Article
citation information:
Gill, A. Non-standard risk model
for applications in railway transport. Scientific Journal of
Silesian University of Technology. Series Transport. 2024, 124, 63-76. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2024.124.5.
Adrian GILL[1]
NON-STANDARD
RISK MODEL FOR APPLICATIONS IN RAILWAY TRANSPORT
Summary. In risk management in
railway transport, standard risk models are usually used based on its typical
definition and discrete quantification. This approach allows for easy
justification of the adopted model, most often by referring to appropriate
norms or standards (such as IRIS). The scientific approach does not disqualify
the practical use of standard risk models, but its disadvantages (especially
typical risk matrices, including their subjectivity) are increasingly being
pointed out. In risk management procedures, most frequently one model is used
to assess the risk of all identified hazards. This may turn out to be a
mistake, considering the specific characteristics of the hazards. A risk model
applied to one hazard may not be adequate to assess the risk of another.
Therefore, it should be individually adapted both in terms of variables and the
ranges of their measurement values. For some hazards, it will even be necessary
to develop or adopt non-standard models. The aim of the article is to present
non-standard risk models that provide a base for their easy implementation in
safety management procedures used by railway entities.
Keywords: railway, risk model, RAMS
1. INTRODUCTION
In risk management in railway transport,
standard risk models based on the typical definition of risk (see risk
definition in subsection 2.1) and discrete mapping of the measures of risk
components are usually used. Slightly more detailed models, i.e. those based on
the FMEA method, are used equally frequently. An example in Poland may be the
SMS/MMS-PR-02 Procedure – Technical and Operational Risk Assessment [25] used
by the administrator of the national railway network, or certain research
papers, for instance [32, 33] as well as the work [15], where FMEA was conducted on the example of
the main railway station in Bielsko-Biala. The situation is also confirmed by
cross-analyses available in literature (conducted, for instance, in papers [31,
40]), as well as (unpublished) documentation for projects carried out in
cooperation with railway market entities. It should be noted, however, that
risk management in railway transport based on standard risk models can be
observed not only in Poland, which is evidenced by other research papers. For
example, the authors of the paper [6] presenting a framework for risk management at
railways, use a two-component risk model (consequences and frequencies of
hazards). The authors of the paper [3], in their Hybrid Model for Optimizing
Reliability, Risk and Maintenance of a Rolling Stock Subsystem, emphasize
identifying critical failure modes using risk priority numbers. The authors of
the paper [27], indicate that FMEA is an effective tool for the risk assessment
of mechanical systems by applying its extended version to rolling stock
operated in an iron ore mine in Sweden. Similarly, the authors of the paper [24],
who present the implementation of a modified FMEA methodology in accordance
with EU Commission Regulation 402/13 on a common safety method for risk
assessment and evaluation in the railway sector.
Reasons for the more extensive use of the
standard risk models can be assumed, taking into consideration the origin of
the popularity of the FMEA method in the railway transport industry. The author
of dissertation [39] associates it with IRIS (International Railway Industry
Standard), which is the basis for quality management systems used by
manufacturers of railway vehicles and railway vehicle equipment. In accordance
with the guidelines provided for IRIS, the FMEA method is the preferred risk
analysis method applicable at any stage of the product life cycle, in
particular in the risk analysis procedure and the RAMS procedure [39]. Such a recommendation may turn out to
be a sufficient reason, as it provides basis for references to legislative
provisions.
In risk management procedures executed this
way, one risk model is used for risk evaluation for all the identified hazards.
This may turn out to be a mistake, taking into account the unique
characteristics of the hazards, including [20] e.g.: the history and probability of hazard
activation, the extent of losses/damage generated in the area of analysis. The
values of hazard characteristics are used to determine the risk component, and
because of such a broad spectrum of those, this provides the basis for a
greater differentiation of risk models.
A risk model applied for one hazard may not be
appropriate for the evaluation of the risk of another hazard. In this case, it
should be individually adapted to the hazard, both in terms of the variables
and the value ranges of their measures. The (theoretical) situation where risk
management procedures consider as many risk models as there are hazards is
therefore correct. Perhaps with some of them, it may be necessary to develop or
adopt non-standard models. A number of needs, obstacles, and challenges related
to risk assessment and risk management processes (including risk models), adapted
to the current and future technological challenges, were mentioned by the
authors of [5].
