changes in the project or system. For the analysis of the importance of system elements and their possible failure modes,

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however, detailed information on these elements is required. When analyzing a larger number of system elements, the study is time-consuming and costly. The analysis often requires the application of computer technology, special computer program and demanding database.[11] Fault Tree Analysis (FTA) The FTA analysis is a graphical-analytical method based on a systematic reverse analysis of the undesirable top event (e.g. failure of infrastructure). The top event and its causal factors are illustrated in the tree diagram.[11] The fault tree can be performed qualitatively in order to identify the potentially critical points of the system or quantitatively, in order to calculate their probability and consequently the probability of a top event occurrence.[3] The FTA analysis is useful in identifying important elements of the system, also in system analysis with many interfaces and interconnected interactions. However, the method is not used to evaluate the impact of the top event (e.g. impacts on society, or impact on other sectors). The method is used to find the probably weakest point of the system, but that does not mean that it identifies the most vulnerable point. The method is also time-consuming and the time demands increase depending on the complexity of the system. The complexity of the system may require computer systems for processing fault trees. The fault tree is only a static model, where the focus is not placed on the mutual time dependence. Event Tree Analysis (ETA) The ETA method is a graphical-statistical method used for the presentation of undesirable events (outcomes) that occurred after the top event (e.g. failure of infrastructure).[2] Like the FTA method, ETA uses an event tree diagram. The ETA method, however, does not address the causes of the top event, but considers the further development of the top event and thus provides an overview of the likely level of possible consequence probability. The method allows us to represent sequences of events that cannot be displayed when using the fault tree; it explains the timing, dependence and domino effects that are too cumbersome to be modeled by the fault tree.[3] Using this method, however, requires knowledge of the possible top events and of the activities of security systems and emergency procedures to mitigate impacts. The method is not suitable for complex branched systems, due to its time-consuming nature. The method also does not reflect the society's sensitivity to the effects of the given threat. Cause – Consequence Analysis (CCA) Analysis of causes and consequences is a combination of the fault tree analysis and the event tree analysis. It is used as a communication tool, as the diagram shows the relationship between the consequences of failures and their root causes.[2] Using the critical incident consequences are analyzed using a combination of logic gates YES/NO showing faults of systems designed to mitigate the effects of the top event. The method is used to analyze the various directions in which the system can go in case that a critical event has occurred. The method can be considered dynamic, as it allows for analyzing the events that evolve over time. The limitation of this analysis is its complexity. It also requires a high level of expertise on the system behavior and critical elements in the system that can cause undesirable events, and knowledge in the area of security systems and emergency procedures. The method also does not deal with the vulnerability of society in terms of the effects of the given threats.

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3.2 Specific methods and tools Specific methods and tools in this article mean methods and tools that are already in use or are recommended to assess the criticality of an infrastructure element. To assess the criticality of a road infrastructure element by [11], [13], methods based on a multi-criteria evaluation and methods based on graph theory are often recommended. Methods for multi-criteria evaluation Multi-criteria evaluation is a suitable method for assessing criticality. This is a method for structuring problems, in which the individual variants are assessed by determining the weights of the individual evaluation criteria.[11] Multi-criteria evaluation is useful for elements that do not form a network, or stationary elements interconnected with other types of infrastructure (e.g. transport ↔ communication and information systems). Among the multi-criteria evaluation methods are e.g. the FMECA method and criticality matrix. Failure Modes, Effects and Criticality Analysis (FMECA) The FMECA analysis is an extension of the FMEA analysis. In this method, each identified failure is classified according to its criticality. In the context of transport infrastructure, this method is recommended for assessing criticality of system elements.[4] Evaluation of criticality is based on a risk model. FMECA performs a classification of each identified failure mode of the given element according to its criticality by determining the criticality index of failure mode. As with the FMEA analysis, the detailed information about these elements is necessary. The analysis can provide a quantitative output, when suitable data on failure intensities are used, and quantitative effects. The disadvantage is its time-consuming and costly nature, especially for complex branched systems. Another disadvantage is that the method does not deal with the sensitivity of the system to undesirable effects of a threat. Criticality Matrix Criticality Matrix is a tool for classifying and displaying criticality of an infrastructure element that uses several differently designed criticality matrices [10]. The advantage is that the matrix is relatively easy to use. It provides rapid classification of infrastructure elements at various levels of significance. Criticality is understood as a function of vulnerability and importance of the system. The disadvantage is that the matrix is designed for a specific problem (factor), and it is difficult to apply it generally to the entire system. This method is very subjective and it is difficult to clearly define the classification scale. Network analyses Network analyses are methods aiming at the identification of critical activities. They are also used to assess the criticality of infrastructure elements. These methods can be used in the evaluation and planning of complex successive operations or time monitoring of interactions and relationships. The model for problem solving here is oriented network graph with time evaluated edges. The methods of network analysis method include for example the CPM method, or its modification PERT and the method of Petri nets. CPM (Critical Path Method) CPM is the basic deterministic critical path method. It is based on graph theory. Its aim is to determine the duration of the project based on the length of the so-called critical path, which is a

