# Evaluating the root causes of fatigue and associated risk factors in the
Brazilian regular aviation industry

Tulio E. Rodrigues1,2,∗, Frida M. Fischer3, Otaviano Helene1, Eduardo
Antunes4, Eduardo Furlan2, Eduardo Morteo2, Alfredo Menquini5, João Lisboa4,
Arnaldo Frank5, Alexandre Simões6, Karla Papazian7 and André F. Helene7
1Experimental Physics Department, Physics Institute, University of São Paulo,
P. O. Box 66318, CEP 05315-970, São Paulo, Brazil  2 Technical Board, Gol
Aircrew Association (ASAGOL), São Paulo, Brazil  3 Department of Environmental
Health, School of Public Health, University of São Paulo, São Paulo, Brazil
4Flight Safety Board, National Aircrew Union (SNA), São Paulo, Brazil
5Technical Board, Brazilian Association of Civil Aviation Pilots (ABRAPAC),
São Paulo, Brazil  6Safety Board, LATAM Aircrew Association (ATL), São Paulo,
Brazil  7Department of Physiology, Institute of Biosciences, University of São
Paulo, São Paulo, Brazil<EMAIL_ADDRESS>
###### Abstract

This work evaluates the potential root causes of fatigue and its relationships
with accident risks using a biomathematical model approach and a robust sample
(N = 8476) of aircrew rosters from the Brazilian regular aviation, extracted
from the Fadigômetro database. The fatigue outcomes derive from the software
Sleep, Activity, Fatigue, and Task Effectiveness Fatigue Avoidance Scheduling
Tool (SAFTE-FAST), which considers the homeostatic process, circadian rhythms
and the sleep inertia. The analyses include data from January 2019 until March
2020 and show relevant group effects comparing early 2019 and 2020, with the
latter presenting lower fatigue outcomes in most cases. The average minimum
SAFTE-FAST effectiveness during critical phases of flight (departures and
landings) decreases cubically with the number of shifts that elapse totally or
partially between mid-night and 6 a.m. within a 30-day period ($N_{NS}$). As a
consequence, the relative fatigue risk increases by 23.3% (95% CI, 20.4-26.2%)
when increasing $N_{NS}$ from 1 to 13. The average maximum equivalent
wakefulness in critical phases also increases cubically with the number of
night shifts and exceeds 24 hours for rosters with $N_{NS}$ above 10. The
average fatigue hazard area in critical phases of flight varies quadratically
with the number of departures and landings within 2 and 6 a.m. ($N_{Wocl}$).
These findings demonstrate that both $N_{NS}$ and $N_{Wocl}$ should be
considered as key performance indicators and be kept as low as reasonably
practical when building aircrew rosters, in order to properly manage the
fatigue risk. All the fittings were performed using the Least Square Method
and the confidence intervals were calculated using uncertainty propagation
techniques and the covariance matrix of the fitted parameters. The
effectiveness scores obtained at 30 minute time intervals allowed a model
estimate for the relative fatigue risk as a function of the time of the day,
whose averaged values show reasonable qualitative agreement with previous
measurements of pilot errors in the cockpit. Moreover, the 2019 data revealed
a risk exposure factor two times (14%) higher than the figures reported by
Mello et al. (2008) (7%), within 0h00 do 05h59. Tailored analyses of the
SAFTE-FAST inputs for afternoon naps before night shifts, commuting from home
to station and vice-versa, and bedtime before early-start shifts were carried
out using the responses of a questionnaire. Wilcoxon signed-rank tests for
matched pairs show significant group effects ($p<0.001$) comparing the groups
with and without afternoon naps, with one or two hours of commuting and with
or without the advanced bedtime feature of the SAFTE-FAST software. The
average fatigue hazard area in critical phases of flight increases by 43 to
63% switching off the afternoon naps, 14 to 21% increasing the commuting from
one to two hours and 35 to 54% switching off the advanced bedtime criterion,
evidencing the need of a better and more accurate understanding of these
parameters when modelling fatigue risk factors.

##  I Introduction

Until the Covid-19 outbreak since early 2020, the commercial aviation industry
has experienced a solid growth during the last decades and it is particularly
characterized as a high standard, strongly regulated and safe transport
category [1, 2]. As airplane systems became more reliable, special attention
has been given for human errors, which, according to a Boeing summary [3],
have contributed with 66% of commercial jet fleet hull-loss accidents between
1992 and 2000. Among all the relevant aspects related with human factors [4],
the physiological issue of mental fatigue plays a relevant role in a 24/7
society [5]. In this regard, countries worldwide are making efforts to
establish effective barriers to mitigate the fatigue risk either via
prescriptive flight and duty time limitations or via the implementation of
fatigue risk management systems [6]. A recent experiment carried out by the
European Aviation Safety Agency (EASA) [7] investigated the effectiveness of
some prescriptive rules and scenarios in Europe using two well-known
biomathematical models: the Sleep, Activity, Fatigue, and Task Effectiveness
Fatigue Avoidance Scheduling Tool (SAFTE-FAST) [8] and the Boeing Alertness
Model (BAM) [9]. One of their findings revealed that despite of being
necessary, the prescriptive rules are not fully sufficient to mitigate the
fatigue risks, specially during disruptive and/or night shifts. Moreover, the
Working Time Society has recently stated that prescriptive rules ignore
biological aspects and become less effective for working activities outside
the normal daytime hours [10]. Such findings reinforce the importance of a
solid safety culture in organizations, as well as the need to strengthen
airlines’ safety management systems (SMS), bridging the gap between the
industry needs and the scientific knowledge in the field.
In Brazil, a new set of prescriptive limits and labour clauses was put in
place by August 2017 in law 13.475/17 [11]. After this change, the National
Civil Aviation Agency (ANAC) established the criteria and requirements for the
implementation by the airlines of a fatigue risk management program/system
based on international civil aviation standards and recommendations [6] via
the Brazilian Civil Aviation Regulation (RBAC 117) [12]. Such set of rules
from RBAC 117 allows some extensions of the prescriptive limits dictated by
the law 13.475/17, as far as the operators comply with additional
requirements.
Together with the global efforts of managing fatigue risks, guidelines
specially developed for the identification of fatigue as a contributing factor
in aviation accidents and serious incidents, like the one recently published
by the National Commission of Human Fatigue [13] (a Brazilian Commission
composed by several stakeholders), also improves the overall knowledge of the
likely causes of fatigue, driving future preventive measures and improvements
for the aviation system. Moreover, the analysis of speech parameters and its
correlations with fatigue and sleepiness under operational circumstances is
also a good practical example of research being successfully applied to
aviation accident investigations [14].
Several model based approaches have been used to predict fatigue and/or
sleepiness outcomes due to sleep loss and/or circadian disruptions [8, 15, 9,
16, 17]. More recently, Cochrane et al. also emphasized the importance of
considering non-linear relationships between fatigue and risk [18]. In a
simulated space mission with sleep restrictions, Flynn‑Evans et al.
successfully described average changes in performance with bio-mathematical
models [19]. Reviews of the basic features of some of the available
biomathematical models usually adopted in the aviation industry can be found
elsewhere [20, 21, 22].
In Brazil, a study carried out in 2012 found strong evidences of a chronic
fatigue scenario by the analysis of pilot reports using the SAFTE-FAST model
[23]. Another study, derived from the continued fatigue monitoring effort
named Fadigômetro, has shown relevant seasonal variations in fatigue
indicators comparing high and low season rosters of 2018 [24]. This first
finding demonstrates the potentialities of the Fadigômetro project as a
reliable tool for the analysis of the impact of regulatory changes, such as
the one in effect since March 2020, when the new rules set by RBAC 117 became
effective. Unfortunately, the outbreak of Covid-19 in Brazil by the second
half of March 2020 coincided with the regulatory change, postponing an
unbiased analysis of its impact until the aviation fully recovers [25].
In this work, we present a detailed statistical analysis, based on the SAFTE-
FAST model outputs and other key performance indicators, for the investigation
of the root causes of fatigue and its corresponding relative fatigue risks in
a huge sample of rosters of the Brazilian regular aviation, extracted from the
Fadigômetro database.

##  II Methods

###  II.1 The Sample

This work included 8476 executed rosters from January 2019 up to mid-March
2020 of aircrew workers pertaining to major Brazilian airlines and a
questionnaire, all extracted from the Fadigômetro database on March 2, 2021.
The period of analysis was chosen with the aim of capturing fatigue outcomes
in a recent past scenario before the Covid-19 outbreak in Brazil (mid-March of
2020).
The questionnaire included sociodemographic, behaviour and health questions
and was filled up by 796 participants. The eligible airlines altogether
comprised 92.5% of the Brazilian regular aviation market share in 2019 [26].

###  II.2 Ethical considerations

The present work is derived from the project ”Analysis of Fatigue in Brazilian
Civil Aviation” approved by the research ethics committee of the Institute of
Biosciences, University of São Paulo (Certificate of Presentation for Ethical
Appraisal no. 89058318.7.0000.5464). It was ensured confidentiality to all
eligible subjects who voluntarily agreed to participate by approving a digital
informed consent form. We declare no commercial, labor duality or conflict of
interest with any representative institution involved in the experiment,
airline or regulator. Confidentiality was ensured for the airlines whose
rosters were analysed.

###  II.3 Rosters: criteria and filtering

As described elsewhere [24] rosters were automatically fed into a web-based
application, being digitized and analysed by means of an on-line algorithm.
Some filters were implemented to extract the comma-separated values (CSV)
files, including an internal identification number (Id), event type (Crewing
for flights and Working for non-crewing tasks), departure/landing times and
locations, crew rank, contractual basis and start/end of the duty times.
Differently from our previous work [24], which included only Crewing events,
this study also considers all Working events in the rosters, such as standbys,
training activities, flying as a passenger for airline purposes (dead-heading
flights), etc. These non-crewing events do not directly contribute for risk
build-up, but may adversely interfere on the sleep opportunities of the
subjects, which, in turn, affects their alertness levels and the overall
fatigue and/or sleepiness outcomes. The inclusion of all the Working events in
the analyses increased the occurrences of inconsistencies in the extracted CSV
files, most frequently associated with erroneous/spurious information, which
caused crashes in the SAFTE-FAST (SF) runs. Furthermore, few rosters also
presented warnings in the SF console due to the large majority of events being
associated with on ground training activities. Among all the eligible rosters,
0.64% to 4.5% had crashes, and 0.2% to 6.3% warnings. All rosters with
problems were excluded from the analyses, resulting in a total of 8476
validated rosters.
Considering that only executed rosters were included (past events), home
standbys - which are Working activities where the crew member stays on-call at
the place of their choice - were disregarded in the analyses. Such procedure
avoids any bias from the model assumption that no sleep event will occur
during these working periods, which does not seem very likely in a realistic
scenario particularly for home standbys during night. As a consequence of this
criterion, our results should be interpreted as lower fatigue limits, as some
of the participants might have poor or actually no sleep while in home
standbys during night, despite of being, for instance, at home.
Similarly as described elsewhere [24], additional filters of minimum crew and
narrow body aircraft were also applied in order to focus on the Brazilian
domestic flights and few mid-haul international flights within Caribbean,
South and North America executed by minimum crew. Such choice prevents the
inclusion of augmented crew flights, which are characterized by inboard sleep
opportunities, a feature not included in our SF input criteria for this
analysis (see Supplementary Section). Since some of the key performance
metrics, such as the fatigue hazard area (FHA), strictly depend on the time
interval of the analysis, epochs of exactly 30 days were fixed for each month
(see Supplementary Section).

