Estimate the useful life for a heating, ventilation, and air conditioning system on a high-speed train using failure models


ACTA IMEKO 
ISSN: 2221-870X 
September 2021, Volume 10, Number 3, 100 - 107 

 

ACTA IMEKO | www.imeko.org September 2021 | Volume 10 | Number 3 | 100 

Estimate the useful life for a heating, ventilation, and air 
conditioning system on a high-speed train using failure 
models 

Marcantonio Catelani1, Lorenzo Ciani1, Giulia Guidi1, Gabriele Patrizi1, Diego Galar2 

1 Department of information engineering, University of Florence via di S. Marta 3, 50139, Florence (Italy) 
2 Luleå University of Technology, Lulea, Sweden 

 

 

Section: RESEARCH PAPER  

Keywords: Reliability; Diagnostic; Railway engineering; failure rate; HVAC; useful life  

Citation: Marcantonio Catelani, Lorenzo Ciani, Giulia Guidi, Gabriele Patrizi, Diego Galar, Estimate the useful life for a heating, ventilation, and air 
conditioning system on a high-speed train using failure models, Acta IMEKO, vol. 10, no. 3, article 10, September 2021, identifier: IMEKO-ACTA-10 (2021)-03-
10 

Section Editor: Lorenzo Ciani, University of Florence, Italy 

Received January 29, 2021; In final form August 2, 2021; Published September 2021 

Copyright: This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, 
distribution, and reproduction in any medium, provided the original author and source are credited. 

Corresponding author: Giulia Guidi, e-mail: giulia.guidi@unifi.it  

 

1. INTRODUCTION 

All devices are constituted from materials that will tend to 
degrade with time. The materials degradation will continue until 
some critical device parameter can no longer meet the required 
specification for proper device functionality [1]-[8]. For this 
reason, as well as the growing complexity of equipment and the 
rapidly increasing cost incurred by loss of operation and for 
maintenance, the interest in reliability is growing in many 
industrial fields.  

Generally reliability could be assessed through different 
methods, such as Reliability prediction, Fault Tree Analysis , 
Reliability Block Diagram etc (see for instance [9]-[12]). Fault tree 
analysis (FTA) [13], [14] is an analytical and deductive (top-
down) method. It is an organized graphical representation of the 
conditions or other factors causing or contributing to the 

occurrence of a defined outcome, referred to as the "top event". 
While, Reliability Block Diagram (RBD) [15] is a functional 
diagram of all the components making up the system that shows 
how component reliability contributes to failure or success of the 
whole system.  

These above-mentioned techniques need input data to be 
performed but sometimes data are not available, and they need 
to be predicted. An accurate reliability prediction should be 
performed in the early stages of a development program to 
support the design process [16]-[21]. A reliability prediction of 
electronic components could be assessed following the 
guidelines of several handbooks, while the prediction of 
mechanical components is more challenging because of the 
following reasons [16], [22]: 

• Individual mechanical components such as valves and 
gearboxes often perform more than one function and 

ABSTRACT 
Heating, ventilation, and air conditioning (HVAC) is a widely used system used to guarantee an acceptable level of occupancy comfort, 
to maintain good indoor air quality, and to minimize system costs and energy requirements. If failure data coming from company 
database are not available, then a reliability prediction based on failure rate model and handbook data must be carried out. Performing 
a reliability prediction provides an awareness of potential equipment degradation during the equipment life cycle. Otherwise, if field 
data regarding the component failures are available, then classical reliability assessment techniques such as Fault Tree Analysis and 
Reliability Block Diagram should be carried out. Reliability prediction of mechanical components is a challenging task that must be 
carefully assessed during the design of a system. For these reasons, this paper deals with the reliability assessment of an HVAC using 
both failure rate model for mechanical components and field data. The reliability obtained using the field data is compared to the one 
achieved using the failure rate models in order to assess a model which includes all the mechanical parts. The study highlights how it is 
fundamental to analyze the reliability of complex system integrating both field data and mathematical model. 

mailto:giulia.guidi@unifi.it


 

ACTA IMEKO | www.imeko.org September 2021 | Volume 10 | Number 3 | 101 

failure data for specific applications of nonstandard 
components are seldom available.  

