The growth in worldwide air traffic, including international long-haul flights, national short-haul flights, night flights, and cargo flights, imposes a 24-h work schedule. Performing flight operations at the pace of today’s air traffic relies on shift work, overtime work, work at night, and work in different and numerous time zones, i.e., varied and unbalanced flight crew schedules. These working hours and workload settings can cause disturbances of the circadian rhythm and sleep disorders among flight crew members; this can result in fatigue and can have an impact on the safety of flight operations [1,2]^[1][2]. Fatigue impacts many cognitive abilities such as vigilance, memory, spatial orientation, learning, problem solving, and decision making. In aviation, fatigue has been identified as a hazard to the safety of flight operations. Due to this, fatigue risk has been widely analyzed and assessed. Due to the severity of fatigue risk, it is necessary to implement risk mitigation measures. Aside from the provisions of the Flight Time Limitations (FTL) regulations [3^[3][4],4], a vital role in fatigue risk mitigation is played by the Fatigue Risk Management System (FRMS), which uses various quantification and objectivation methods to measure fatigue [5,6]^[5][6].

The Fatigue Risk Management System (FRMS), as defined by the International Civil Aviation Organization (ICAO), represents a data-driven method of constant monitoring, data collecting, analyzing, and mitigating fatigue-related safety risks in flight operations using scientific methods, previous knowledge, and operational experience [5,7]^[5][7].

The data and information collected regarding crew vigilance and readiness are constantly analyzed by FRMS methods and tools and used to control fatigue-related safety risks in flight operations. FRMS can be established as a standalone system or as a part of a Safety Management System (SMS) [5,8]^[5][8].

The FRMS aims to ensure that the flight crew and cabin crew members are sufficiently vigilant and rested to work at a satisfactory level of performance. The principles and processes of the Safety Management System (SMS) are applied to manage the specific risks associated with a crew member’s level of fatigue ^[8]. In the same manner as SMS, the FRMS aims to achieve a balance between safety, productivity, and cost ^[5]. It seeks to proactively identify opportunities to improve operational processes and reduce risks, as well as to recognize shortcomings after adverse events. The structure of the FRMS is modelled on the SMS basic framework ^[8]. Its basic activities are safety risk management and safety assurance. These basic activities are governed by FRMS policy and supported by FRMS promotion processes ^[5].

SMS and FRMS rely on the concept of an effective reporting culture, where staff are trained and are constantly encouraged to report hazards whenever they are recognized in the work environment ^[9].

The goals of the FRMS are to “manage, monitor and mitigate the effects of fatigue to improve flight crew members’ alertness and reduce performance errors”, as well as to balance safety and productivity ^[10].

As part of the FRMS, the most commonly used methods for the measurement of flight crew fatigue include subjective fatigue scales, psychomotor vigilance tests, actigraphy, predictive models, and sleep diaries [9,11]^[9][11]. The subjective measurement of fatigue is also commonly applied in fatigue reports, which can be used as data-collection tools. Predictive models can be found in modern crew management software; they can warn crew planners about fatigue risk (usually with warning messages and color schemes, from green, meaning no risk, to red, indicating a high fatigue risk). Other objectivation methods have been used in fatigue studies for specific cases when required by an airline (e.g., for certain types of flight operations) [9,11]^[9][11].