###  II.4 Modelling the fatigue risk

Following the steps described in our previous work [24], some key performance
indicators, such as the SF Effectiveness ($E_{SF}$), are useful to address the
probability of mental fatigue and its relationship with the risk of cognitive
impairment, mishaps and, ultimately, serious incidents or accidents. The SF
model [8] is a three step algorithm that takes into account the homeostatic
process, the circadian rhythms associated with sleep and wakefulness and the
sleep inertia. Such biomatematical model has being successfully validated
against human factor railroad accidents [27, 28], as well as with psychomotor
vigilance test (PVT) measurements under aviation operational environments [15]
and in a simulated space mission with sleep restrictions [19]. As we have
shown recently, the relative probability of railroad accidents caused by human
factors, herein denoted as $P_{HF}$, increases inversely with $E_{SF}$, such
that:

$P_{HF}(E_{SF})=b/E_{SF},$ (1)

with $b=79.6\pm 3.0\%$ and $E_{SF}$ given as a percentage from 0 to 100%,
where 100% represents an optimum individual performance [24].
During the so-called Window of Circadian Low (WOCL), which is considered as
default from 2 to 6 a.m. in the SF model, individuals have a higher
probability of being fatigued and/or sleepy, with usually lower performance
scores related with alertness and attention. However, in the 24/7 aviation
industry, flight operations are still needed within these less favourable
hours of the day, requiring additional protective barriers to mitigate the
fatigue risks. In this regard, it is very useful to investigate the $E_{SF}$
scores in the critical phases of flight, which comprise the first and last 30
minutes of each flight sector [24]. Consequently, the most degraded fatigue
scores, usually called hot spots of fatigue, for a given crew-member within a
period of analysis can be given by the minimum $E_{SF}$ score in the critical
phases of flight for Crewing events, herein denoted as $EM_{C}$. Additionally
with $EM_{C}$, the minimum sleep reservoir (R) in the critical phases of
flight, herein denoted as $RM_{C}$, also represents a key performance variable
strictly related with the sleep debt ($SD$) and wakefulness ($t_{awake}$). As
described elsewhere [8], the sleep reservoir R varies from 0 to 100%,
increasing during sleep periods and decreasing during wakefulness, with a
score of 75% representing 8 hours of sleep debt. So, considering the equations
presented in Ref. [8], the following linear relationships hold:

$SD=32\left(1-\frac{R}{100}\right)$ (2)

and

$t_{awake}=\frac{2880}{0.5\times 60}\left(1-\frac{R}{100}\right)=3\times SD,$
(3)

with $SD$ and $t_{awake}$ in hours. So, given a minimum sleep reservoir in
critical phases of flight one can easily obtain the corresponding maximum
sleep debt $SD^{max}$ and the maximum equivalent time awake $t_{awake}^{max}$.
Differently from $EM_{C}$ and $RM_{C}$, which represent plausible metrics to
identify fatigue hot spots in crew rosters, the FHA brings the concept of a
cumulative fatigue score for a given individual within a given period of
analysis. This metric was first proposed by Rangan and Van Dongen in 2013 [16]
and represents the area of the SF effectiveness lineshape along time under a
given threshold. Such additive metric represents an overall quantitative
fatigue score, which could help to guide preventive actions to mitigate the
fatigue risks in hundreds or even thousands of crew rosters. Following the
same steps described elsewhere [24], we have adopted a SF effectiveness
threshold of 77% in order to calculate the FHA during critical phases of
flight, herein denoted as $FHA_{C}$.
The SF parameters and criteria used in our model calculations are described in
detail in the Supplementary Section and are strictly the same adopted in our
previous work [24]. However, in this work, we have also investigated - using
behavioural information from the questionnaire - three important SF inputs:
(1) afternoon naps prior to night shifts, (2) commuting from home to station
and vice-versa, and (3) the advanced bedtime feature of the software. For the
afternoon naps prior to night shifts, the standard parametrization of the
software considers no nap for the individuals with less than 8 hours since the
last sleep event and a 60, 90, 120 and 180 minute nap if the individual is
within 8 to 10 hours, 10 to 12 hours, 12 to 14 hours or more than 14 hours
since the last sleep event, respectively. For this input a tailored analysis
was carried out switching off the Auto-Nap feature, which means the software
will not include afternoon naps regardless of the wakefulness period, for
those individuals who declared not being used to take any nap before night
shifts [364 out of 796 responders (45.6%)]. For the commuting from home to
station and vice-versa, we have also run analyses with two hours (extended
commuting), in contrast with our standard parametrization of one hour. For
this input, we have considered the individuals that declared a commuting of
two hours [200 out of 796 responders (25.1%)]. For the advanced bedtime
feature, the software assumes that individuals go to bed earlier than usual
(considering the standard bedtime of 11 p.m. [24]), as a sleep strategy before
early-start shifts, typically between 6 and 8 a.m., regardless of having or
not any significant sleep deprivation prior to the sleep event. So, in our
calculations, we have investigated a scenario without the advanced bedtime
feature of the SF model for the individuals who reported not doing any
anticipation of the bedtime [262 out of 796 of the responders (31.9%)]. All
these customized runs were performed for two high (February and July) and two
low (May and June) productivity months of 2019.

###  II.5 Variables, statistical analyses and fitting procedures

The dependent variables include: $EM_{C}$, $RM_{C}$, $FHA_{C}$, $SD^{max}$,
$t_{awake}^{max}$ and $P_{HF}$. The independent variables include: time of the
day, $t_{clock}$; duty time, $DT$; number of night shifts, $N_{NS}$; number of
consecutive night shifts, $N_{CNS}$; number of Working events, $N_{work}$;
number of Crewing events (flight sectors), $N_{crew}$; and number of WOCL
events, $N_{wocl}$. Both $N_{NS}$ and $N_{CNS}$ include Crewing and Working
events where any portion of the duty period occurs between mid-night and 6
a.m. $N_{wocl}$ includes all the departures and arrivals within 2 and 6 a.m.
for Crewing events only. The independent variables $DT$, $N_{NS}$, $N_{CNS}$,
$N_{work}$, $N_{crew}$ and $N_{wocl}$ are closely related with workload and
will be denoted throughout the paper as productivity metrics. All the analyses
were done for exact 30-day epochs to avoid any bias when comparing months of
different lengths (see Supplementary Section for details). Another set of
dependent variables derived from our calculations include the relative fatigue
risk as a function of $N_{NS}$, $RFR(N_{NS})$; the SF effectiveness as a
function of $t_{clock}$, $E_{SF}(t_{clock})$; the relative fatigue risk as a
function of $t_{clock}$, $RFR(t_{clock})$; and the flight proportion as a
function of $t_{clock}$, $FP(t_{clock})$.
For the normality hypothesis we have adopted the Shapiro-Wilk test [29]. For
the evaluation of group effects we applied the Mann-Whitney test for two
independent samples and the Wilcoxon signed-rank test for paired samples,
depending on the situation. All the statistical tests were performed with the
IBM SPSS software version 25. The calculations of the effect size (dz) were
performed by G*Power version 3.1.9.7 [30].
All the fitting procedures were carried out using the least square method
[31], where the best fit parameters correspond to the minimum $\chi^{2}$,
defined as:

$\chi^{2}=\sum_{i=1}^{n}\frac{[\tilde{f}(x_{i})-y_{i}]^{2}}{\sigma
y_{i}^{2}},$ (4)

where $\tilde{f}(x_{i})$ stands for the fitted function calculated at each
$x_{i}$ value, $y_{i}$ the corresponding data point, $\sigma y_{i}$ its
respective standard error and n the total number of data points to be fitted.
Given that all the data presented throughout this paper depend linearly on the
parameters, the optimal properties of the least square method of minimum
variance and unbiased fitting are fully satisfied. All the fits are considered
successful if the probability of exceeding the $\chi^{2}$ (p-value) is $\geq
0.05.$
The uncertainties of the fitted functions $\sigma_{\tilde{f}}$ where obtained
by the propagation of the uncertainties of the fitted parameters taking into
account its full covariance matrix, as similarly described in a recent
calculation applied for the COVID-19 pandemic spread [32]. The 95% confidence
intervals of the fitted functions were assumed as $\sim 2\sigma_{\tilde{f}}$.
In some model estimates, standard uncertainty propagation techniques were also
applied [31].

##  III Results

###  III.1 Sociodemographic parameters of the sample

The Fadigômetro questionnaire, containing sociodemographic, behaviour and
health questions was filled up by 796 aircrew workers without distinction of
sex, race, rank, age or years in the job from July 19, 2018 until March 02,
2021. Among all responders, 66.6% (530) were male, 51.8% pilots (412) and
48.2% (384) flight attendants (cabin crew). Of the 412 pilots, 54.1% (223)
were captains and 45.9% (189) first officers. The average ages and standard
deviations (in years) were 40.8$\pm$9.5 (N=512), 35.6$\pm$7.1 (N=256),
41.8$\pm$9.9 (N=400), 36.0$\pm$7.0 (N=368), 47.1$\pm$9.2 (N=368) and
35.6$\pm$6.5 (N=184) for Male, Female, Pilots, Flight Attendants, Captains and
First Officers, respectively. The number of validated responses for each group
differs from the total number of responders since some of the responses were
not provided.

###  III.2 SAFTE-FAST outputs and productivity metrics

In this section we present all SAFTE-FAST outputs (software version
4.0.3.207), as well as our productivity metrics for 30-day epochs rosters from
January 2019 until February of 2020. A 15-day epoch was also used for mid-
March of 2019 and 2020. Considering that several filters were adopted to
extract the input CSV files (see Methods), the Ids whose rosters were analysed
vary from month by month and represent a fraction of the eligible participants
of the study. For this reason, the modelling results not necessarily include
all the eligible Ids, neither all the Ids that contributed for the
questionnaire, but the Ids that fulfilled the filter requirements defined
previously.
The results of monthly averages and corresponding standard errors of the SF
outputs for $EM_{C}$, $RM_{C}$, $FHA_{C}$ are presented in Table 1, together
with our estimates of $SD^{max}$ and $t_{awake}^{max}$, calculated from Eqs. 2
and 3, respectively. The first column of Table 1 shows the total number of
validated rosters for each period, which varies between 389 to 680 depending
on the month, with a consistent increase since June of 2019. January 2019
presents the highest fatigue scores with an average $EM_{C}$ around 71.8%, in
contrast with June of 2019, which presented a much higher average of $\sim$
78.1%. Considering the average minimum sleep reservoir, January 2019 also
presents the lowest score of $\sim$ 75.8%, which is consistent with an average
maximum sleep debt of almost 8 hours (7.75 h) and an average equivalent
maximum time awake of almost 24 hours (23.25 h). Considering one standard
error, the relative uncertainties of $EM_{C}$, $RM_{C}$, $FHA_{C}$ and
$SD^{max}$ (or $t_{awake}^{max}$) vary typically from 0.30 to 0.51%, 0.17 to
0.27%, 5.4 to 9.3% and 0.60 to 0.93%, respectively; thus evidencing the high
precision characteristic of our model estimates.