• Failure rates of mechanical components are not usually 
described by a constant failure rate distribution because 
of wear, fatigue and other stress-related failure 
mechanisms resulting in equipment degradation. Data 
gathering is complicated when the constant failure rate 
distribution cannot be assumed and individual times to 
failure must be recorded in addition to total operating 
hours and total failures. 

• Mechanical equipment reliability is more sensitive to 
loading, operating mode and utilization rate than 
electronic equipment reliability. Failure rate data based 
on operating time alone are usually inadequate for a 
reliability prediction of mechanical equipment 

• Definition of failure for mechanical equipment 
depends upon its application. Lack of such information 
in a failure rate data bank limits its usefulness. 

The above listed problems demonstrates the need for 
reliability prediction models that do not rely solely on existing 
failure rate data banks [23], [24].  

Trying to solve these needs, this paper aims to introduce a 
reliability assessment procedure which integrates failure rate 
models and field data to optimize the reliability analysis of a 
railway heating, ventilation and air conditioning (HVAC) system. 
The paper uses both FTA and RBD techniques to estimate the 
system reliability based on realistic failure rate models for 
mechanical components. 

The rest of the paper is organized as follow: section 2 
illustrates the aim of an HVAC and it presents the high-level 
taxonomy of the system under test; section 3 presents the failure 
rate prediction of three mechanical components (compressor, 
heat exchanger and blower) using failure models; section 4 shows 
the results of the reliability assessment carried out using FTA and 
RBD techniques and finally section 5 compares the results 
achieved with the different techniques. 

2. HVAC FOR HIGH-SPEED TRAIN 

Underground transport and rail systems become more and 
more frequent as they allow rapid transit times while transporting 
a large number of users [25]. Consequently, RAMS (reliability, 
availability, maintainability and safety) analysis has become a 
fundamental tool during the design of railway systems [25]-[27]. 
The network of high-speed trains and also standard rails are more 
and more transferred to underground tunnels in order to mitigate 
the environmental impact. 

Both applications need ventilation rates. In Metros the influx 
of a large number of people and the presence of moving trains 
generate a reduction of oxygen and an increase in heat and 
pollutant. Mechanical ventilation is then required to achieve the 
necessary air exchange and grant users of the underground train 
systems comfortable conditions. 

Ventilation systems have a second and even more important 
purpose. That is to guarantee safety in case of fire emergency. In 
order to create a safe and clean environment for escaping 
mechanical ventilation both in tunnels and in the stations is 
activated. In rails the ventilation of tunnels is mainly dedicated to 
fire emergencies where it is vital to keep under control the smoke 
propagation and create safe areas and clear environment for the 
users. 

Furthermore, efficient temperature regulation is becoming a 
necessity to face overcrowded carriages [28]-[30]. HVAC is the 

best way of regulating temperature and air quality on crowded 
trains [31]. One of the most important guarantees that rail 
manufacturers should look for during the design of an air 
conditioning systems is reliability under the actual operating 
conditions [28], [32].  

During the design of an HVAC system it is necessary to 
achieve information about the HVAC equipment and their 
uses[33]. The taxonomy is a systematic classification of items into 
generic groups based on factors possibly common to several of 
the items (location, use, equipment subdivision, etc.).  

Referring to Figure 1, levels 1 to 5 represent a high-level 
categorization that relates to industries and plant application 
regardless of the equipment units (see level 6) involved. This is 
because an equipment unit (e.g., air conditioning unit) can be 
used in many different industries and plant configurations and, 
for analysing the failure/reliability/maintainability of similar 
equipment, it is necessary to have information about the 
operating context. Taxonomic information on these levels (1 to 
5) shall be included in the database for each equipment unit as 
“use/location data”. Levels 6 to 9 are related to the equipment 
unit (inventory) with the subdivision in lower indenture levels 
corresponding to a parent-child relationship.  

The taxonomy of the system under test, from level 1 to level 
5 is reported in Table 1. The levels from 6 to 9 are very structured 
and include the level of the components divided also in the part 
sections. 

3. FAILURE RATE MODELS 

Predicting the life of a mechanical element is not easy, it includes 
mathematical equations to estimate the design life of mechanical 
components [16]. These reliability equations consider the design 
parameters, environmental extremes and operational stresses to 
predict the reliability parameters. The total failure rate of the 

 

Figure 1. Taxonomy classification with taxonomic levels (SOURCE ISO 14224 
- 2016 [34]).  