The problem in applying non-standard risk
models may, however, be their excessively academic and abstract nature. At the
same time, a considerable amount of input data is required for them, which is
not always available in the practice of operating railway transport systems.
Academic literature presents many detailed, but also relatively complex risk
models that require a considerable amount of data (see subsection 2.2).
The validity of the application of risk models
verified in practice (such as the FMEA) is not questioned. However, noticing
their flaws (e.g., work [27]), and sometimes even their debatable value in the
context of certain hazards [14], different authors are trying to develop risk
models constituting an extension to the FMEA. Such a model was proposed, among
others, by the authors of [14, 24]. At times, the FMEA or FMECA also becomes part
of hybrid models (e.g. in [3]), constituting a combination of several
methods used in safety engineering. A broader description of the models was
included in subsection 2.2.
The inclination to use the already proven
models (sometimes even in spite of their perceived invalidity for certain
hazards) is related to the lack of inclusion of non-standard models in the
norms. And although the application of approaches based e.g. on the FMEA is not
imposed by legislation, it seems easier to justify for entities required to
manage risk. Ultimately, a conclusion can be made that the lack of information
about the existence of non-standard models simply contributes to their
non-application.
In academic literature, other, relatively
simple risk models are known which may turn out to be convenient in the risk
assessment in railway systems. An example may be the model presented by Schöne
i Mahboob in their book [29] or Aven’s model provided in his publication [4]. Although example applications were provided
for such models and the adopted variables were explained, in the perspective of
their convenient implementation in risk management procedures, the need for
their broader interpretation and discussion of the applied variables is
observed.
The paper is aimed at presenting a non-standard
risk model, providing grounds for convenient implementation in the safety
management procedures used by entities in the railway industry. The article
presents such a model in section 3. An example application of the model for the
estimation of the risk of hazard of a collision between a railway vehicle and
a road vehicle at category B level crossings was also presented.
2. MATERIALS AND METHODS
2.1. What a risk model is
A risk model is said to be a way of
mapping the properties of the area of analysis (existing in hazard conditions),
significant in terms of safety, with the use of a finite set of symbols and
mathematical or logical relationships, including a function of transition from
a set of hazards to a set of undesirable events, taking into account their
effects (damage, losses) and uncertainty
[20]. It is worth noting that the above definition
clearly indicates the need to map the uncertainty measure in the risk model
(which is also mentioned and applied in risk models e.g. by Aven [4, 35] or the
Society for Risk Analysis [31]).
A risk model can be a set of
symbols, i.e. it can be a graphical model without mathematical relationships.
The geometric or topological properties of a graphic unit then serve to
represent the geometric properties, logical relationships or functions of the
executed process. A graphical risk model is often presented in regulations
dedicated to risk management processes, for instance those related to RAMS
specifications.
Graphical models, no matter how
useful they may be for the visualisation of an issue or problem, are, however,
usually converted into any other formal form – usually mathematical
(deterministic, statistical or simulation). It might be said that risk as a
measure of hazard severity is then expressed with the value of the relevant
function (in generalised form provided in relationship (1)).
Mathematical risk models frequently
contain several components whose values or levels are determined in the risk
analysis process in accordance with the adopted criteria. What components a
risk model should contain is specified by the definition of risk itself, for
instance the one proposed by Vincoli [36] or a similar one, formulated by the Center
for Chemical Process and Safety – New York [9]: “a measure of human injury, environmental
damage, or economic loss in terms of both the incident likelihood and the
magnitude of the loss or injury. A simplified version of this relationship
expresses risk as the product of the likelihood and the consequences (i.e. Risk
= Consequence x Likelihood) of an incident”.
An example of a more detailed
approach to a risk model, in particular in the context of expressing the
likelihood and uncertainty of events, is presented e.g. by MacDonald in [12]. The risk model he proposes includes a
coincidence of three different measures related to hazard activation: frequency
and duration of exposure, probability of hazardous event, possibility to avoid
or limit harm.
If a risk model is to be presented
in mathematical form, its form may always be notated in generalised form
as follows [21]:
, 
(1)
where ri(zk) is a component of the
risk of the k-th hazard.