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sequence of interdependent activities with the least slack time.[12] By using the critical path method we obtain a tool which can reveal the interactions and connections in the system under consideration. We can also reveal weaknesses in the system. Application of CPM is suitable for solving the problems associated with the identification of critical elements, critical networks, critical activities, critical technologies and critical infrastructures. This method can accurately estimate the length of all activities that constitute the project. However, it does not take into account the possibility of change of these time characteristics. This method also does not include all the factors affecting the system criticality of the elements. It also implies the need to complement the estimated values of the criticality with the connections between infrastructure elements. PERT (Program Evaluation and Review Technique) PERT is a generalization of the CPM critical path method. This method is used to control complex events of a stochastic nature.[12] The purpose of this method is again searching for the critical path. Here, the duration of each sub-activity is understood as a random variable having a probability distribution. Like the CPM method, the advantage of the PERT method lies in solving problems associated with the identification of critical elements and networks, critical activities, critical technologies and critical infrastructures. Compared to the CPM method, this method is more dynamic – the difference is to determine the probability for the critical path – it better reflects the common reality. As with the CPM method it is necessary to supplement the estimated values of the importance with the connections between the infrastructure elements. Petri Net Method Petri net [8] is a universal graphical and mathematical tool for describing the logical interactions and dynamics of complex systems. The method is sufficiently general and applicable to the description of a large number of different systems. It enables to describe management activities and dependencies within the system. A condition of using this method is a preliminary analysis of the examined problem with the layout of nodes and activities together with assessment or estimate of the duration of these activities. Practical application of Petri nets is hampered by a significant limitation which is the static nature of the network structure and its flatness. This means that the positive properties of Petri nets appear with full effect only in very large models. If we need to model more details, the model necessarily becomes more complex and less clear and the application of Petri nets here would be very problematic and time-consuming. Methods to evaluate the criticality of an infrastructure element The methods used to assess the criticality of an infrastructure element, and therefore its classification into a specialized system of protection, includes the ACIS method and a method for creating an inventory of critical infrastructure protection. ACIS Method (Analysis of Critical Infrastructures) A tool to obtain a quick evaluation of the various infrastructure sectors is the ACIS method [1], used in Germany. This method creates the overview of various infrastructure sectors that are further divided. For individual industries or services it is necessary to identify and define the operational processes. They will then become subject to the assessment of criticality. Only the processes that have significance in terms of criticality are assessed. The resulting tool for assessing the level of criticality is the criticality matrix in which the criticality is expressed by the relation between the probability and impact of malfunction on the infrastructure functioning.

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The advantage of this method is the awareness of critical elements, or infrastructure objects in their process from production to consumption. However, the ACIS method does not consider how the undesirable phenomenon affects the element or object of infrastructure, therefore it is not possible to accurately determine or estimate the probability or frequency. To determine the probability of an infrastructure element outage it is necessary to use other methods, such as expert estimation method which reduces the accuracy of the result. Method for making an inventory of critical infrastructure protection (Methode zur Erstellung des SKI - Inventars) This method [9], used mainly in Switzerland, aims to mark objects of infrastructure with a high level of criticality. Among others, this method identifies objects/elements that are critical on national or regional level. National critical infrastructure elements are analyzed with respect to various critical components, probability, risks and vulnerability. Criticality of objects relate to consequences that may arise from the outage, malfunction or destruction of an infrastructure element. Criticality is determined using standardized criteria, which can be used for determining the possible extent of damage of the elements in all critical sectors or their sub-sectors. The advantage of this method is the interconnectedness of the individual steps in assessing the criticality of infrastructure objects as well as that criticality of an infrastructure element is assessed on the basis of the size of the impact on society. A major drawback of this method is that the criteria needed to assess the degree of criticality do not bear weight value, making it difficult to prioritize infrastructure elements in detail.