Table 1:  Average values and standard errors for the minimum effectiveness ($EM_{C}$), minimum sleep reservoir ($RM_{C}$), fatigue hazard area ($FHA_{C}$), maximum sleep deficit ($SD^{max}$) and maximum equivalent time wake ($t_{awake}^{max}$) during critical phases of flight from January 2019 up to February 2020 in 30-day epochs. Also shown the total number of rosters for each period (N) and the SF results for 15-day epochs (*) for mid-March of 2019 and 2020. Period | N |  $\langle EM_{C}\rangle$ (%) |  $\langle RM_{C}\rangle$ (%) |  $\langle FHA_{C}\rangle$ (min) |  $\langle SD^{max}\rangle$ (h) |  $\langle t_{awake}^{max}\rangle$ (h)
---|---|---|---|---|---|---
Jan-19 | 419 | 71.75$\pm$0.28 | 75.78$\pm$0.21 | 8.01$\pm$0.48 | 7.75$\pm$0.07 | 23.25$\pm$0.20
Feb-19 | 435 | 74.13$\pm$0.33 | 76.90$\pm$0.19 | 5.50$\pm$0.36 | 7.39$\pm$0.06 | 22.17$\pm$0.19
Mar-19 | 404 | 75.72$\pm$0.39 | 77.95$\pm$0.20 | 4.73$\pm$0.38 | 7.06$\pm$0.07 | 21.17$\pm$0.20
Apr-19 | 389 | 75.73$\pm$0.35 | 77.92$\pm$0.19 | 4.01$\pm$0.32 | 7.06$\pm$0.06 | 21.19$\pm$0.18
May-19 | 399 | 76.57$\pm$0.34 | 78.41$\pm$0.18 | 3.30$\pm$0.31 | 6.91$\pm$0.06 | 20.73$\pm$0.17
Jun-19 | 554 | 78.11$\pm$0.35 | 79.32$\pm$0.19 | 2.85$\pm$0.21 | 6.62$\pm$0.06 | 19.86$\pm$0.18
Jul-19 | 673 | 74.04$\pm$0.26 | 77.09$\pm$0.15 | 6.02$\pm$0.35 | 7.33$\pm$0.05 | 21.99$\pm$0.15
Aug-19 | 635 | 74.92$\pm$0.25 | 77.59$\pm$0.14 | 4.37$\pm$0.27 | 7.17$\pm$0.04 | 21.52$\pm$0.13
Sep-19 | 644 | 74.92$\pm$0.28 | 77.45$\pm$0.17 | 4.79$\pm$0.30 | 7.22$\pm$0.05 | 21.65$\pm$0.16
Oct-19 | 652 | 75.01$\pm$0.28 | 77.74$\pm$0.16 | 5.04$\pm$0.33 | 7.12$\pm$0.05 | 21.37$\pm$0.15
Nov-19 | 649 | 76.04$\pm$0.29 | 78.75$\pm$0.16 | 3.92$\pm$0.25 | 6.80$\pm$0.05 | 20.40$\pm$0.15
Dec-19 | 674 | 74.58$\pm$0.25 | 77.76$\pm$0.15 | 4.79$\pm$0.30 | 7.12$\pm$0.05 | 21.35$\pm$0.15
Jan-20 | 680 | 73.94$\pm$0.22 | 77.57$\pm$0.14 | 5.29$\pm$0.28 | 7.18$\pm$0.04 | 21.53$\pm$0.13
Feb-20 | 670 | 75.29$\pm$0.26 | 78.21$\pm$0.15 | 4.32$\pm$0.26 | 6.97$\pm$0.05 | 20.92$\pm$0.14
Mar-19 (1/2)* | 400 | 78.45$\pm$0.40 | 79.54$\pm$0.19 | 2.55$\pm$0.24 | 6.55$\pm$0.06 | 19.64$\pm$0.19
Mar-20 (1/2)* | 599 | 80.09$\pm$0.34 | 81.06$\pm$0.17 | 1.69$\pm$0.15 | 6.06$\pm$0.05 | 18.18$\pm$0.16

Table 2 presents the results of our productivity metrics extracted by a
dedicated filter algorithm for the same group of rosters that generated the SF
fatigue outcomes of Table 1. As clearly shown in Table 2, these metrics
present large variations from month to month, providing a workload profile for
2019 and early 2020. Once again, Jan-19 presents the highest scores for all
metrics, except $N_{work}$, which is associated with non-crewing and mostly
training activities. The typical high season months in South-America of Jan-19
and Jul-19 have the highest scores regarding the average number of night
shifts ($6.56\pm 0.11$ and $6.46\pm 0.10$) and the average number of
departures and landings between 2 and 6 a.m. ($4.55\pm 0.15$ and $4.51\pm
0.13$), respectively. On the other hand, Jan-20, which should also be
considered a high season month, presents a lower score for $N_{NS}$ ($6.19\pm
0.11$), when compared with Aug-19 ($6.27\pm 0.10$) and Sep-19 ($6.23\pm
0.11$). These results show that other factors beyond the trivial high/low
seasonal variation do play a relevant role in the fatigue outcomes.

Shapiro-Wilk normality tests showed that the SF outputs $EM_{C}$, $RM_{C}$ and
$FHA_{C}$, as well as the productivity metrics $N_{NS}$, $DT$, $N_{crew}$ and
$N_{wocl}$ are unlikely to be originated from a normal distribution
($\textit{p}<0.038$ in all cases). For this reason, non-parametric Mann-
Whitney tests for independent samples were applied for the investigation of
group effects when comparing the early months of 2019 and 2020. The results of
the 2020/2019 ratios and the corresponding p-values are depicted in Table 3
for 30- (January and February) and 15- (March) day epochs for 2019 and 2020.
Except for $N_{NS}$ and $N_{wocl}$ in the comparison between Feb-19&Feb-20 (p
= 0.091 and 0.058, respectively) and Mar-19&Mar-20 (p = 0.279 and 0.159,
respectively), all the other results show a quantitative decrease in the
fatigue scores between early 2019 and 2020. The 2020/2019 ratios for
$FHA_{C}$, $N_{NS}$, $DT$, $N_{crew}$ and $N_{wocl}$ vary between 0.66 to
0.79, 0.94 to 1.04, 0.89 to 0.94, 0.89 to 0.92 and 0.92 to 0.94, respectively.

Table 2:  Average values and standard errors for the number of night shifts ($N_{NS}$), number of consecutive night shifts ($N_{CNS}$), duty time ($DT$), number of Crewing events ($N_{crew}$), number of Working events ($N_{work}$) and number of departures and arrivals within 2 and 6 a.m. ($N_{wocl}$) from January 2019 until February 2020 in 30-day epochs. Also shown the same productivity metrics for 15-day epochs (*) for mid-March of 2019 and 2020. Period | $\langle N_{NS}\rangle$ | $\langle N_{CNS}\rangle$ | $\langle DT\rangle(h)$ | $\langle N_{crew}\rangle$ | $\langle N_{work}\rangle$ | $\langle N_{wocl}\rangle$
---|---|---|---|---|---|---
Jan-19 | 6.56$\pm$0.11 | 2.07$\pm$0.06 | 116.77$\pm$1.17 | 33.64$\pm$0.53 | 2.73$\pm$0.12 | 4.55$\pm$0.15
Feb-19 | 5.87$\pm$0.13 | 1.80$\pm$0.06 | 110.60$\pm$1.54 | 31.80$\pm$0.65 | 2.98$\pm$0.12 | 4.11$\pm$0.15
Mar-19 | 5.26$\pm$0.14 | 1.55$\pm$0.06 | 105.65$\pm$1.56 | 29.57$\pm$0.63 | 3.68$\pm$0.15 | 3.67$\pm$0.16
Apr-19 | 5.68$\pm$0.13 | 1.62$\pm$0.06 | 110.88$\pm$1.48 | 30.99$\pm$0.65 | 3.92$\pm$0.16 | 3.56$\pm$0.15
May-19 | 5.36$\pm$0.13 | 1.47$\pm$0.06 | 108.12$\pm$1.54 | 30.53$\pm$0.65 | 4.41$\pm$0.15 | 3.25$\pm$0.14
Jun-19 | 4.25$\pm$0.13 | 1.16$\pm$0.05 | 82.51$\pm$2.05 | 23.53$\pm$0.68 | 3.23$\pm$0.13 | 2.64$\pm$0.11
Jul-19 | 6.46$\pm$0.10 | 1.98$\pm$0.05 | 113.13$\pm$1.01 | 32.54$\pm$0.52 | 4.63$\pm$0.16 | 4.51$\pm$0.13
Aug-19 | 6.27$\pm$0.10 | 1.93$\pm$0.05 | 113.93$\pm$1.07 | 32.47$\pm$0.51 | 5.37$\pm$0.17 | 3.95$\pm$0.13
Sep-19 | 6.23$\pm$0.11 | 1.98$\pm$0.05 | 107.13$\pm$1.23 | 30.44$\pm$0.52 | 5.28$\pm$0.17 | 4.08$\pm$0.13
Oct-19 | 6.06$\pm$0.11 | 1.85$\pm$0.05 | 107.33$\pm$1.21 | 30.83$\pm$0.53 | 5.36$\pm$0.16 | 3.99$\pm$0.13
Nov-19 | 5.24$\pm$0.11 | 1.55$\pm$0.05 | 101.80$\pm$1.38 | 27.79$\pm$0.54 | 5.49$\pm$0.19 | 3.21$\pm$0.11
Dec-19 | 5.81$\pm$0.10 | 1.83$\pm$0.06 | 108.21$\pm$0.98 | 29.80$\pm$0.46 | 5.19$\pm$0.17 | 3.61$\pm$0.13
Jan-20 | 6.19$\pm$0.11 | 2.01$\pm$0.06 | 109.98$\pm$1.01 | 30.99$\pm$0.49 | 4.60$\pm$0.16 | 4.28$\pm$0.13
Feb-20 | 5.62$\pm$0.10 | 1.68$\pm$0.05 | 103.68$\pm$1.12 | 28.30$\pm$0.48 | 5.22$\pm$0.19 | 3.79$\pm$0.12
Mar-19(1/2)* | 2.81$\pm$0.09 | 0.78$\pm$0.04 | 56.19$\pm$0.80 | 15.64$\pm$0.33 | 1.91$\pm$0.09 | 2.03$\pm$0.11
Mar-20(1/2)* | 2.91$\pm$0.07 | 0.85$\pm$0.03 | 50.23$\pm$0.80 | 14.43$\pm$0.32 | 2.57$\pm$0.13 | 1.88$\pm$0.10
Table 3:  2020/2019 ratios and Mann-Whitney tests for independent samples (p-values) for $EM_{C}$, $RM_{C}$, $FHA_{C}$, $N_{NS}$, $DT$, $N_{crew}$ and $N_{wocl}$ in 30-day epochs for early 2019 and 2020. Also shown the comparison of 15-day epochs (*) for March 2019 and 2020. Variables | Parameters | Groups
---|---|---
Jan-19&Jan-20 | Feb-19&Feb-20 | Mar-19 (1/2)&Mar-20 (1/2)*
$EM_{C}$ | 2020/2019 ratio | 0.970 | 0.985 | 0.980
p-value | $<0.001$ | 0.001 | 0.004
$RM_{C}$ | 2020/2019 ratio | 0.977 | 0.983 | 0.981
p-value | $<0.001$ | $<0.001$ | $<0.001$
$FHA_{C}$ | 2020/2019 ratio | 0.66 | 0.79 | 0.66
p-value | $<0.001$ | 0.004 | $<0.001$
$N_{NS}$ | 2020/2019 ratio | 0.94 | 0.96 | 1.04
p-value | 0.037 | 0.091 | 0.279
$DT$ | 2020/2019 ratio | 0.94 | 0.94 | 0.89
p-value | $<0.001$ | $<0.001$ | $<0.001$
$N_{crew}$ | 2020/2019 ratio | 0.92 | 0.89 | 0.92
p-value | 0.001 | $<0.001$ | 0.010
$N_{wocl}$ | 2020/2019 ratio | 0.94 | 0.92 | 0.93
p-value | 0.041 | 0.058 | 0.159

###  III.3 Potential root causes of fatigue

####  III.3.1 Average minimum SF Effectiveness versus $N_{NS}$

The minimum SF effectiveness during critical phases of flight ($EM_{C}$)
represents the worst fatigue score (hot spot) for a given subject during a
given period of analysis. For this reason, it is likely that crew members with
the same amount of night shifts would have similar values of $EM_{C}$, since
the latter depends on the sleep opportunities of the rosters, which are
adversely affected by night shifts. In that sense, crew members with a large
number of night shifts are likely to have lower minimum effectiveness scores
in critical phases of flight.
The relationship between the average $EM_{C}$, herein denoted as $<EM_{C}>$,
and $N_{NS}$ is shown in the upper panel of Fig.1, which includes all 2019
rosters for 30-day epochs with $1\leq N_{NS}\leq 13$. The average values of
$<EM_{C}>$ (data points) are satisfactorily fitted by a third degree
polynomial, represented by the solid blue line ($\chi^{2}$ = 9.00, d.o.f. = 9
and p = 0.437). The dashed-dotted red and green lines represent, respectively,
the upper and lower limits considering a 95% confidence interval (CI). The
fitting was performed using the least square method [31] and the confidence
intervals were obtained using uncertainty propagation techniques and the
covariance matrix of the best-fit parameters, as similarly described elsewhere
[32]. It is verified that $<EM_{C}>$ drops more significantly for
$1<N_{NS}\lesssim 5$ and $N_{NS}\gtrsim 10$. The error bars are higher for
$N_{NS}\geq 10$, since there are fewer rosters within this range.