Table 1. Taxonomy of the system from level 1 to level 5. 

Taxonomy level Description 

Level 1 - Industry Railway 

Level 2 - Business Category High Speed 

Level 3 - Installation S121 

Level 4 - Unit Front car 

Level 5 - System HVAC system 



 

ACTA IMEKO | www.imeko.org September 2021 | Volume 10 | Number 3 | 102 

component is the sum of the failure rates for the parts for a 
particular time period in question. The equations rely on a base 
failure rate derived from laboratory test data where the exact 
stress levels are known. More information about the failure rate 
data used in this work could be found in [19].  

The most critical components of an Heating, Ventilation and 
Air Conditioning (HVAC) system are the compressor, the heat 
exchanger and the blower[25], [35]. In order to improve the 
failure rate of these items, the relative failure models have been 
analysed in the following sections. 

3.1. Compressor model 

A compressor system is made up of one or more stages. The 
compressor compresses the gas, increasing its temperature and 
pressure [16], [36]. The total compressor may be comprised of 
elements or groups of elements in series to form a multistage 
compressor based on the change in temperature and pressure 
across each stage. 

Every compressor to be analyzed will be characterized by a 
unique design and it will be comprised of many different 
components. According to [16] and to the compressor datasheet, 
the designed HVAC compressor is a reciprocating type 
compressor. The following equation has been obtained in order 
to estimate the failure rate of the actual compressor used in the 
considered HVAC design. 

𝜆C = (𝜆FD ∙ 𝐶SF)+𝜆CA + 𝜆BE + 𝜆VA + 𝜆SE + 𝜆SH , (1) 

where 

• 𝜆C is the total failure rate of compressor  

•  𝜆FD is failure rate of fluid driver 

• 𝐶SF is the compressor service multiplying factor 

• 𝜆CA is the failure rate of the compressor casing  

• 𝜆BE is the total failure rate of compressor shaft bearings  

• 𝜆VA is the total failure rate of control valve assemblies  

• 𝜆SE is the total failure rate of compressor seals  

• 𝜆SH is the failure rate of compressor shaft. 
Different compressor configurations such as piston, rotary 

screw and centrifugal have different parts within the total 
compressor and it is important to obtain a parts list for the 
compressor prior to estimating its reliability. The failure rate for 
each part comprising the compressor must be determined before 
the entire compressor assembly failure rate, λC, can be 
determined. Failure rates for each part will depend on expected 
operational and environmental factors that exist during 
compressor operation.  

The total failure rate of compressor shaft bearings is: 

𝜆BE = 𝜆BE,B ∙ 𝐶R ∙ 𝐶V ∙ 𝐶CW ∙ 𝐶t ∙ 𝐶SF ∙ 𝐶C , (2) 

where 

• 𝜆BE is the total failure rate of bearing 

•  𝜆BE,B is base failure rate  

• 𝐶R is life adjustment factor for reliability 

• 𝐶V is multiplying factor for lubricant 

• 𝐶CW is multiplying factor for water contaminant level 

• 𝐶t is multiplying factor for operating temperature 

• 𝐶SF is multiplying factor for operating service 
conditions 

• 𝐶C is multiplying factor for lubrication contamination 
level. 

The total failure rate of control valve assemblies is given by: 

𝜆VA = 𝜆PO + 𝜆SE + 𝜆SP + 𝜆SO + 𝜆HO , (3) 

where 

• 𝜆VA is the total failure rate of total valve assemblies  

• 𝜆PO  is the failure rate of poppet assembly  

• 𝜆SE is the failure rate of the seals  

• 𝜆SP is the failure rate of spring(s)  

• 𝜆SO is the failure rate of solenoid  

• 𝜆HO is the failure rate of valve housing  
Consequently, using the failure data illustrated in [19] it is 

possible to solve equation (2)-(3). Then, the compressor failure 
rate could be estimated integrating these results into equation (1), 
as follow: 

𝜆C =  1.56 ∙ 10
−5 failure/h (4) 

Usually, failure rates of components implemented in railway 
applications are expressed in failure/km or for sake of simplicity 
FPMK (Failure Per Million Kilometers).  