2.2. Literature review on risk
models used in railway transport
An illustrative example of a risk
model which is mathematically advanced and requires a considerable amount of
data is the cloud model-based risk assessment [38]. It was developed for
application with railway tunnels, more precisely in the risk assessment for the
existing Guangzhou-Shenzhen-Hong Kong railway tunnel. In the adopted
methodology, a risk assessment index is used, developed based on the tests of
the geological condition, the condition of the natural environment, the tunnel
design scheme, and construction management. The cloud model, in turn, is
intended to provide a basis for the transformation of uncertainty between its
qualitative concepts and quantitative expressions.
Another example is a risk model
expressed with the probability of a hazardous event (dynamic hybrid model;
DHM), presented by [2]. The DHM makes use of the Bayesian method of
factorisation and network variable elimination as a complex aggregation
of frequency and severity distributions. The DHM verifies the predicted
risk using machine learning based on the Bayesian expectation-maximisation,
evidence of expert knowledge propagation, and learned data [2].
An interesting example of a risk
model which can be categorised as non-standard is one using the logistic
regression method, presented in paper [8]. It was developed with reference to level
crossings, but it seems flexible enough for it to be easily adapted to risk
assessment and monitoring in different areas of the railway system. Another
such example is the risk model presented by [13]. It is entirely a probabilistic model, i.e. it
is based on an index constituting a relationship between the probability of an
event calculated with Markov processes/models and statistical probability
(based on real events).
A similar example is [34],
constituting a risk model based on the estimated number of accidents on
platforms. As a result of its development, 16 factors were defined, such as
platform structure and passenger traffic. Poisson regression and negative
binomial regression models were used to estimate and analyse the number of
accidents from the station’s database (158 platforms from 52 stations in
Japan).
In academic studies on risk models,
a trend of establishing risk models based on the fuzzy set theory emerges.
Examples of such solutions (applicable to railway transport), intended for
different stages of the systems’ life cycle and their areas of application, can
be identified. For instance, at the stage of designing railway structures –
papers [16, 24], railway traffic control – paper [10] (using so-called fuzzy-AHP, i.e. the fuzzy
analytical hierarchy process, which is a combination of the AHP and the
fuzzy set theory; described in detail with reference to railway transport by An
and Chen in book [1]), carriage systems – paper [14], as well as trespassing on the railway tracks
– paper [19]. It is pointed out that the reason for such an
approach lies in the flaws of the typical risk matrices, including their
subjectivity. It was observed that they can be reduced by mapping the
relationship between the risk assessment value and its category scale in a
linear or logarithmic manner [10], or in a different way that is not discrete
mapping. A significant degree of mapping discretisation may lead to low quality
and usability of the results of risk assessments [10, 11].
Fuzzy logic finds application
primarily in the elimination of the flaws of the FMEA models, in particular the
RPN (risk priority number) index. Among the most criticised flaws of the RPN,
Fu et al. [14] include: the algebraic product of the value of
the index components may be debatable and introduce excessive sensitivity to
the model, different combinations of the index component values may give the
same value of the index, which is not effective in practical risk management,
precisely determining the index component values may be difficult in many real
scenarios, in the conventional FMEA approach, the relative significance of the
index components may be overlooked.
In their article [14], they presented an extended FMEA model based
on the cumulative prospect theory and the VIKOR method (with type-2 fuzzy sets)
for determining the priority of hazards related to trains. Such an extension
was aimed at eliminating the limitations of the traditional FMEA approach and
examining the crucial types of damage to the elements of the operated train.
The essence of the method they developed is the adoption of triangular
intuition-based type-2 fuzzy numbers for mapping uncertainty in risk analysis.
Similarly, Macura et al. [24] presented the use of a risk model with the
FMEA method based on fuzzy logic. They used interval type-2 fuzzy logic which,
by assumption (i.e. through the fuzzification of the membership function of
fuzzy sets), provides better mapping of the degree of uncertainty, in this case
– uncertainty resulting from risk assessment. The validity of the use of fuzzy
logic is justified by the authors with the possibility to use data which is
uncertain or vague. Many events (occurring during the construction or
modernisation of railway infrastructure projects) are defined with more than
just simple binary values. In this case, the fuzzy FMEA is the best choice, in
particular with sensitive models. In order to illustrate the importance and the
potential of the developed model, the presented approach was applied and
demonstrated with reference to railway infrastructure projects in the Republic
of Serbia.
The use of the fuzzy set theory and
classical FMEA-based risk models results in the development of non-classical
models (they may be called extended FMEA/FMECA). Meanwhile, the use of a
standard model in combination with other techniques or methods leads to the
development of hybrid models with structures dependent on the methods applied.