####  III.3.2 Relative Fatigue Risk versus $N_{NS}$

Considering that the probability of human factor accidents vary inversely with
$E_{SF}$ (see Eq.1), one can estimate the relative fatigue risk as a function
of $N_{NS}$ by $RFR(x)\cong b/f(x)$, where $f(x)$ stands for the fitted
function and $x\equiv N_{NS}$. Under this approximation, one can also
calculate the 95% CI’s of $RFR(x)$ by the propagation of the uncertainties of
$f(x)$ and b. The results of this relative risk estimate and its upper/lower
limits are shown by the solid blue and dashed-dotted red/green lines of the
center panel of Fig.1, respectively. As expected, the relative fatigue risk
increases with $N_{NS}$. Increasing the number of night shifts from 1 to 13
increases the relative risk by 23.3% (95% CI, 20.4 - 26.2%).

Figure 1: Upper Panel: Average values and standard errors of $EM_{C}$ (data
points) as a function of $N_{NS}$ and its corresponding third degree
polynomial fitting (solid blue line). Center panel: Relative Fatigue Risk
(RFR) as a function of $N_{NS}$ (blue line). Lower panel: Average equivalent
maximum time awake during critical phases of flight as a function of $N_{NS}$
(data points), its corresponding third degree polynomial fitting (solid blue
line) and a 24 hour time awake reference (dotted black line). In all panels
the dashed-dotted red and green lines represent the upper and lower limits,
respectively, considering a 95% CI.

####  III.3.3 Average maximum equivalent time awake versus $N_{NS}$

The lower panel of Fig.1 presents the average maximum equivalent time awake
($t_{awake}^{max}$) - associated with the average minimum SF sleep reservoir
during critical phases of flight - as a function of $N_{NS}$ (data points) and
its corresponding standard errors (error bars). Once again, a third degree
polynomial fitting ($\chi^{2}$ = 16.32, d.o.f. = 9 and p = 0.060) successfully
describes the data. It is also verified that $t_{awake}^{max}$ has a higher
slope for $N_{NS}\geq 10$, exceeding more than 24 hours of equivalent
wakefulness for $N_{NS}\geq 11$.

Table 4:  Best-fit parameters and fitting results for $\langle EM_{C}\rangle$, $\langle t_{awake}^{max}\rangle$ and $\langle FHA_{C}\rangle$. Fitting | $\langle EM_{C}\rangle$ | $\langle t_{awake}^{max}\rangle$ | $\langle FHA_{C}\rangle$
---|---|---|---
| Model | $f(x)=a+bx+cx^{2}+dx^{3}$ | $f(x)=a+bx+cx^{2}$
| $x\equiv N_{NS}$ | $x\equiv N_{wocl}$
Results | a | 87.4 $\pm$ 0.5 % | 14.95 $\pm$ 0.25 h | 0.246 $\pm$ 0.028 min
b | -4.55 $\pm$ 0.31 % | 2.26 $\pm$ 0.17 h | 0.468 $\pm$ 0.035 min
c | 0.50 $\pm$ 0.05 % | -0.250 $\pm$ 0.032 h | 0.115 $\pm$ 0.005 min
d | -0.0204 $\pm$ 0.0028 % | 0.0113 $\pm$ 0.0018 h | –
$\chi^{2}$ | 9.00 | 16.32 | 16.68
d.o.f. | 9 | 9 | 14
p-value | 0.437 | 0.060 | 0.274

####  III.3.4 Fatigue hazard area versus $N_{wocl}$

The cumulative $FHA_{C}$ is expected to increase with the number of departures
and landings within the WOCL period, representing a consistent overall fatigue
score for a given subject in a given period of analysis. Fig.2 shows the
average values of $FHA_{C}$ as a function of $N_{wocl}$ (data points) and
their respective standard errors (error bars), for all the 6527 rosters of
2019. At this time, the data are consistently fitted ($\chi^{2}$ = 16.68,
d.o.f. = 14 and p = 0.274) by a parabolic function (solid blue line), with the
dashed-dotted red/green lines representing the upper/lower limits,
respectively, considering a 95% CI. The data point at $x=18.3\pm 0.7$ and
$y=40.0\pm 3.9$ min represents x\- and y-average values for all rosters with
$16\leq N_{wocl}\leq 22$. The x-axis error (0.7) corresponds to the standard
error of the x-average and was propagated to the y-axis error (3.9 min) in
order to perform the fitting procedure. All the fitting results shown in Figs.
1 and 2 are summarized in Table 4.

Figure 2: Average fatigue hazard area in critical phases of flight as a
function of $N_{wocl}$ (data points). The solid blue line represents a second
degree polynomial fitting, where the dashed-dotted red and green lines
represent, respectively, the upper and lower limits, considering a 95% CI.

###  III.4 Modelling the monthly-averaged fatigue hazard area

The average $FHA_{C}$ in 30-day epochs presented in Table 1 represents an
overall fatigue metric for any given set of rosters. In this regard, a
suitable model to estimate $\langle FHA_{C}\rangle$ for a given $N_{wocl}$
distribution is highly desirable, given its practical relevance to guide
airline policies and management strategies for those involved in crew
rostering processes. Consequently, the monthly-averaged fatigue hazard area in
critical phases of flight can be written as:

$\langle FHA_{C}^{j}\rangle=\sum_{i=0}^{i_{max}}W^{j}(x_{i})f(x_{i}),$ (5)

where $W^{j}(x_{i})$ represents the normalized $N_{wocl}$ distribution for a
given month j, $f(x_{i})$ the fitted parabola of Fig.2, both calculated at
each $x_{i}$ value, with the sum going from zero up to $x_{i_{max}}$, which
represents the maximum $N_{wocl}$ of the distribution. Fig. 3 presents our
model estimates for $\langle FHA_{C}\rangle$ (blue line) with its upper and
lower 95% CI given by the dashed-dotted red and green lines, respectively. The
insert of Fig. 3 shows, as an example, the normalized $N_{wocl}$ distribution
for all the 670 rosters of Feb-2020. The 95% CI of $\langle
FHA_{C}^{j}\rangle$ was calculated propagating the uncertainties of $f(x_{i})$
and $W^{j}(x_{i})$ at each $x_{i}$ value. The latter is assumed as
$\frac{\sqrt{n^{j,i}}}{n^{j,i}}W^{j}(x_{i})$, with $n^{j,i}$ representing the
number of events for each $x_{i}$ value at a given j month. As observed in
Fig. 3, the model calculations do reproduce the several structures that appear
in $\langle FHA_{C}\rangle$, with all data falling within the 95% CI, except
for Jan-19, which is considerably higher than the model predictions. This
latter can be explained considering that January 2019 has a $\langle
FHA_{C}\rangle$ score substantially higher than the average figures of 2019,
which were used as a baseline do determine the polynomial best-fit parameters.
Both January and February of 2020 are also well reproduced by our model
estimates, despite of not being included in the fitting shown in Fig. 2, to
avoid any seasonal bias in mixing two months of 2020 with our annual based
metric for 2019.

Figure 3:  $\langle FHA_{C}\rangle$ and its corresponding standard errors for
each 30-day epochs (data points) and the model predictions based on the
$N_{wocl}$ distributions of each period (solid blue line). The dashed-dotted
red and green lines represent the upper and lower limits, respectively,
considering a 95% CI.

###  III.5 Circadian variations of fatigue outcomes and associated risk

The SAFTE-FAST software provides effectiveness scores for all the individuals
at each 30 minute time interval, allowing the verification of circadian
oscillations in $E_{SF}$ as a function of the time of the day. The results of
this analysis - which includes all the 742521 30-min crewing events of 2019 -
are presented in the upper panel of Fig. 4. The solid black squares represent
the average values of $E_{SF}$ for each 30 min bin, considering all
effectiveness scores of all individuals during all flights of 2019. The error
bars represent the standard errors and range from 0.013 up to 0.056%, showing
the high precision of $\langle E_{SF}\rangle$. The dashed-dotted black line is
an interpolated curve only to guide the eyes, whereas the dashed-dotted
magenta line corresponds to $\langle E_{SF}\rangle=79\%$, which occurs at
$02h04$ and $06h03$, considering the Brazilian legal time. Such time interval
encompasses the worst fatigue outcomes for all the 30-min crewing assessments,
reinforcing our choice to establish the WOCL events within 02h00 and 06h00. As
verified, the average effectiveness varies quite significantly as a function
of $t_{clock}$ and drops below 90% between 11:45 p.m. and 9:15 a.m. The lower
panel of Fig. 4 shows our model estimate for the relative fatigue risk as a
function of $t_{clock}$ (solid blue line) calculated as $RFR(t_{clock})\sim
P_{HF}(t_{clock})\cong b/\langle E_{SF}(t_{clock})\rangle$. The dashed-dotted
red and green lines, represent, respectively, the upper and lower limits
considering a 95% CI and were obtained propagating the uncertainty of b. The
uncertainty of $\langle E_{SF}\rangle$ in the RFR was not taken into account,
given its negligible values ($\leq 0.056\%$).
In order to compare our model predictions for the relative fatigue risk ratios
as a function of the time of the day with previous measurements of pilot
errors in the cockpit [33] we firstly averaged the continuous function
$RFR(t_{clock})$ within the same time intervals investigated in Ref. [33].
Secondly, we normalized our results by equalling our lowest RFR average
(within 18:00 and 23:59) to unit. The results of these procedures are
presented by the solid blue histogram in the upper panel of Fig. 5, together
with the upper (dashed-dotted red) and lower (dashed-dotted green) limits
considering a 95% CI and the normalized risk ratios found by Mello et al. 2008
[33] (data points). For the latter, we have also assumed an error bar
proportional to the ratio of $\frac{\sqrt{N}}{N}$, where N stands for the
absolute number of errors within a given time interval. Such approximation
holds if the probability of errors follow a Poisson distribution. As verified,
our estimates agree qualitatively with the objective measurements performed in
Ref. [33] (see Limitations Section). The lower panel of Fig. 5 shows the
proportion of flights as a function of the time of the day reported by Mello
et al., 2008 [33] (dashed-dotted black histogram) in comparison with our
estimates for the proportion of events using all 2019 data (dashed-dotted
magenta histogram). As shown in the lower panel of Fig. 5, the risk exposure
presents a significant increase (from 7 to 14%) within 0h00 and 5:59,
comparing the flight proportion found in 2005 (when the data of Ref. [33] were
collected) with 2019.