Moreover, the duty cycle of the compressor must be taken 
into account in order to obtain a more accurate evaluation. 
Consequently, considering an approximate annual distance for 
high-speed train of half a million kilometers and a duty cycle of 
30 %, the failure rate of the compressor becomes: 

𝜆Compressor =  8.22 ∙ 10
−2 FPMK . (5) 

The failure rate achieved above must be compared with the 
failure rate provided by the manufacturer of the component 
(MERAK) which is obtained integrating field data and internal 
company tests.  

𝜆Compressor,merak =  7.79 ∙ 10
−2 FPMK . (6) 

Comparing equations (5) and (6) it is possible to note that the 
failure rate obtained using the compressor model provides a 
value slightly higher than the one provided by the compressor 
manufacturer. The several variables considered by the failure 
model in equation (1) produce the different results since the 
Merak value is based mainly on field data.  

Figure 2 shows the reliability curves relative to the failure rates 
of equations (5) and (6).  

The blue line represents the reliability calculated with the 
manufacturer “MERAK” failure rate while the red one the 
reliability calculated using the failure model of the compressor. 
The curve obtained using the model decreases faster because its 
failure rate is higher than the MERAK failure rate. Anyway, the 
difference of the two curves is limited, at the beginning the 

 

Figure 2. Reliability curves of the compressor assembly calculated through 
Merak data and compressor model given by equation (1).  



 

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curves are approximately equal then they decrease with different 
exponential decay rates. 

3.2. Heat exchanger model 

Heat exchangers are essential part of any kind of HVAC 
system nowadays. The main function of a heat recovery system 
is to increase the energy efficiency by reducing energy 
consumption and also by reducing the cost of operating by 
transferring heat between two gases or fluids, thus reducing the 
energy consumptions. In heat exchangers, as the name suggests, 
there is a transfer of energy from one fluid to another. Both these 
fluids are physically separated and there is no direct contact 
between the fluids. There are different types of heat exchangers 
such as shell and tube, U tube, shell and coil, helical, plate etc. 
The transfer of heat can be between steam and water, water and 
steam, refrigerant and water, refrigerant and air, water and water.  

The HVAC system’s compressor generates heat by 
compressing refrigerant. This heat can be captured and used for 
heating domestic water. For this purpose, a heat exchanger is 
placed in between the compressor and the condenser. The water 
that is to be heated is circulated though this heat exchanger with 
the help of a pump whenever the HVAC system is on.  

The heat exchanger included in the system under test is 
composed by a tube and an expansion valve. The failure rate of 
a fluid conductor is extremely sensitive to the operating 
environment of the system in which it is installed as compared 
to the design of the pipe. Each application must be evaluated 
individually because of the many installation, usage and 
maintenance variables that affect the failure rate. The failure of a 
piping assembly depends primarily on the connection joints and 
it can be estimated with the following equation [16]: 

𝜆P = 𝜆P,B ∙ 𝐶E = 2.2 ∙ 10
−6 failure/h (7) 

where 

• 𝜆P is the failure rate of pipe assembly  

• 𝜆P,B is the base failure rate of pipe assembly, which is 

1.57 ∙ 10−6 failure/h 

• 𝐶E is the environmental factor equal to 1.4 in case of a 
railway application.  

For the expansion valve the failure rate is provided by [16] 

and it is 𝜆VA = 4.5 ∙ 10
−6  failure/h. Therefore, the whole 

failure rate of the heat exchanger is given by the sum of the 
failure rate of the pipe and the failure rate of the valve, each one 
weighted on its own duty cycle. In particular, the duty cycle of 
the pipe is 80 % while the duty cycle of the valve is 30 %. 
Consequently, the failure rate of the heat exchanger is given by:  

𝜆heat exchanger = 3.11 ∙ 10
−6 failure h⁄  . (8) 

Quite the same as the compressor, also the failure rate of the 
heat exchanger must be converted from failure/h into FPMK. 
The heat exchanger failure rate in case of railway application is 
the following: 

𝜆heat exchanger = 5.4 ∙ 10
−2 FPMK . (9) 

Also in this case, the failure rate based on field data has been 
provided by the component manufacturer MERAK and it is 
equal to:  

𝜆heat exchanger,merak = 4.124 ∙ 10
−2 FPMK . (10) 

Figure 3 shows the two different reliability curves, the blue 
one is related to MERAK data while the red one is related to the 

model results achieved in equation (9). The model line results a 
pessimistic estimation also for this component.  