2. Background on Research Related to the Impact of Fatigue in Flight Operations

Fatigue is defined as the result of personal and work-related factors [7,18,19,20]^{[7][12][13][14]}. Personal factors are related to age, chronotype (morning type, evening type) [21]^[15], gender, genetic predisposition, and personality, which have an impact on tolerance to shift work [22]^[16]. Individual lifestyle regarding physical activity or inactivity, e.g., the time spent in front of a television or computer, has an effect on the length and quality of sleep [23,24]^[17][18]. For the flight crew, work-related factors refer to shift work that includes early/late/night duties [25]^[19], unpredictable monthly crew schedules (duties can change due to operational reasons, sickness, or other reasons), time zone crossings, standby duties, and others. The listed factors, together with the major biological mechanisms affecting periods of wakefulness and drowsiness (the circadian rhythm, homeostatic sleep pressure, and sleep inertia), can lead to sleep loss and sleep debt. Sleep is a biological need; its main mechanisms are homeostatic sleep pressure and circadian rhythm. A recent study of fatigue phenomena discovered molecular mechanisms controlling the circadian rhythm [26]^[20]. A small sleep debt is needed to fall asleep (“The probability of falling asleep means a combination of two opposing forces: burden of sleep minus the level of excitement” [27]^[21]), but great sleep debt can lead to falling asleep while driving. Performance, as measured by reaction time or the number of mistakes in a given task, is worse among individuals who are sleep deprived [28]^[22]. One study showed slow reaction time and poor performance of motorcycle driving [29]^[23] because of sleep deprivation. Fatigue has physical manifestations (general feeling of tiredness, decreased alertness, an irresistible desire for sleep, microsleep, lethargy, and prolonged reaction time) and mental manifestations (difficulty with memorizing, forgetting information and actions, a lack of concentration, slow understanding, poor decision-making, and apathy). In flight operations, fatigue can be a cause of inaccurate flight procedures, missed radio calls, missed or slow responses to system warnings, routine tasks being performed inaccurately or being forgotten, a loss of situational awareness, microsleeping and task fixation, and poor communication among crew members [1,2,11]^[1][2][11]. In addition, fatigue may affect judgment or performance in the critical phases of flight (take-off/landing), as well as making it difficult to remain alert when the workload is reduced (cruising). Some of the identified causes of fatigue in short-haul operations include restricted sleep due to early duty reporting times, multiple high workload periods during the duty day, multiple sectors, long duty hours, restricted sleep due to short rest breaks, and high-density airspace. Workload elements that may be able to mitigate fatigue risk in flight operations include the length of duty, total flight time, number of sectors, rest period duration, time of day, pattern of duty, rest facilities (management of sleep during layover periods), number of time-zone transitions, and number of consecutive duty days [11,30]^[11][24]. In Europe, traditional fatigue management approaches and ways to protect crew members from excessive fatigue levels are described in the Flight Time Limitations (FTL) regulations [25]^[19]. However, restrictions on work hours are different from country to country giving rise to inconsistencies in terms of restrictions on permitted flight duty, length of rest periods, and other FTL elements [3,4]^[3][4]. Furthermore, the prescriptive nature of these limitations prohibits some elements in a crew’s schedules but allows others that can be very fatigue-inducing. Although the EU FTL [25]^[19] promotes active fatigue risk management systems, it does not oblige airlines to apply a FRMS except in certain specific cases (e.g., the use of reduced rest operations). At the same time, EU FTL also requires airlines to ensure that flight duty periods are planned in a way that enables crew members: to remain sufficiently free from fatigue so that they can operate at a satisfactory level of safety; to take into account the relationship between the frequencies and pattern of flight duty and rest periods and consider the cumulative effects of undertaking long duty hours interspersed with minimum rest; to allocate duty patterns which avoid undesirable practices such as alternating day/night duties in order to minimize serious disruptions of established sleep/work patterns; to provide rest periods of sufficient duration, especially after long flights crossing multiple time zones; and to enable crew members to overcome the effects of their previous duties by the time they start a new flight duty period [11,25]^[11][19]. In the USA, regulations pertaining to the fatigue risk management systems for aviation safety are overseen by the Federal Aviation Administration (FAA). Basic FRMS concepts are prescribed to ensure that aviation industry employees perform their duties safely. They provide information on the components of an FRMS applied to aviation, describe how to implement an FRMS within aviation operations, and define an FRMS as an operator-specific process. While all FRMSs have common elements, the specifics can be tailored according to a given set of conditions. It provides detailed guidance on how to prepare for the FRMS approval process, develop the required documentation, develop and apply fatigue risk management and safety assurance processes, collect and analyze data, and develop flight crew FRMS operations procedures [31]^[25]. Within a FRMS, the most commonly used methods to measure and objectivate flight crew fatigue are [9,11]^[9][11]:

• Subjective fatigue scales (Samn Perelli, Karolinska);
• Psychomotor vigilance tests;
• Actigraphy;
• Predictive models (biomathematical algorithms);
• Sleep diaries.