Figure 4: Upper panel: Average SF effectiveness scores (black squares) and its
standard errors (error bars) for all the 30-min assessments during all crewing
events of 2019. The dashed-dotted black line is only to guide the eyes and the
dashed-dotted magenta line corresponds to $\langle E_{SF}\rangle=79\%$. Lower
panel: Model estimates for the RFR as a function of the time of the day (solid
blue line) and its upper (dashed-dotted red) and lower (dashed-dotted green)
limits considering a 95% CI. Figure 5: Upper panel: Relative risk ratios from
Mello et al. 2008 (data points) in comparison with the Fadigômetro predictions
(solid blue histogram) and its upper (dashed-dotted red) and lower (dashed-
dotted green) limits considering a 95% CI. Lower panel: Flight proportion (%)
reported by Mello et al. 2008 (dashed-dotted black histogram) versus the
fraction of events from the Fadigômetro data (dashed-dotted magenta
histogram).

###  III.6 Tailored analyses of SAFTE-FAST inputs

In this section we demonstrate quantitative variations in some SAFTE-FAST
outputs when tailoring some key input metrics related to afternoon naps,
commuting, and bedtime constraints.
For the afternoon naps, the SAFTE-FAST console has a standard input
parametrization (Auto-Nap) that assumes a nap before a night duty, which
depends on the hours of sustained wakefulness since the last sleep event (see
Supplementary Section). This particular input can be switched off, which means
that no afternoon nap will be added automatically, regardless of the time
period since the last sleep event (Auto-Nap OFF).
For the commuting from home to base station and vice-versa, we have adopted a
standard metric of one hour and also an extended commuting profile of 2 hours.
So, for check-in purposes, we consider one hour of preparation at home, hotel
or rest facility and one (standard) or two (extended) hours of commuting from
home to station and vice-versa.
For the bedtime parameter, the SAFTE-FAST algorithm adopts 11 p.m. as default,
which is also adopted in our calculations. However, the model also has an
advance bedtime function, i.e. a feature that assumes an individual will go to
bed earlier than usual should an early start shift is scheduled in the
following morning, regardless of the sleep deficit accumulated in previous
shifts. This feature can also be switched off, which means that the standard
bedtime of 11 p.m. will be a fixed constraint for all main sleep events during
night.
The quantitative effects in few SAFTE-FAST outputs related with the variations
of these input criteria are shown in Table 5, considering two months with low
(May and June of 2019) and high (February and July of 2019) productivity
profiles. The calculations were done using the fractions of the monthly
rosters related with the Ids who declared that are not used to get afternoon
naps prior to night shifts (within 42.2 to 45.4% of the responders), two hours
of commuting from home to station and vice-versa (22.6 to 25.3% of the
responders), or not used to advance the bedtime before early-starts (32.1 to
33.3% of the responders). Wilcoxon signed-rank tests for matched pairs show
significant group effects ($p<0.001$) for $EM_{C}$, $RM_{C}$ and $FHA_{C}$
comparing the groups with and without the afternoon nap, with one or two hours
of commuting and with or without the advanced bedtime feature. Pearson’s
correlations (effect sizes), with and without the the Auto-Nap function
enabled, are equal or higher than 0.967 (0.765), 0.926 (0.674), and 0.941
(0.544) for $EM_{C}$, $RM_{C}$ and $FHA_{C}$, respectively. For the comparison
between one and two hours of commuting, Pearson’s correlations (effect sizes)
are equal or higher than 0.970 (0.409), 0.912 (0.530) and 0.921 (0.300) for
$EM_{C}$, $RM_{C}$ and $FHA_{C}$, respectively. For the groups with and
without the advanced bedtime feature, Pearson’s correlations (effect sizes)
are equal or higher than 0.970 (0.714), 0.926 (0.852) and 0.894 (0.418) for
$EM_{C}$, $RM_{C}$ and $FHA_{C}$, respectively. The average fatigue hazard
area in critical phases of flight increases by 43 to 63% when switching off
the afternoon naps, 14 to 21% when increasing the commuting time from home to
station and vice-versa from one to two hours and 35 to 54% when switching off
the advanced bedtime criterion.

Table 5:  Average values and standard deviations (SD) for $EM_{C}$, $RM_{C}$ and $FHA_{C}$ with or without the Auto-Nap function, with one or two hours of commuting and with or without the Advanced bedtime (BT) feature for February, May, June and July of 2019. Also shown the total number of responders (N) for each period and input, the corresponding fraction of responders (%), as well as the p-values, the Pearson’s correlations, the effect sizes (dz) and the ratios of $\langle FHA_{C}\rangle$ for each matched pair of the analyses. SF Input |  |  | $EM_{C}(\%)$ | $RM_{C}(\%)$ | $FHA_{C}(min)$
---|---|---|---|---|---
|  | Feb-19 | May-19 | Jun-19 | Jul-19 | Feb-19 | May-19 | Jun-19 | Jul-19 | Feb-19 | May-19 | Jun-19 | Jul-19
Auto-Nap | ON | Average | 73.76 | 76.54 | 78.29 | 74.07 | 76.92 | 78.35 | 79.44 | 77.19 | 5.52 | 3.27 | 2.67 | 5.64
SD | 7.33 | 6.60 | 8.28 | 6.49 | 4.22 | 3.52 | 4.48 | 3.70 | 6.50 | 6.68 | 4.69 | 6.85
OFF | Average | 72.15 | 75.22 | 76.74 | 72.16 | 75.80 | 77.45 | 78.32 | 75.83 | 8.20 | 4.69 | 4.35 | 8.95
SD | 8.07 | 7.24 | 9.24 | 7.35 | 4.58 | 3.65 | 5.02 | 4.10 | 8.86 | 7.91 | 7.11 | 9.73
N | 194 | 181 | 234 | 288 | 194 | 181 | 234 | 288 | 194 | 181 | 234 | 288
Fraction (%) | 44.6 | 45.4 | 42.2 | 42.8 | 44.6 | 45.4 | 42.2 | 42.8 | 44.6 | 45.4 | 42.2 | 42.8
p-value 111Wilcoxon signed-rank tests for matched pairs performed with SPSS version 25 | $<0.001$ | $<0.001$ | $<0.001$
Pearson’s $\rho$ | 0.967 | 0.976 | 0.986 | 0.976 | 0.940 | 0.931 | 0.956 | 0.926 | 0.960 | 0.950 | 0.957 | 0.941
Effect size, dz 222Effect size dz calculated with G*Power version 3.1.9.7 [30] | 0.763 | 0.803 | 0.886 | 1.097 | 0.716 | 0.673 | 0.743 | 0.877 | 0.840 | 0.545 | 0.569 | 0.823
|  | Ratio OFF/ON | 1.48 | 1.43 | 1.63 | 1.59
Commuting | 1 hour | Average | 73.90 | 76.48 | 78.13 | 74.30 | 77.11 | 78.21 | 79.38 | 77.52 | 4.57 | 4.07 | 2.66 | 5.35
SD | 6.20 | 7.63 | 8.05 | 6.90 | 3.70 | 3.96 | 4.15 | 3.83 | 4.93 | 6.22 | 4.70 | 6.60
2 hours | Average | 73.11 | 75.62 | 77.21 | 73.51 | 76.17 | 77.33 | 78.44 | 76.58 | 5.51 | 4.64 | 3.04 | 6.36
SD | 5.95 | 7.24 | 7.84 | 6.72 | 3.65 | 3.96 | 4.32 | 3.93 | 5.75 | 7.16 | 5.15 | 7.61
N | 99 | 101 | 132 | 152 | 99 | 101 | 132 | 152 | 99 | 101 | 132 | 152
Fraction (%) | 22.8 | 25.3 | 23.8 | 22.6 | 22.8 | 25.3 | 23.8 | 22.6 | 22.8 | 25.3 | 23.8 | 22.6
p-value 111Wilcoxon signed-rank tests for matched pairs performed with SPSS version 25 | $<0.001$ | $<0.001$ | $<0.001$
Pearson’s $\rho$ | 0.973 | 0.980 | 0.970 | 0.973 | 0.929 | 0.941 | 0.912 | 0.921 | 0.921 | 0.983 | 0.972 | 0.959
Effect size, dz 222Effect size dz calculated with G*Power version 3.1.9.7 [30] | 0.551 | 0.560 | 0.470 | 0.496 | 0.678 | 0.647 | 0.527 | 0.608 | 0.414 | 0.368 | 0.304 | 0.446
|  | Ratio 2 hours/1 hour | 1.21 | 1.14 | 1.14 | 1.19
Advanced BT | ON | Average | 73.50 | 76.62 | 78.57 | 74.36 | 76.43 | 78.17 | 79.35 | 77.20 | 6.45 | 3.68 | 2.81 | 6.18
SD | 6.90 | 6.95 | 7.99 | 7.22 | 4.19 | 3.46 | 4.39 | 4.18 | 9.08 | 7.61 | 5.31 | 9.65
OFF | Average | 72.04 | 75.24 | 77.18 | 73.06 | 74.88 | 76.84 | 78.00 | 75.85 | 9.50 | 4.96 | 4.31 | 8.37
SD | 6.76 | 6.81 | 8.11 | 7.09 | 4.55 | 3.82 | 4.83 | 4.34 | 12.08 | 4.96 | 7.12 | 12.76
N | 145 | 128 | 178 | 217 | 145 | 128 | 178 | 217 | 145 | 128 | 178 | 217
Fraction (%) | 33.3 | 32.1 | 32.1 | 32.2 | 33.3 | 32.1 | 32.1 | 32.2 | 33.3 | 32.1 | 32.1 | 32.2
p-value 111Wilcoxon signed-rank tests for matched pairs performed with SPSS version 25 | $<0.001$ | $<0.001$ | $<0.001$
Pearson’s $\rho$ | 0.971 | 0.970 | 0.971 | 0.974 | 0.933 | 0.926 | 0.945 | 0.942 | 0.894 | 0.970 | 0.890 | 0.930
Effect size, dz 222Effect size dz calculated with G*Power version 3.1.9.7 [30] | 0.884 | 0.816 | 0.716 | 0.794 | 0.946 | 0.921 | 0.849 | 0.925 | 0.537 | 0.551 | 0.441 | 0.422
|  | Ratio OFF/ON | 1.47 | 1.35 | 1.54 | 1.35