One example may be paper [3], in which Appoh et al. use a standard risk
model (FMECA) in the form of RPN in order to identify critical forms of damage.
This is a classic definitional use of this index. However, they treat the
procedure of identifying the form of damage and determining its criticality as
one of the components of the hybrid model, integrating the issues of
reliability, risk, and operating techniques in damage analysis and resource
management. It might be said that their work constitutes an application of the
risk management procedure according to the RBM (risk-based maintenance) idea.
Apart from the articles mentioned
above, those which do not present risk models directly, but provide grounds for
their development may be pointed out. These include papers [18, 22] concerning
risk analysis or hazard identification processes. However, they will not be
analysed in more detail in this article.
3. RESEARCH ISSUES
The model is based
on the classical definition of risk and the principles of the RAMS standards [26], but its
essence lies in the original mapping of the component related to hazard
activation (“transformation” of undesirable system states into a hazardous
event involving measurable losses). It was performed taking into consideration
the assumptions and graphical risk model provided in the RAMS specification
standards (Fig. 1). The distinctive feature of this risk model is the division
of hazards into:
- hazards at
the level of the analysed (or considered) system,
-
hazards in the supersystem of the analysed system (hazards at the railway
system level).
The relationship
between the listed systems may be explained in simple terms as follows: the
analysed/considered system is implemented in the railway system. In reality,
the emergence of an undesirable state (a state which may lead to an accident)
in a railway system is the development of an undesirable state in the
analysed/considered system. This was shown symbolically in Fig. 1 and as a
formal notation with relationship (2).
Fig. 1. The concept of hazard “development” in
railway systems, presenting the division of hazards according to risk model as
per the PN-EN 50126-2 standard
If we were to call a single event, event
sequence, factors, or properties of the area of analysis conditions leading to
an accident, then the set of conditions may be divided into subsets of
conditions applicable to the considered system (called hazards at the level of
the considered system), conditions applicable to the railway system (as the
supersystem of the considered system), called hazards at the level of the
railway system.
If we were to further mark the set of all the
conditions leading to a hazardous event (accident) with a Z, then the
relationships between the hazards at different levels of system decomposition
can be notated as follows:
(2)
where 
is a subset of conditions leading to an
accident at the level of the considered system, and 
is a subset of conditions leading to an
accident, applicable to the railway system.
Using the
assumptions adopted here and relationship (1), the mathematical form of the
RAMS model can be expressed as follows:
(3)
where:
– risk
component expressing the probability of the w-th
type of a hazardous event resulting from the activation of the k-th hazard,
– risk
component expressing losses arising due to the occurrence of the w-th type of a hazardous event resulting
from the activation of the k-th
hazard.
In this risk model, it is assumed
that the losses arising due to a hazardous event can be mapped in the form of
one generalised measure (regardless of the number of loss categories or the
size of the spectrum of these losses). A principle of maximum possible loss or
most probable loss may be adopted here, yet still, the conditional probability
of the occurrence of the given type of loss Sw
is assumed to be certain, i.e.:
(4)
In the simplest, but also the most critical case, the
hazard at the level of the analysed system may be caused by (may be the effect
of) one factor, error, form of damage or – generalising – hazard source (ZZ).
Such event sequences are analysed in the FMEA method or e.g. the Bowtie method.
One type of damage/error or failure to fulfil a function leads to the
occurrence of a local effect, primarily in the form of an undesirable state of
the analysed system (i.e. definitionally, hazard at the level of the analysed
system). In such a case, the relationships between the hazardous events,
hazards, and their sources (hazard factors, types of damage, function error,
etc.), can be notated as the following sequence:
ZZ ZA
ZB
ZN.
If we assume that the probability of the occurrence of
the state/hazard 
depends not only on the occurrence of its
source, but also the “chance” that the given source is causing this state, then
the relationship for the probability of this state/hazard may be expressed as
follows:
(5)
where:
– probability
of the occurrence of the i-th hazard
source (form of damage, function error, etc.),
– probability of the emergence of a hazard at
the level of the analysed system provided that the i-th hazard source occurs (Willis calls this vulnerability with
respect to the risk of terrorist threat [37]).
If we then, similarly to relationship (5), notate
that:
(6)
(7)
where:
– the (conditional) probability of the
occurrence of the k-th hazard at the
level of the railway system provided that the j-th hazard occurs at the level of the analysed system.