The difference between the two reliability trends is extremely 
low. This is mainly due to the fact that for a simpler element like 
the heat exchanger, the manufacturer MERAK and model lead 
to a similar result. 

3.3. Blower model 

One of the most common downfalls of installed HVAC 
systems is their inability to distribute the correct amount of air to 
where it’s needed most. When systems are restrictive, or blowers 
aren’t powerful enough, the air simply doesn’t make it to where 
it needs to go. 

A blower is composed by:  

• an AC motor;  

• two bearings;  

• a fan.  
The failure rate of a motor is affected by such factors as 

insulation deterioration, wear of sliding parts, bearing 
deterioration, torque, load size and type, overhung loads, thrust 
loads and rotational speed. The failure rate model developed is 
based on a fractional or integral horsepower AC type motor. The 
reliability of an electric motor is dependent upon the reliability 
of its parts, which may include bearings, electrical windings, 
armature/shaft, housing, gears and brushes. Failure mechanisms 
resulting in part degradation and failure rate distribution (as a 
function of time) are considered to be independent in each failure 
rate model. The total motor system failure rate is the sum of the 
failure rate of each of the parts in the motor: 

𝜆motor = 𝜆M,B ∙ 𝐶SF + 𝜆WI + 𝜆ST + 𝜆AS + 𝜆BE + 𝜆GR + 𝜆C, (11) 

where 

• 𝜆motor  is the total failure rate for the motor system 

• 𝜆M,B is the base failure rate of motor 

• 𝐶SF is the motor load service factor 

• 𝜆WI  is the failure rate of electric motor windings 

• 𝜆ST is the failure rate of the stator housing 

• 𝜆AS  is the failure rate of the armature shaft 

• 𝜆BE is the failure rate of the bearing evaluated using 
equation (2) and the suitable factors 

• 𝜆GR is the failure rate of gears 

• 𝜆C is the failure rate of capacitor. 
The bearings failure rate could be estimated following the 

guidelines in section 3.1. 
The fans are modelled in according to MIL-STD-217F [37] 

by: 

 

Figure 3. Reliability curves of the heat exchanger assembly calculated through 
Merak data and heat exchanger model according to equation (9).  



 

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𝜆Fan = [
𝑡 2

𝛼𝐵
3

+
1

𝛼𝑊
] failure/h (12) 

where 

• t is the motor operating time period 

• 𝛼B the Weibull characteristics life for motor bearing 

• 𝛼W the Weibull characteristics life for motor windings 
Finally, the whole blower failure rate is given by the sum of 

the failure rates of its components, so: 

𝜆Blower = 𝜆motor + 2 ∙ 𝜆bearing + 𝜆Fan
= 1.328 ∙ 10−5 failure/h . 

(13) 

Then considering the duty cycle of 100 % and the required 
conversion from failure/h into FPMK, the blower failure rate 
become: 

𝜆Blower = 2.33 ∙ 10
−1 FPMK (14) 

The failure rate achieved analyzing field data has been 
provided by the component manufacturer MERAK, and it is 
illustrated in the following:  

𝜆Blower,merak = 7.97 ∙ 10
−2 FPMK . (15) 

Figure 4 shows the two reliability curves, the blue one is 
related to the MERAK data and the red one is related to the 
model data. 

Like for the other components, the reliability calculated 
through the models provides a pessimistic reliability trend 
respect the reliability calculated with the field data provided by 
MERAK. This time, the differences between field data and 
model data is quite remarkable. This could be due to the harsh 
operating condition considered by the failure rate model in [16]. 

4. RELIABILITY ANALYSIS 

When the data (coming from tests or from the manufacturer) 
are available, techniques such as FTA or RBD could be used to 
estimate the useful life of the system.  

4.1. Fault tree analysis 

Fault tree diagrams consist of gates and events connected with 
lines. The AND and OR gates are the two most commonly used 
gates in a fault tree. To illustrate the use of these gates, consider 
two events (called "input events") that can lead to another event 
(called the "output event")[14], [35]. If the occurrence of either 
input event causes the output event to occur, then these input 
events are connected using an OR gate. Alternatively, if both 

input events must occur in order to the occurrence of the output 
event, then they are connected by an AND gate. 