##  IV Discussion

The SAFTE-FAST model outputs and most of the productivity metrics showed a
consistent reduction in the comparison between early 2019 and 2020, as
depicted in Table 3. However, such finding does not allow an unambiguous
conclusion about possible improvements of fatigue management policies from the
operators, given that the productivity metrics of $DT$ and $N_{crew}$ are also
lower ($p<0.010$) for early 2020. So, it is likely that this workload
reduction reflected positively in the model outputs of $EM_{C}$, $RM_{C}$ and
$FHA_{C}$ ($p<0.001$ in all cases), but did not change quite substantially the
root causes of fatigue given by $N_{NS}$ and $N_{wocl}$ for February
($p=0.091$ and 0.058) and mid-March ($p=0.279$ and 0.159), respectively. These
results show that the SF outputs are quite sensitive to minor changes in
$N_{NS}$ and $N_{wocl}$. For instance, for January 2020, the average value of
$N_{wocl}$ is 6% lower than for 2019, but the average $FHA_{C}$ is 34% lower.
For mid-March 2020, the average $N_{wocl}$ is 7% lower than the 2019 average,
but without a significant group effect ($p=0.159$). On the other hand, the
average $FHA_{C}$ dropped 34% in the same pair of samples ($p<0.001$).
The fatigue indicators of $EM_{C}$ and $t_{awake}^{max}$ show non-linear
relationships with the productivity metric of the number of night shifts
$N_{NS}$ (see Table 4), which has an adverse effect on the flight schedules
and drives the worst fatigue scores. Exceeding 10 night shifts in a 30-day
time interval causes an average maximum equivalent time awake higher than 24
hours, or, equivalently, an average maximum sleep deficit of more than 8
hours. Indeed, Lamond and Dawson have found [34] that 20-25 hours of
continuous wakefulness can be associated with decrements in performance scores
related with reasoning and attention, and that these degradations could be
comparable for individuals with a blood alcohol concentration of 0.10 %. The
adverse effects of long periods of wakefulness were also pointed as a probable
cause for aviation accidents. The National Transportation Safety Board (NTSB)
concluded that fatigue was a probable cause for the accident of American
International Airways flight 808 in Guantanamo Bay on August 18, 1993 [35].
The NTSB final report determined that ”…the probable causes of this accident
were the impaired judgement, decision-making, and flying abilities of the
Captain and flightcrew due to the effects of fatigue…”. In fact, the analyses
of the sleep/wake periods revealed that the Captain had been awake for 23.5
hours within the 28.5 hours prior to the accident [35, 36]. Consequently, our
finding supports the recommendation that flight schedules should be planned
with the lowest achievable number of night shifts, and not exceeding
$N_{NS}=10$ within a 30-day time interval.
The $FHA_{C}$ also presents a non-linear relationship with the number of
departures and landings within 2 and 6 a.m., $N_{wocl}$ (see Table 4). This
result shows that cumulative fatigue builds up quadratically with the number
of WOCL operations, reinforcing its adverse impact on the overall fatigue
score for a given individual within a given time interval. Our model estimate
for the monthly averaged $FHA_{C}$ for all the 30-day epochs of 2019
reproduces quite reasonably, except for January 2019, several structures that
appear in the data (see Fig. 3), which present huge variations month by month.
Consequently, our model approach allows the calculation of $\langle
FHA_{C}\rangle$ for any given $N_{wocl}$ distribution, representing a suitable
method for fatigue risk assessment. For the specific case of January 2019,
however, our model is not able to reproduce the datum, which is significantly
above the average figures found in 2019.
The $N_{wocl}$ distributions (see the insert of Fig. 3 for a typical
distribution of February 2020) drive the cumulative fatigue in rosters and
should be concentrated within the lowest possible $N_{wocl}$ values. In fact,
among all 2019 rosters, only 0.4% present $16\leq N_{wocl}\leq 22$ and are
associated with an average $FHA_{C}$ of $40.0\pm 3.9$ min (see Fig. 2).
Consequently, it is highly recommended that scores of $N_{wocl}>15$ are
avoided in rosters, given its huge impact on overall fatigue and its
negligible effect on crew productivity. Furthermore, only 3.6% of the rosters
had more than 10 WOCL operations within a 30-day time interval, giving room
for safety improvements with minimal operational impact. Both the number of
night shifts and the number of WOCL operations deserve a special attention
when building crew rosters and operators should be encouraged to adopt them as
key performance indicators to drive management policies and, whenever
possible, rostering optimization processes. In order to avoid cumulative
fatigue, these optimization processes should consider a dynamical evaluation
of continuous 30-day time periods.
The relative fatigue risk as a function of the number of night shifts
represents the inverse function of $EM_{C}$ and $N_{NS}$, times the parameter
b (see the central panel of Fig. 1). Increasing $N_{NS}$ from 1 to 10
increases the relative risk by 16.9% (95% CI, 16.0-17.8%). Additionally,
increasing $N_{NS}$ from 10 to 13 increases the risk by 5.5% (95% CI,
3.5-7.5%). Once again, it is quite evident the safety benefit of avoiding more
than 10 night shifts within a 30 days time interval.
The SF effectiveness as a function of the time of the day shows a relevant
decrease within 11:45 p.m and 09:15 a.m, reaching its maximum and minimum
scores around 8 p.m. and 4 a.m., respectively. Moreover, the SF effectiveness
drops below 79% within the WOCL period (from 2 to 6 a.m.), reinforcing the
relevance of effective fatigue risk mitigation policies within these less
favourable hours of the day. Among the several fatigue countermeasures deeply
discussed in Refs. [5, 37], controlled rest does represent an effective method
to mitigate fatigue. As shown quite extensively in the literature [38, 39, 40,
41], naps have a consistent positive impact to mitigate the adverse effects of
sleep loss and/or circadian disruptions. Unfortunately, the Brazilian
regulations (RBAC 117) do not allow the use of controlled rests for minimum
crew, which is allowed, for instance, in Australia, Bolivia, Canada, China,
Europe, Israel, New Zealand, Turkey, and the United Arab Emirates [42].
Another relevant drawback of not having controlled rest allowed by the
regulatory framework is the potentially hazardous occurrence of unintentional
naps during flight operations. In fact, a recent Brazilian study [43] found a
prevalence of 57.8% of unplanned sleep in a sample of Brazilian pilots, making
explicit the need of a regulatory review. It is worth-mentioning, however,
that the controlled rest should not be adopted with the intent of increasing
flight and/or duty time limitations, but exclusively for fatigue mitigation
purposes.
The relative fatigue risk as a function of the time of the day is proportional
to the inverse of the effectiveness and has a maximum value around 4 a.m. (see
the lower panel of Fig. 4). Our averaged values for the RFR, normalized to
unit within 18h00 and 23:59, agree qualitatively with the objective
measurements of pilot errors in the cockpit [33]. However, the comparison
between these results should be done with caution. Firstly because pilot
errors along the time of the day are not exclusively a consequence of fatigue.
Secondly because our relative risk estimate is not parametrized as the
probability of human errors in a complex aviation environment, but rather by
the probability of railroad accidents. In that sense, the pilot errors
reported by Mello et al. [33] are more closely related with cognitive mishaps,
besides several other human factor issues not exclusively related with fatigue
(see the Limitations Section). Our calculations for the risk exposure, given
by the probability of crewing events as a function of the time of the day, are
a factor two (14%) higher than the figures reported by Mello et al. [33] (7%)
within 0h00 and 05h59, showing a relevant change of the Brazilian Commercial
aviation flight schedules from 2005 to 2019.
Tailored analyses of the SF inputs related with afternoon naps prior to night
shifts, commuting from home to station (and vice-versa) and the advanced
bedtime feature of the model were investigated for two low and two high
productivity months of 2019 using the responses of the questionnaire. The
rosters for the Ids who reported not used to take afternoon naps prior to
night shifts, two hours of commuting and not used to advance the bedtime prior
to early-starts shifts were run with the standard and the tailored
parametrizations, showing relevant group effects ($p<0.001$) for $EM_{C}$,
$RM_{C}$ and $FHA_{C}$ in Wilcoxon signed-rank tests for matched pairs (see
Table 5). The average $FHA_{C}$ increases by 43 to 63% when discarding the
afternoon naps, 14 to 21% when increasing the commuting from one to two hours
and 35 to 54% when switching off the advanced bedtime criterion, thus showing
the high sensitivity of the SF model to these input parameters.
Given that the outbreak of the Covid-19 pandemic in Brazil coincided with the
new rules prescribed by the RBAC 117 (March of 2020), the impacts of the new
regulatory framework are still unknown, motivating the acquisition of more
data to shed light on this issue, as scheduled flights and the commercial
aviation industry resume their pre-pandemic levels.

##  V Limitations of the study

The main limitation of this study is related to the model dependency of all
the findings and results. Furthermore, the SF inputs and constraints are set
in accordance with subjective assessments from the questionnaire, operational
experiences and/or educated guessing. For this reason, objective sleep
measurements from actigraphy, for instance, would be highly desirable to
provide more accurate estimates for the relevant model inputs and criteria.
However, these objective measurements are beyond the scope of this work, which
is exclusively dedicated to model analyses.
Other minor limitations are the non-inclusion of home standby duties and
unwind periods when analysing rosters. The home standby events were not taken
into account in our model calculations given the uncertainties of the expected
amount and quality of sleep. This decision was taken to avoid bias, since the
SAFTE-FAST model prevents any sleep event during the entire standby
activities. This does not seem very realistic during the night time, as most
aircrew workers stay at their homes or at an adequate rest facility. The
unwind periods, which encompass the elapsed time from the end of commuting
(station to hotel, station to home or station to rest facility) up to the
start of the rest period, were also not included. These periods may vary
considerable from person to person and include personal needs of hygiene,
eating, social activities in preparing for sleep. Such limitations make clear
that the fatigue outcomes obtained should be interpreted as lower bounds of
fatigue, since some of the crew members might have poor or actually no sleep
during home standby duties, as well as relevant unwind episodes at home, hotel
or rest facility.
Another relevant limitation is related with the extrapolation of the
probability of railroad accidents for the aviation scenario. Aviation
accidents have a low absolute probability, making it difficult to establish a
relationship, for instance, between the SAFTE-FAST effectiveness and human
factor accidents with the desirable statistics, as the one obtained in Ref.
[24]. Indeed, the investigation of 55 human-factor accidents in aviation [44]
demonstrates a relative incidence (accidents proportion per exposure
proportion) 5 times higher for duties with 13 hours or more, when compared
with duties up to 9 hours. However, these data do not allow the delineation of
statistically relevant relationships between fatigue outcomes and accident
risks, since only eleven accidents occurred above 10 hours in duty. In this
regard, the comparison of our relative risk ratios as a function of the time
of the day with objective measurements of pilot errors in the cockpit [33]
(see the upper panel of Fig. 5) should be done with caution and under a
qualitative approach.

##  VI Conclusions

This work adopts a modelling approach to provide a comprehensive statistical
analysis of the root causes of fatigue in a robust sample of aircrew rosters
of the Brazilian regular aviation, derived from the Fadigômetro database. The
SAFTE-FAST fatigue outputs and some productivity metrics delineate an overall
fatigue profile for minimum crew, which show a workload decrease comparing
early 2019 and 2020. The rosters are fully characterized by non-linear
relationships between the SAFTE-FAST variables of minimum effectiveness (and
the maximum equivalent time awake) and the number of night shifts, as well as,
the fatigue hazard area and the number of departures and landings within 2 and
6 a.m. (WOCL period), all considered during the critical phases of flight. The
95% confidence intervals for all the fittings were calculated with the
covariance matrix of the fitted parameters and using standard uncertainty
propagation techniques. The several structures found for the monthly averaged
fatigue hazard areas are consistently interpreted using the distributions of
WOCL operations. The relative fatigue risk increases by 23.3% (95% CI,
20.4-26.2%) increasing the number of night shifts from 1 to 13. Moreover, the
relative risk ratios as a function of the time of the day agree qualitatively
with pilot errors in the cockpit. On the other hand, the risk exposure found
in this work (14%) is a factor two higher than the figures reported by Mello
et al. [33]. Tailored analyses of some key SAFTE-FAST inputs were done by
switching off afternoon naps prior to night shifts, increasing the commuting
from home to station (and vice-versa) from 1 to 2 hours and switching off the
advanced bedtime criterion of the model, showing significant group effects
($p<0.001$) for all variables when compared with the standard parametrization.
Such finding shows the high sensitivity of the model to these parameters and
the need of a deeper investigation to determine more accurately the associated
fatigue risk factors. The impact on fatigue caused by the regulatory change
with RBAC 117 is still unknown, given the time coincidence with the Covid-19
outbreak in Brazil by mid-March 2020. More studies - preferably aggregating
objective sleep measures from actigraphy - are very welcome to provide more
stringent constraints to the model inputs and criteria.