– the (conditional) probability of the occurrence
of the w-th hazardous event resulting from the activation of the k-th hazard at the level of the railway
system provided that this hazard occurs,
then the probability of risk component will
be equal to:
(8)
The RAMS model, demonstrated with relationships (3)
and (8), is so universal that giving the conditional probabilities appropriate
interpretations will transform it into standard models. For instance, giving the
conditional probabilities the interpretation of undetectability will cause a
transformation of the RAMS model into the FMEA model and the RPN index, i.e.:
(9)
where
, 
, 
is
the detectability of: the hazard source, the hazard at the level of the
analysed system, and the hazard at the level of the railway system,
respectively. Other examples of conditional probability interpretations were
adopted in the second risk model, presented further on in the article –
relationship (12).
The interpretation of conditional probabilities
(relationship (8)) as the efficacy or inefficacy of the fulfilment of the
safety function, i.e. the effect of the risk reduction measure on the hazard
source, the hazard at the level of the analysed system, and the hazard at the
level of the railway system, respectively, is also valid. Such efficacy may be
expressed and understood in various ways. It is a synthetic measure, i.e. it
usually combines the component of probability of the effect (inclusion) of the
measure and the component of certain susceptibility of the hazard source to the
effect of the risk reduction measure. In literature on the subject, other
examples of understanding and estimating efficacy are also proposed. Bianchini
et al. [7] suggest determining the value of the efficacy index (EI), the value of which
is obtained based on the costs of the consequences of the event and the costs
of preventing these events. The works of Saracinoa et al., e.g. [28], presenting an index used to
express the effect of the properties of the workplace on employee health in
quantitative terms, are also worth noting.
Although it is difficult to express efficacy in
measurable characteristics (which is why it is often mapped qualitatively with
the use of linguistic variables or in other ways, verbally or descriptively),
for the purpose of this model, it will be convenient to express it as a
probabilistic measure. For its introduction, the following events are then
defined:
Q – activation of risk reduction measure,
V – reaction of the hazard or undesirable event to the
effect of risk reduction measure,
C – fulfilment of function by risk reduction measures.
In a statistical sense, event V is dependent on event Q.
If 
, then the probability of the product of
events Q and V equals [17]:
(10)
If we mark the efficacy further with E, i.e.:
(11)
then the inefficacy of or failure to fulfil
the safety function by the risk reduction measure having an effect on the
hazard sources, hazards at the level of the analysed system, and hazards at the
level of the railway system, can be expressed, respectively, as:
, 
, 
(
). The RAMS risk model will then be a
function of five variables:
(12)
It should be noted that undesirable system states
(hazards both at the level of the analysed system and at the level of the
railway system) may be the consequence of a number of causes. Moreover, various
relationships may occur between these causes. A hazard at the level of the
considered system may
be, for instance, a coincidence of several hazard sources 
. If we want to map such relationships in
the RAMS model presented herein, then appropriate interpretations should be
given to individual (non-conditional) probabilities. In the case of a
conjunction of events:
and 
(13)
In the following example of using the method, road
user errors, resulting in entering the trackage, are taken into account. The
reason for this is people’s limited susceptibility to the effects of safety systems
in the form of light signals which remain switched on while the barriers are
closed. This is primarily due to road users’ mechanisms of making errors
(including violations). Based on literature, e.g. [29], it may be concluded
that the probability of a human making an error may be as high as 2e-02
(assuming actions based on knowledge and an unusual/stressful situation).
The results of the estimation of the risk of a
collision between a railway vehicle and a road vehicle at the level crossing for
the assumed exemplary probability values described were presented in Tables 1.
Tab. 1
Adopted
exemplary values of the measures of the RAMS risk model components
|
Risk model component |
Symbol and numerical value |
Remarks |
|
Hazard
source probability |
|
|
|
Hazard
probability at the level of the analysed system |
|
Assuming
that: |
|
Hazard
probability at the level of the railway system |
|
For |
|
Hazardous
event probability |
|
Assuming
that |
|
Losses
resulting from the hazardous event |
|
Assuming a
passenger vehicle with up to 5 people |
|
Risk value |
|
Assuming an
algebraic product of the components |
For the purpose of the RAMS model, the
following states and events were formulated:
- hazard
source (ZZ1): damaged barrier driver,
- hazard
at the level of the level crossing (
): barriers blocked in the upper end position
due to barrier drive failure,
- hazard
at the level of the railway system (
): possibility of road vehicles entering the
level crossing while the light signals are on,
- hazardous
event (ZN): collision between a railway
vehicle and a road vehicle,
- losses
related to the hazardous event: death of
a few people.