Fault tree analysis gates can also be combined to create more 
complex representations. In case of the HVAC system under 
analysis, the top event is “HVAC failure” and it’s caused by four 
different events, as illustrate in Figure 5: 

• “Possible fire”, when some events could involve a risk 
of fire in the railway cabin. 

• “Loss of emergency ventilation”, when the emergency 
ventilation doesn’t work. 

• “Loss of functions caused by a single event”, when a 
single event causes a direct loss of all the cooling, 
heating, ventilation function 

• “Indirect loss of cooling heating and ventilation”, when 
some events cause independently a loss of cooling, 
heating and ventilation functions. 

The top event “HVAC failure” is linked to the above-
described input events trough an OR gate, that means if at least 
one of the four input events happens the whole system fails. 
Every one of the input events in Figure 5 is in turn caused by an 
extremely complex combinations of several events.  

The complete FTA diagram is very large and structured, and 
it is not possible to show it entirely. So, for the sake of simplicity, 
Figure 5 shows only an extract of these FTA. 

The reliability trend considering the FTA configuration is 
shown in Figure 6. The curve is a decreasing exponential, it starts 
from a unitary reliability and it tends to zero. The analysis is 

simulated starting from 0 km up to 6∙106 km. According to an 

annual forecast distance traversed of about 487∙103 km, the 
simulation in term of time is over 12 years.  

At distance 0.5∙106 km (approximately 1 year) the reliability is 

around the 80 %, while after 1∙106 km (approximately 2 years) is 
decrease approximately to the 60 % and then it tends to zero at 

5∙106 km (approximately 10 years). These results are justified by 
two reasons: 

• The mechanical nature of the whole system, that 
contributes to a fast decrease of the reliability. 

• The OR gate that lead to the top event, which is the 
worst-case scenario between the several ones 
considered during the design. 

4.2. Reliability block diagram 

An overall system reliability prediction can be made by 
looking at the reliabilities of the components that make up the 
whole system or product. In order to construct a reliability block 
diagram, the reliability-wise configuration of the components 
must be determined. Consequently, the analysis method used for 
computing the reliability of a system will also depend on the 
reliability-wise configuration of the components/subsystems. 

 

Figure 4. Reliability curves of the blower assembly calculated through Merak 
data and blower model as in equation (14).  

 

Figure 5. Extract of the FTA Diagram for the HVAC system under analysis.  



 

ACTA IMEKO | www.imeko.org September 2021 | Volume 10 | Number 3 | 105 

That configuration can be as simple as units arranged in a pure 
series or parallel configuration. There can also be systems of 
combined series/parallel configurations or complex systems that 
cannot be decomposed into groups of series and parallel 
configurations. 

The HVAC system under analysis could be described using a 
series of three main blocks (see Figure 7): 

• Cooling system 

• Heating system 

• Ventilation system. 

Therefore, supposing the exponential distribution for all the 
items [18], [38], [39], the reliability equation of the whole system 
is: 

𝑅SYS(𝑡) = e
−(𝜆cooling+𝜆heating+𝜆ventilation)∙𝑡  . (16) 

Figure 8 shows a comparison between cooling, heating and 
ventilation reliability curves. The figure also shows the whole 
system reliability trend calculated with equation (16), which is 
illustrated using a dashed black line. 

The red line represents the heating system, the blue line the 
ventilation system and the green line the cooling system. The 
worst system, in reliability terms, is the cooling system, because 
it contains a lot of series elements and most of them are 
mechanical items. 

The three systems are connected in a series configuration, 
where the component with the least reliability has the biggest 
effect on the system's reliability. As a result, the reliability of a 
series system is always less than the reliability of the least reliable 
component. 

That’s why the black line, representing the whole system 
reliability is lower than the cooling curve (the least reliable). 

4.3. Comparison between FTA and RBD results 

Table 2 shows the comparison of the reliability trends 
between the two proposed methods: Reliability Block Diagram 
and Fault Tree Analysis.  

The two curves are very similar, but the RBD reliability is 
always higher than the FTA results (at every distance). The 
differences could be caused by: 

• Different algorithm used by the software for the 

calculation of the reliability. 

•  The FTA analysis results are more complete and 

they consider all the possible path that lead to the 

top event, so it considers also the relationship 

between failures. 