##  VII CRediT author statement

Tulio E. Rodrigues: Conceptualization, Methodology, Validation, Formal
analysis, Data Curation, Writing - Original Draft and Project Administration.
Frida M. Fischer: Conceptualization, Methodology, Writing - Review & Editing,
Supervision. Otaviano Helene: Methodology, Formal analysis, Writing - Review &
Editing, Supervision. Eduardo Antunes: Conceptualization, Validation, Data
Curation, Writing - Review & Editing. Eduardo Furlan: Validation, Data
Curation, Writing - Review & Editing. Eduardo Morteo: Conceptualization,
Validation, Data Curation, Writing - Review & Editing. Alfredo Menquini:
Conceptualization, Validation, Data Curation, Writing - Review & Editing. João
Lisboa: Validation, Data Curation, Writing - Review & Editing. Arnaldo Frank:
Writing - Review & Editing. Alexandre Simões: Writing - Review & Editing.
Karla Papazian: Data Curation. André F. Helene: Conceptualization,
Methodology, Writing - Review & Editing, Supervision.

##  VIII Acknowledgment

We thank the Brazilian Association of Civil Aviation Pilots (ABRAPAC), Gol
Aircrew Association (ASAGOL), LATAM Aircrew Association (ATL) and the National
Aircrew Union (SNA) for their financial support; Mr. Denys Sene, from IASERA,
for the development and support to the roster conversion web-based platform;
to Dr. Steven Hursh for the fruitful scientific exchanges and contributions to
the manuscript and staff at Institutes for Behavior Resources (IBR) for the
SAFTE-FAST customization for the hazard area calculation. We also thank the
National Commission of Human Fatigue (CNFH) and Azul Linhas Aéreas Brasileiras
for their institutional support in promoting, endorsing and encouraging the
study within the aviation community. We finally thank all the crew members who
voluntarily agreed to participate in the study.

##  IX Supplementary Section

###  IX.1 Most frequent locations of the roster’s sample

The dominant domestic short-haul characteristic of the roster’s sample is
clearly shown in Figure 6, which presents the fraction of departures and
landings for the airports with more than 0.5% of all the 394,970 flight
operations of 2019. Buenos Aires (EZE), with a frequency around 0.8%, stands
alone as the only foreign destination among the 31 most frequent locations.
Congonhas (CGH), Guarulhos (GRU), Campinas (VCP), Confins (CNF), Santos Dumont
(SDU) and Brasilia (BSB) altogether comprise 49.1% of the total flight
operations (Crewing events only).

Figure 6:  Percentage of departures and arrivals for the airports with more
than 0.5% of the total operations of 2019.

###  IX.2 Epochs for the analyses

Exact 30 and 15-day epochs were adopted to standardize the extraction of
flight schedules, given that fatigue hazard area and duty time have a
cumulative character. Also, the number of night shifts, consecutive night
shifts, crewing/working events and WOCL operations also depend on the time
interval. Even the SAFTE-FAST minimum effectiveness and minimum sleep
reservoir depend on the time interval, as longer months have a higher
probability for lower scores by chance. Table 6 shows the 30 and 15-day epochs
adopted in this work.

Table 6:  30 and 15-day epochs adopted for the extraction of flight schedules from the Fadigômetro database. Period | Begin date111mm/dd/yy hh:mm | End date111mm/dd/yy hh:mm | time interval
---|---|---|---
(days)
Jan-19 | 1/1/19 0:00 | 1/31/19 0:00 | 30
Feb-19 | 1/31/19 0:00 | 3/2/19 0:00 | 30
Mar-19 | 3/2/19 0:00 | 4/1/19 0:00 | 30
Apr-19 | 4/1/19 0:00 | 5/1/19 0:00 | 30
May-19 | 5/1/19 0:00 | 5/31/19 0:00 | 30
Jun-19 | 5/31/19 0:00 | 6/30/19 0:00 | 30
Jul-19 | 7/1/19 0:00 | 7/31/19 0:00 | 30
Aug-19 | 8/1/19 0:00 | 8/31/19 0:00 | 30
Sep-19 | 8/31/19 0:00 | 9/30/19 0:00 | 30
Oct-19 | 10/1/19 0:00 | 10/31/19 0:00 | 30
Nov-19 | 10/31/19 0:00 | 11/30/19 0:00 | 30
Dec-19 | 12/1/19 0:00 | 12/31/19 0:00 | 30
Jan-20 | 1/1/20 0:00 | 1/31/20 0:00 | 30
Feb-20 | 1/31/20 0:00 | 3/1/20 0:00 | 30
Mar-19 (1/2) | 3/1/19 0:00 | 3/16/19 0:00 | 15
Mar-20 (1/2) | 3/1/20 0:00 | 3/16/20 0:00 | 15

###  IX.3 SAFTE-FAST parameters and criteria

In this section we describe all the parameters and criteria - adopted to mimic
behaviours and operational routines before, during and after the working and
crewing activities of the Brazilian civil aviation aircrews (Part 121
Passenger Operations) - for the runs with the SAFTE-FAST software version
4.0.3.207.

####  IX.3.1 SAFTE-FAST input parameters

For most cases, the start (check-in) and the end (check-out) of the duty
periods were captured directly from the rosters. For some rosters format,
however, these information were not available and we set 60 minutes prior to
the take-off for the check-in and 30 or 45 minutes after the landing for the
check-out, depending if the flight sector was domestic or international,
respectively. These figures follow the usual practice for scheduled flights in
Brazil and also comply with current regulations [11, 12].
For the input commuting we set a standard 60-minute time interval from home to
station, hotel to station and rest facility to station and vice-versa. We also
applied an extended commuting of 120 minutes from home to station and vice-
versa for some of the runs, based upon the responses of the questionnaire.
For the preparation time, defined as the average time the crew member usually
takes to prepare himself for the flight, we set 60 minutes either at home,
hotel or rest facility.
Owing to the lack of data or reliable information, the unwind time at home,
hotel or rest facility was set to zero in our SAFTE-FAST input (see the
Limitation Section).
Regarding the Auto-Sleep controls of the SAFTE-FAST, we have included both the
Auto-Nap and the Advanced bedtime functions. The Auto-Nap function adds
automatically an afternoon nap prior to night shifts. The amount of nap
depends on the continuous wakefulness period until the last sleep event. For 8
to 10 hours, 10 to 12 hours, 12 to 14 hours or more than 14 hours since the
last sleep event, the software adds 60, 90, 120 or 180 minutes of nap,
respectively. The Advanced bedtime function allows the software to anticipate
the beginning of sleep if an early start would significantly shorten the
typical sleep quantity of 8 hours. Both the Auto-Nap and the Advanced bedtime
functions can be switched off, as shown for the tailored analyses presented in
Table 5. All the sleep metrics adopted in the SAFTE-FAST runs are summarized
in Table 7.

Table 7:  Sleep metrics adopted in the SAFTE-FAST runs. SAFTE-FAST Auto-Sleep | Value or Status
---|---
Controls and Parameters
AUTO-NAP function | ON (standard)
OFF (tailored)
Advanced bedtime function | ON (standard)
OFF (tailored)
Normal bedtime | 11 p.m.
Minimum Sleep Duration | 60 minutes
Maximum Wok Day Sleep | 8 hours
Maximum Rest Day Sleep | 9 hours
Max Recovery Nap 111Recovery Nap is automatically added following work duties that end between Normal bedtime and the start of the Awake Zone if the sleep in the past 16 hours is not optimal. | 210 minutes
Awake Zone 222The period of the day that the software prevents sleep events, except for afternoon naps prior to night shifts or advanced bedtime events due to early-start shifts. | 1 to 8 p.m.
Sleep quality (home, hotel and rest facility) | Excellent
Inflight Sleep | Not included

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# RPC based tracking system at CERN GIF++ facility

K. Mota Amarilo<EMAIL_ADDRESS>A. Samalan  M. Tytgat  M. El Sawy  G.A.
Alves  F. Marujo  E.A. Coelho  E.M. Da Costa  H. Nogima  A. Santoro  S.
Fonseca De Souza  D. De Jesus Damiao  M. Thiel  M. Barroso Ferreira Filho  A.
Aleksandrov  R. Hadjiiska  P. Iaydjiev  M. Rodozov  M. Shopova  G. Soultanov
A. Dimitrov  L. Litov  B. Pavlov  P. Petkov  A. Petrov  E. Shumka  S.J. Qian
H. Kou  Z.-A. Liu  J. Zhao  J. Song  Q. Hou  W. Diao  P. Cao  C. Avila  D.
Barbosa  A. Cabrera  A. Florez  J. Fraga  J. Reyes  Y. Assran  M.A. Mahmoud
Y. Mohammed  I. Crotty  I. Laktineh  G. Grenier  M. Gouzevitch  L. Mirabito
K. Shchablo  I. Bagaturia  I. Lomidze  Z. Tsamalaidze  V. Amoozegar  B.
Boghrati  M. Ebraimi  M. Mohammadi Najafabadi  E. Zareian  M. Abbrescia  G.
Iaselli  G. Pugliese  F. Loddo  N. De Filippis  R. Aly  D. Ramos  W.
Elmetenawee  S. Leszki  I. Margjeka  D. Paesani  L. Benussi  S. Bianco  D.
Piccolo  S. Meola  S. Buontempo  F. Carnevali  L. Lista  P. Paolucci  F.
Fienga  A. Braghieri  P. Salvini  P. Montagna  C. Riccardi  P. Vitulo  E.
Asilar  J. Choi  T.J. Kim  S.Y. Choi  B. Hong  K.S. Lee  H.Y. Oh  J. Goh  I.
Yu  C. Uribe Estrada  I. Pedraza  H. Castilla-Valdez  A. Sanchez-Hernandez  R.
L. Fernandez  M. Ramirez-Garcia  E. Vazquez  M. A. Shah  N. Zaganidis  A. Radi
H. Hoorani  S. Muhammad  A. Ahmad  I. Asghar  W.A. Khan  J. Eysermans  F.
Torres Da Silva De Araujo
on behalf of the CMS Muon Group

###### Abstract

With the HL-LHC upgrade of the LHC machine, an increase of the instantaneous
luminosity by a factor of five is expected and the current detection systems
need to be validated for such working conditions to ensure stable data taking.
At the CERN Gamma Irradiation Facility (GIF++) many muon detectors undergo
such studies, but the high gamma background can pose a challenge to the muon
trigger system which is exposed to many fake hits from the gamma background. A
tracking system using RPCs is implemented to clean the fake hits, taking
profit of the high muon efficiency of these chambers. This work will present
the tracking system configuration, used detector analysis algorithm and
results.