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EVALUATION OF APPLICATION OF METHODS AND TOOLS FOR ASSESSMENT OF CRITICALITY OF A ROAD INFRASTRUCTURE ELEMENT

An important component of deciding which method is best (most applicable) to assess the criticality of a road infrastructure elements, is the evaluation process, under which the value of the researched entity is determined according to the value scale. 4.1 Comparison of methods and tools for assessing criticality of a road infrastructure element The classification shows how the methods and tools are applicable with regard to criticality of the elements of road infrastructure in the following steps (in the stages set out in Chapter 2): identification of the elements; criticality analysis – systemic importance; sectorial importance; societal importance; relevancy ranking; vulnerability analysis; vulnerability assessment; evaluation of criticality. These methods are compared using a multi-criteria evaluation according to the following criteria:   

Implementation simplicity – simplicity of implementation in this article means less time and financial costs of the method to perform valuable analyses and studies. Method complexity – the method should allow for an overall view of criticality in the individual stages of the evaluation of infrastructure elements criticality. Result relevancy – relevancy of results determines the significance, importance (or compliance) of results when compared to the desired result or goal.

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 

Applicability – the condition of this criterion is that the methods must be applicable in the context of network infrastructures with regard to criticality. No expert knowledge required – to perform analyses with informative value, some methods place high demands on the work team, which also increases their cost. Therefore in the method evaluation, methods not requiring expert knowledge will be preferred.

Each of the criteria is then evaluated by the corresponding weight so that the criteria that have considerable importance in terms of assessing the criticality of the elements of road infrastructure, more significantly influence the final evaluation of methods. The sum of weights of all criteria must equal 1. Weights of the individual criteria are summarized in Table 1. Table 1: Evaluation criteria with corresponding weights Criterion name Criterion weight Implementation simplicity [S] 0,15 Method complexity [C] 0,25 Result relevancy [R] 0,3 Applicability [A] 0,2 No expert knowledge required [K] 0,1

Criterion weight abbr. [v S ] [v C ] [v R ] [v A ] [v K ]

Table 2 shows the scale of qualitative evaluation with the appropriate conversion to a semiquantitative evaluation. The criteria are rated on three levels – high, medium and low. A high level indicates that the method in terms of the given criteria in the given criticality assessment phase has a high informative value (e.g. it is not time-consuming and it is inexpensive; it is applicable in the context of network infrastructures; the results of the given criticality assessment phase are valuable and meaningful; to evaluate the analyzes no expert knowledge is required, etc.). Medium level indicates that the method has in terms of the given criteria in the given criticality assessment phase medium information value (e.g. it is not expensive, but it is timeconsuming; the method is able to identify critical elements, but it is unable to assess their degree of criticality; the method does not require expert knowledge, but requires enough information about the system, etc.). Low level means that the method, in terms of the given criteria in the given criticality assessment phase, has low information value (e.g. it is expensive and timeconsuming; it is not applicable in the context of network infrastructure; the method is not feasible without expert knowledge, etc.). Table 2: Numerical evaluation of an individual criterion Value Verbal evaluation for criteria 3 High 2 Medium 1 Low The numerical values in Table 2 are then used in the next step of the multi-criteria evaluation – grading of individual criteria. The process of evaluating the individual criteria is performed as a product of the weight of the relevant criteria in Table 1 and selected numerical value in Table 2. The overall evaluation (E) is then obtained by summing the obtained values of the individual criteria according to the following formula (1), where the maximum value equals 3. The higher the total criteria value, the more suitable the method is in the given stage of assessing the criticality of the elements of road infrastructure. 𝑬 = 𝑺 ∙ 𝒗𝑺 + 𝑪 ∙ 𝒗𝑪 + 𝑹 ∙ 𝒗𝑹 + 𝑨 ∙ 𝒗𝑨 + 𝑲 ∙ 𝒗𝑲

(1)

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The evaluation of applicability of methods and tools is provided in Table 3, so that the total value of criteria (E) is equally divided into three intervals, where SA means that the method is “strongly applicable”, A indicates that the method “applicable” and NA indicates that the method is unfit for use – “not applicable”. Table 3: Evaluation of applicability of methods and tools Evaluation Total value interval SA (2,3;3> A (1,67;2,33> NA Methods and tools mentioned in the third chapter of this article are in Table 4 evaluated in the different phases of the criticality evaluation according to Table 3 This allows for an easy overview of suitability or unsuitability of these methods and tools for assessing criticality of the elements of road infrastructure.

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Vulnerability evaluation

Criticality evaluation

SA SA SA A A A SA SA SA SA SA A

SA A SA A A A SA SA SA SA A A

NA A A A SA A A A A A NA SA

NA A A NA NA NA A A A A NA A

A NA NA A A A SA SA A A A A

A NA NA NA NA NA NA A NA NA NA NA

A NA NA NA NA NA NA A NA NA NA NA

A NA NA NA NA NA SA SA SA SA A SA

SA

A

A

A

A

SA

A

SA

Systemic importance Sectorial importance Societal importance

Vulnerability analysis

Index Methods What-If Analysis FMEA Analysis FTA Analysis ETA Analysis CCA Analysis FMECA Analysis Criticality Matrix CPM Method PERT Method Petri Nets Method ACIS Method Method for making an inventory of critical infrastructure protection