4. FINAL REMARKS
In risk management in railway transport, standard risk
models are usually used, based on the classical definition of risk and discrete
mapping of the measures of risk components. Slightly more detailed models, i.e.
those based on the FMEA method, are used equally frequently. Such an approach
has a number of advantages, mentioned in this article, yet it does also have a
good many flaws demonstrated in academic literature and observed due to the
article author’s professional experience. The major flaws of such an approach
include the following: the models are multiplicative, highly sensitive, the
combinations of the input values give the same output value, there are no
scales in the form of continuous functions, and the model components/variables
are inadequate for the hazards. This is why the need for choice and the
presentation of mathematical risk model, which is not the typical ones,
included in risk management norms or standards. At the same time, it provides
grounds for easy implementation in safety management procedures used by railway
entities.
First of all, the reasons for the attractiveness of
the standard models, as well as the issues with applying non-standard models,
were analysed. In the first category, the relatively simple structure of the
standard models should be mentioned, enabling their easy understanding and
application. Moreover, what is extremely important in this case is the legislative
foundation. Referring to standards or norms, it is easier to justify the choice
of methods and execution of risk assessments. The identified issues with the
application of non-standard models include their excessively academic and
abstract character, a considerable amount of input data or resources required,
lack of inclusion in the standards, and sometimes also simply unavailability of
information about non-standard risk models. For this reason, an academic
literature review was carried out next, focused on risk models applied in
railway transport. The analysis has shown that the risks elaborated in academic
literature are very frequently an extension to the FMEA resulting from the
perceived faults of this analysis, or they are hybrid models, i.e. combining
several different methods of hazard identification or risk analysis. There are
also models which are very mathematically advanced and require large amounts of
data. Their description, due to the adopted principle of easy implementation in
risk management systems of railway entities, was limited for the purpose of
this article. As evidenced by the literature review, the extension of the
classic FMEA usually consists in the application of type-2 fuzzy sets.
In order to provide a proper description and interpretation
of these models, a generalised mathematical risk model was first adopted. Risk
treated as a measure of hazard severity is mapped with a function with multiple
components (variables). The model which was elaborated, called the RAMS model,
is a two-component risk model based on the classical definition of risk. Its
non-standard character consists in original mapping of the component related to
hazard activation. It stems from the assumptions of the RAMS standards and the
graphical risk model presented there (which was, however, never presented in
mathematical form). Thanks to expressing the hazard activation component with a
sequence of probabilities, including conditional probabilities, the RAMS model
provides numerous calculation possibilities, depending on the available
information. For instance, if the probability of a hazardous event is known,
the application of a risk model with two components will be the easiest (even
if other probabilities are also known). Certainly, when (apart from the hazardous
event probability) the probability of the occurrence of the hazard source is
known, the value of detectability can be calculated and a model with three
components can be developed (such as RPN, for instance). Additionally, the RAMS
model is so universal that giving the conditional probabilities appropriate
interpretations makes it possible to transform it both into standard models and
other non-standard ones.
The models presented herein are not intended to
replace those currently in use, but complement the resources of available tools
for risk assessment. Perhaps a temporary problem which will emerge in the first
applications of the models will be mastering them properly and applying them
with ease. Even though the presented risk models do not use an advanced
mathematical apparatus, the notations are (and should remain) properly
formalised in order to ensure their clarity and lack of ambiguity. Moreover,
there will always be the issue of the input data – it would be best if it was
not just a result of the exploration of expert knowledge, but constituted
statistical analyses based on the quantitative data collected. It is for the
application of such data that the proposed models (particularly the RAMS model)
will prove to be useful.
Summing up the work carried out, it may be concluded
that there is a possibility to easily extend the currently used risk assessment
procedures with the proposed non-standard models. In their structures, they
draw on the well-known and legislatively accepted models. But they do introduce
additional components and ways of expressing them (measures and mathematical
forms) referring to the characteristics of hazards identified in railway
systems.
Acknowledgements
The research was conducted with a subsidy for the
support and development of research potential from the Faculty of Civil and
Transport Engineering at Poznan University of Technology.
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Received 10.01.2024; accepted in revised
form 29.03.2024
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