###### keywords:

Resistive plate chambers , CMS Experiment , gaseous detectors , HL-LHC

###### PACS:

0000 , 1111

###### MSC:

0000 , 1111

††journal: Nuclear Instruments and Methods in Physics Research A

[a]Ghent University, Dept. of Physics and Astronomy, Proeftuinstraat 86,
B-9000 Ghent, Belgium. [aa]Université Libre de Bruxelles, Avenue Franklin
Roosevelt 50-1050 Bruxelles, Belgium. [b]Centro Brasileiro Pesquisas Fisicas,
R. Dr. Xavier Sigaud, 150 - Urca, Rio de Janeiro - RJ, 22290-180, Brazil.
[c]Dep. de Fisica Nuclear e Altas Energias, Instituto de Fisica, Universidade
do Estado do Rio de Janeiro, Rua Sao Francisco Xavier, 524, BR - Rio de
Janeiro 20559-900, RJ, Brazil. [d]Bulgarian Academy of Sciences, Inst. for
Nucl. Res. and Nucl. Energy, Tzarigradsko shaussee Boulevard 72, BG-1784
Sofia, Bulgaria. [e]Faculty of Physics, University of Sofia,5 James Bourchier
Boulevard, BG-1164 Sofia, Bulgaria. [f]School of Physics, Peking University,
Beijing 100871, China. [g]State Key Laboratory of Particle Detection and
Electronics, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100049, China. [gg]University of Chinese Academy of Sciences, No.19(A)
Yuquan Road, Shijingshan District, Beijing 100049, China. [h]Universidad de
Los Andes, Carrera 1, no. 18A - 12, Bogotá, Colombia [i]Egyptian Network for
High Energy Physics, Academy of Scientific Research and Technology, 101 Kasr
El-Einy St. Cairo Egypt. [ii]Suez University, Elsalam City, Suez - Cairo Road,
Suez 43522, Egypt. [j]Center for High Energy Physics(CHEP-FU), Faculty of
Science, Fayoum University, 63514 El-Fayoum, Egypt. [jj]Department of Physics,
Faculty of Science, Ain Shams University, Cairo, Egypt. [jjj] Physics
Department Faculty of Science Helwan University Ain Helwan 11795 Cairo Egypt.
[k]Univ Lyon, Univ Claude Bernard Lyon 1, CNRS-IN2P3, IP2I Lyon, UMR
5822,F-69622, Villeurbanne, France. [l]Georgian Technical University, 77
Kostava Str., Tbilisi 0175, Georgia. [m]School of Particles and Accelerators,
Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531,
Tehran, Iran. [mm]School of Engineering, Damghan University, Damghan,
3671641167, Iran. [n]INFN, Sezione di Bari, Via Orabona 4, IT-70126 Bari,
Italy. [o]INFN, Laboratori Nazionali di Frascati (LNF), Via Enrico Fermi 40,
IT-00044 Frascati, Italy. [p]INFN, Sezione di Napoli, Complesso Univ. Monte S.
Angelo, Via Cintia, IT-80126 Napoli, Italy. [pp]Dipartimento di Ingegneria
Elettrica e delle Tecnologie dell’Informazione - Università Degli Studi di
Napoli Federico II, IT-80126 Napoli, Italy. [q]INFN, Sezione di Pavia, Via
Bassi 6, IT-Pavia, Italy. [qq]INFN, Sezione di Pavia and University of Pavia,
Via Bassi 6, IT-Pavia, Italy. [r]Hanyang University, 222 Wangsimni-ro, Sageun-
dong, Seongdong-gu, Seoul, Republic of Korea. [s]Korea University, Department
of Physics, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Republic of Korea. [t]Kyung
Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of
Korea. [u]Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-
do 16419, Republic of Korea. [v]Benemerita Universidad Autonoma de Puebla,
Puebla, Mexico. [w]Cinvestav, Av. Instituto Politécnico Nacional No. 2508,
Colonia San Pedro Zacatenco, CP 07360, Ciudad de Mexico D.F., Mexico.
[x]Universidad Iberoamericana, Mexico City, Mexico. [y]Sultan Qaboos
University, Al Khoudh,Muscat 123, Oman. [z]National Centre for Physics, Quaid-
i-Azam University, Islamabad, Pakistan. [za]Massachusetts Institute of
Technology, 77 Massachusetts Ave, Cambridge, MA 02139, United States. [zc]III.
Physikalisches Institut (A), RWTH Aachen University, Sommerfeldstrasse
D-52056, Aachen, Germany.

##  1 Introduction

The Resistive Plate Chambers (RPC) act as muon triggering detector in the Muon
System of the Compact Muon Solenoid (CMS) experiment [1]. With the coming
upgrade of the Large Hadron Collider (LHC) machine, the High Luminosity LHC
(HL-LHC) [2], many detector systems are preparing to improve their
capabilities. In particular, the CMS RPC project has two important planned
activities – the replacement of the off-detector electronics (called link
system) and the extension of the RPC coverage from $|\eta|=$ 1.9 to 2.4 with
the new improved RPC (iRPC) detectors [3].

To study the performance and stability of RPCs in the HL-LHC conditions, tests
are taking place in the CERN Gamma Irradiation Facility (GIF++), where a high
energy particle beam (normally muons) and photons from a gamma source (13 TBq,
137Cs) are combined [4]. The maximum expected background rate for the RPCs in
the current CMS Muon system is 600 Hz/cm2 and for the new iRPCs it goes up to
2 kHz/cm2 (including the safety factor of three) [3]. Such high rates can pose
a challenge to the measurement, as the fake hits can bias the data-taking.

All results shown in this work were recorded during GIF++ test beam in October
2021.

##  2 Experimental Setup

Figure 1 shows a representation of the setup in GIF++. There are two trolleys
where the RPC detectors are placed for irradiation. In addition to the RPCs,
two scintillators are placed on each trolley to trigger on the muon beam. The
data acquisition is performed using a CAEN Time-to-Digital Converter (TDC)
module of type V1190A where the frontend electronics of the chambers are
connected. A V1718 VME controller module is responsible for the communication
between the TDC and the computer where the data are stored. To host the VME
controller and the TDC a 6U VME 6021 crate is used.

Figure 1: Experimental setup at GIF++.

In the trolley farther from the gamma source, there are two tracking RPC
chambers with their strip planes oriented perpendicular to each other to allow
measurement in two directions. The chambers used are the following:

  * 1.

Tracking chambers: Referred to as GT1 and GT2, these are double gap chambers
made of 2 mm thick High Pressure Laminate (HPL, also known as bakelite). They
are equipped with a strip plane with 32 strips of 1.45 cm pitch. The signals
are read with the CMS FrontEnd electronics with threshold set to 150 fC.

  * 2.

Test Chamber: Referred to as KODEL-C, this is also a double gap chamber made
of HPL with 1.4 mm thickness. It is equipped with a strip plane with 32 strips
of 1.95 cm pitch and custom FrontEnd electronics with threshold set to 75 fC.

All the chambers are flushed with the CMS RPC standard gas mixture (95.2%
freon ($C_{2}H_{2}F_{4}$), 4.5% isobutane ($iC_{4}H_{10}$), and 0.3% sulphur
hexafluoride ($SF_{6}$)) with a relative humidity of $\approx$40%. The
tracking chambers are always powered on with the high voltage (HV) working
point (WP) applied to their electrodes.

##  3 Tracking algorithm

To enable the tracking analysis, at least one hit is required in both tracking
chambers inside the muon time window defined by a Gaussian fit, as indicated
in Fig. 2. A 2D hit profile is made to check their alignment with the muon
beam, as shown in Fig. 3. The hit profile is also determined for the test
chamber and it is used for alignment between the chambers.

Figure 2: Hits time profile of the tracking chamber GT2. The time window where
the hits are accepted in the analysis is represented in the red hatched box.
Figure 3: 2D hit profile of the strips signals for the hits in the muon time
window.

The tracking algorithm relies on the assumption that the beam is perpendicular
to the strip plane, therefore it is only needed to extrapolate the position of
the hit from the tracking to the test chamber and check for a matching hit.
For every event, the following steps are taken:

  1. 1.

Perform the clusterization of the hits in the tracking chambers, where events
with more than one cluster are rejected. The cluster barycentres are defined
as the mean position in the cluster;

  2. 2.

Perform the clusterization for the test chambers and calculate the clusters’
barycentres;

  3. 3.

Form a perpendicular track starting from the tracking cluster barycentre;

  4. 4.

Check for a match in any cluster on the test chamber.

Figure 4 shows an example of event where the analysis was performed and a
matching hit was found.

Figure 4: Example of one event in which the hit on tracking chamber was
matched on the test chamber. The strips in red represent the hits and the
point in black is the cluster barycentre.

##  4 Performance of the Tracking Algorithm

Efficiency curves of the test chambers were used to evaluate the validity of
the tracking in rejecting the fake hits caused by the gammas. On Fig. 5 the
efficiency curves are compared for three gamma background conditions. There
are three curves in each plot. The black curve is calculated without the
tracking, taking into consideration all the hits in the muon time window. For
the blue one, only the hits that passed the tracking criteria were considered.
Finally, for the red curve, the HV was recalculated to remove the voltage drop
caused by the resistance of the electrodes - this correction decouples the
shift to the right of the curve on higher cluster rates, caused by the
increase of the current. Therefore, HVgas is the effective HV applied to the
gas volume.

As expected, in Fig. 5(a), where the data were taken in a run with source OFF,
the three curves are equivalent since the cluster rate (CLR) and the currents
are low. in Fig. 5(b) with CLR $\approx$ 648 Hz/cm2, a shift to the right on
the tracking corrected curve is observed, and it is much more evident in Fig.
5(c) with CLR $\approx$ 1.8 kHz/cm2. The increase of the maximum efficiency on
the raw efficiency curve from the Fig. 5(b) to 5(c) indicates high gamma
contamination.

(a)

(b)

(c)

Figure 5: Efficiencies and their sigmoid fits measured at three photon fluxes
with measured at the working-point high voltages gamma cluster rates of 1.804
kHz (a), 0.645 kHz (b), and 1.48 Hz (c), respectively. The curve in black is
the efficiency calculated with all hits inside the muon window, the blue one
is with applied tracking correction and the one in red – with tracking and
resistance correction.

In Fig. 6(a), it is possible to see the curves with tracking and resistance
correction. The shift to the right is caused by the reduction of the gas gain
at higher rates, while the drop in the maximum efficiency is caused by the
dead-time of the electronics. In Fig. 6(b), no resistance correction is
applied, so the main reason for the shift is the voltage drop over the
electrode’s resistance, coupled with the reasons mentioned before.

(a)

(b)

Figure 6: Efficiency curves for various gamma background rates. In (a) the HV
applied is corrected only by pressure and temperature (HVeff), while in (b)
the HV is also corrected by the resistance of the gaps (HVgas)

.

##  5 Conclusion

The implementation of the tracking system was motivated by the necessity to
test the CMS RPC chambers at the conditions of the HL-LHC. The results show
that the tracking system performs very well to remove fake hits from the gamma
background, even at rates as high as 2 kHz/cm2. The test chamber performed
very well and showed increase on the working point of $\approx$650 V with
efficiency loss of $\approx$ 7.5%, using the custom electronics with threshold
of 75 fC. This system is currently being used for the ageing studies of the
CMS RPC system.

## Acknowledgements

We would like to thank our colleagues from CERN Gamma Irradiation facility. We
would also like to acknowledge the enduring support for the Upgrade of the CMS
detector and the supporting computing infrastructure provided by the following
funding agencies: FWO (Belgium); CNPq, CAPES and FAPERJ (Brazil); MES and BNSF
(Bulgaria); CERN; CAS, MoST, and NSFC (China); MINCIENCIAS (Colombia); CEA and
CNRS/IN2P3 (France); SRNSFG (Georgia); DAE and DST (India); IPM (Iran); INFN
(Italy); MSIP and NRF (Republic of Korea); BUAP, CINVESTAV, CONACYT, LNS, SEP,
and UASLP-FAI (Mexico); PAEC (Pakistan); DOE and NSF (USA).

## References

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  * [2] O. Aberle, et al., High-Luminosity Large Hadron Collider (HL-LHC): Technical design report, CERN Yellow Reports: Monographs, CERN, Geneva, 2020.  doi:10.23731/CYRM-2020-0010.
URL https://cds.cern.ch/record/2749422

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URL https://cds.cern.ch/record/2283189

  * [4] R. Guida, GIF++: The new CERN irradiation facility to test large-area detectors for HL-LHC, in: 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), IEEE, 2015, pp. 1–4.