The first column of Table 2 reports the distance travelled by 
the train, the second the corresponding time, the third and the 
fourth the reliability values of the FTA and RBD respectively. 
The last one reports the absolute percentage difference of the 
two previous columns. All the values relative to the RBD are 
higher than the FTA, but their difference is lower than 6 %. 
Figure 9 shows the trend of the difference between the two 
curves, it illustrates that the maximum value is 6.5 %, so the 
difference is very low. At the beginning the difference is not 
remarkable, in particular before 1000000 km is lower than 4 %, 
then it increases, and the peak is between 1500000 km and 
2500000 km where the difference is 6 %. After that, it decreases 
slowly and it reaches the value of 2 % at 6000000 km. 

Therefore, the two methods provide comparable results, and 
both the outcomes are valid. 

5. COMPARISON BETWEEN FIELD DATA AND MODEL DATA 

A comparison between the failure estimation of the previous 
paragraphs and the failure data provided by the manufacturer of 
the HVAC has been carried out in order to investigate how the 
model-based failure rates affect the reliability trend of the whole 
system. 

The model-based failure rates of compressor, blower and heat 
exchanger are used to calculate the whole HVAC reliability 
together with the failure rate estimation of the other 
components, which make up the system. 

 

Figure 6. Reliability trend of the FTA.  

 

Figure 7. Reliability block diagram of the HVAC system.  

 

Figure 8. Reliability trends of cooling, heating and ventilation systems 
(continuous lines) compared with the HVAC system reliability (dashed line).  

Table 2. Reliability data of OR type FTA and RBD. 

Distance  
km 

time Rfta Rrbd Difference 

0.5 ∙ 106 1 year 0.78 0.80 3 % 

1 ∙ 106 2 years 0.60 0.64 4 % 

2 ∙ 106 4 years 0.34 0.40 6 % 

3 ∙ 106 6 years 0.18 0.24 6 % 

4 ∙ 106 8 years 0.1 0.14 4 % 

5 ∙ 106 10 years 0.05 0.08 3 % 

6 ∙ 106 12 years 0.03 0.05 2 % 



 

ACTA IMEKO | www.imeko.org September 2021 | Volume 10 | Number 3 | 106 

Figure 10 shows three reliability curves, the blue trend is 
related to the FTA reliability, the red one is calculated with the 
RBD analysis, while the green one is related to the failure rate of 
the components calculated using the failure models. 

It’s possible to note that the model-based failure rates 
contribute to reduce the reliability and have an important 
contribution to the whole system reliability.  

The failure rate models provide a pessimistic reliability results 
for the three components analyzed before. Consequently, their 
reliability curves affect the whole system reliability, producing a 
trend lower than the ones calculated with the manufacturer data 
(in case of both FTA and RBD techniques.  

6. CONCLUSION 

The paper deals with a heating, ventilation and air 
conditioning system mounted on a high-speed train. The first 
part of the paper illustrates the taxonomy of the system under 
study. The architecture of an HVAC system includes several 
critical components, such as: a fan (blower), a heat exchanger and 
a compressor. 

A detailed study on the failure rates of the HVAC most critical 
components is presented in this paper. Compressor, heat 
exchanger and blower show a model-based reliability lower than 
the reliability achieved using the field data provided by the 
manufacturer of the HVAC “MERAK”. Then, the reliability of 
the complete HVAC system has been estimated using two well-
known techniques: Fault Tree Analysis and Reliability Block 
Diagram. FTA and RBD methods take the field data provided 
by MERAK as input to evaluate the system reliability over 
distance travelled by the train. The final analysis shows how the 
model failure rates affect the whole HVAC reliability comparing 
the results achieved using FTA and RBD with the one obtained 
using the failure rate models. The model-based failure rate 
provides a pessimistic result because it considers every possible 

failure modes and failure mechanisms of each subitem that make 
up the component. Despite this. it could be not so realistic since 
it doesn’t properly consider the real operating conditions of the 
system under test. Quite the opposite, the reliability evaluated 
using the field data takes into account the real context of the 
HVAC but some of the failure mechanisms might be not occur 
during the observed time interval. For these reasons. it is 
fundamental to analyze the reliability of such complex system 
integrating both techniques.  

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Figure 9. Absolute percentage difference between the two reliability trends 
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Figure 10. Reliability curves of the HVAC assembly calculated through Merak 
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