Element identification

Methods and tools

Importance evaluation

Table 4: Application of evaluation of methods and tools applicability Importance analysis

CONCLUSION

The implemented analysis of methods and tools used in risk management and methods and tools recommended for assessing criticality of the elements of infrastructure (with regard to road infrastructure) show that these methods have different time requirements and costs, and provide different levels of detail of the considered element (or system of these elements). The analysis also shows that most methods do not consider some important factors such as vulnerability of society, the mutual influence of infrastructure elements and other systems (infrastructures),

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or impacts on society. The results also show that the most appropriate methods to assess criticality of the elements of road infrastructure seem to be the network analyses, which are used to assess criticality of infrastructure elements and allow for the identification of critical activities and routes. They are suitable for complex branched systems and allow for tracking interrelationships and connections within the system over time. From the network analysis methods, the most appropriate methods are especially the CPM and PERT methods, despite the need to supplement the evaluation of individual infrastructure elements. Other suitable methods for assessing criticality of the elements of road infrastructure are methods for multi-criteria evaluation, which assess criticality based on determining the weights of the individual evaluation criteria. Their use is mainly focused on the elements that are interconnected with other types of infrastructures. These methods also analyze vulnerability of infrastructure elements. The article was compiled using the results obtained in the project SP2013/152 entitled "Definition of criteria and their implementation in determining the criticality of the elements of the transport infrastructure." References: 1. Analysis of Critical Infrastructures - The ACIS methodology [online], Bundesamt für Sicherheit in der Informationstechnik. Bonn, 2004, 8 s. [cit. 2013-10-09]. Available at: https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/Kritis/acis_paper_en_ pdf.pdf?__blob=publicationFile. 2. BERNATÍK, Aleš. Prevence závažných havárií I. 1st ed. Ostrava: Sdružení požárního a bezpečnostního inženýrství, 2006, 86 p. ISBN 80-866-3489-2. 3. ČSN EN 31010. Management rizik - Techniky posuzování rizik. Praha: Úřad pro technickou normalizaci, metrologii a státní zkušebnictví, 2011, 80 p. 4. FUCHS, Pavel, Miroslav KELEMEN, Radovan SOUŠEK, Jaroslav ZAJÍČEK and Jiří HAVLÍČEK. Dopravní infrastruktura jako prvek kritické infrastruktury státu: hodnocení kritičnosti v ČR. 1st ed. Košice: Vysoká škola bezpečnostného manažérstva v Košiciach, 2011. 122 p. ISBN 978-80-89282-56-2. 5. Glossar: Kritikalität. [online]. Bundesamt für Sicherheit in der Informationstechnik, Bundesamt für Bevölkerungsschutz und Katastrophenhilfe [cit. 2013-10-11]. Available at: http://www.kritis.bund.de/SubSites/Kritis/DE/Servicefunktionen/Glossar/ Functions/glossar.html?lv2=1902462&lv3=2254842. 6. GRASSEOVÁ, Monika, Radek DUBEC and David ŘEHÁK. Analýza v rukou manažera: 33 nejpoužívanějších metod strategického řízení. 1st ed. Brno: Computer Press, 2010, 325 p. ISBN 978-80-251-2621-9. 7. HARRIS, Tony and James KIMMANCE. Security of Road Transport Networks: SERON. Identification and Risk Classfication of Critical Infrastructures [online]. 2011, No. 1, p. 1-15 [cit. 2013-10-07]. Available at: http://www.seronproject.eu/download/SeRoN_D200_RiskClassification_summary_V1.0.pdf. 8. PETERSON, James Lyle. Petri Net Theory and the Modeling of Systems. Englewood Cliffs, New Jersey: Prentice-Hall, 1981, 290 p. ISBN 01-366-1983-5. 9. Programm zum Schutz Kritischer Infrastrukturen. Methode zur Erstellung des SKIInventars [online]. 2010, p. 17 [cit. 2013-09-25]. Available at: http://www.bevoelkerun gsschutz.admin.ch/internet/bs/en/home/themen/ski/publikationen_ski.parsys.37885.Dow nloadFile.tmp/methodeskiinventard.pdf. 10. PROCHÁZKOVÁ, Dana. Bezpečnost kritické infrastruktury. 1st ed. Praha: České vysoké učení technické, 2012. 318 p. ISBN 978-80-01-05103-0. - 1164 -

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Contact information Ing. Jana Pupíková, Ing. Petr Rostek Vysoká škola báňská - Technical University of Ostrava, Faculty of Safety Engineering Lumírova 13, 700 30 Ostrava - Výškovice Tel.: 597 322 835 e-mail: [email protected], [email protected]

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