One of the main data sources for fatigue research, especially in flight operations, is subjective fatigue scales. The application of subjective scales is described in recent research regarding flight crew fatigue and the effect of the length of duty and time of day. In some such studies, pilots reported their subjective fatigue levels using the Samn Perelli scale [32,33]^[26][27]. The subjective measurement of fatigue is also commonly used in fatigue reporting that can, in turn, be used as a data collection tool ^[7]. Other studies have used methods such as actigraphy, sleep diaries, performance vigilance tests, and biomathematical predictive models, where the influence of fatigue was studied via different quantification methods [34,35,36,37]^{[28][29][30][31]}. Predictive models, which warn crew planners about fatigue risk (usually by displaying warning messages and color schemes), can be found in modern crew management software. Besides objectivation methods of quantifying flight crew fatigue, cognitive abilities which deteriorate as fatigue increases, can be measured using chronometric approaches, e.g., an electronic CRD system of standardized chronometric cognitive tests. CRD series have been used in various studies since 1969 [38]^[32]. Information regarding the instruments, methodology, measuring parameters, etc. used in such tests is provided in the CRD handbook [38]^[32]. CRD series have been used for study on psychomotor disturbances in scuba divers [39]^[33]. Another study showed differences between the working abilities of a driver, a train operator, and a dispatcher during day and night shifts [40,41]^[34][35]. CRD series have also been used to evaluate the psychomotor abilities of military pilots [42]^[36] and in research regarding workloads and work efficiency over certain periods of time [43,44]^[37][38]. Recent research has included several innovative approaches, such as assessing the sleep patterns of flight attendants during the off-duty period using a photovoice technique [45]^[39], studying new tools for use by pilots and the aviation industry to manage risks pertaining to work-related stress and wellbeing [46]^[40], analyzing the workloads of aircraft pilots using Heart Rate Variability (HRV) and the NASA Task Load Index questionnaire [47]^[41], applying multimodal analyses of eye movements and fatigue in a simulated glass cockpit environment [48]^[42], studying work type influence on fatigue among air traffic controllers based on data-driven PERCLOS detection [49]^[43], identifying pilot fatigue status based on functional near-infrared spectroscopy [50]^[44], examining fatigue among different crew compositions on long-haul flights during the COVID-19 pandemic [51]^[45], and examining fatigue, work overload, and sleepiness on a sample of commercial airline pilots [52]^[46]. For the purpose of finding correlations among various sets of indicators, causal modeling techniques and methods are used. These methods use datasets of collected data and build causal models that show causal relations among them. Using causal models, specifically, detected causal relations (impacts), it is possible to determine which variables should be modified to obtain the desired performance of targeted indicator(s). Previous research regarding causality and its variations has focused on causal time series analyses [53^[47][48][49],54,55], the causes and origins of human error [56]^[50], assumptions and methods for turning observations into causal knowledge [57]^[51], the human perception of the relationship between cause and effect [58]^[52], the role that human factors play in major aviation accidents [59]^[53], the use of causal models to control and manage aircraft accident risk [60]^[54], graphical causal models that can serve as powerful tools for detecting interrelations between variables [61]^[55], and others. Recent studies have used causal modeling methods to identify causal relationships among aviation hazards in order to define efficient measures to prevent future hazards from turning into adverse events [14,15,16]^[56][57][58].

3. Correlations 

Due to the severity of fatigue risk in flight operations, it is necessary to constantly seek and improve mitigation measures. As discussed, fatigue issues in flight operations have been frequently addressed. Various methods had been adopted to address fatigue related issues. The most commonly used methods include the application of subjective scales in flight crew fatigue research as the main data collection tool, such as in research done by Powell and others in 2007 and 2008. Other studies have included methods such as the actigraphy, sleep diaries, performance vigilance tests, and biomathematical predictive models, such as in research done by Yi and Moochhala in 2013, Powell and others in 2014, Gander and others in 2014, and Van den Berg and others in 2015. Recent research has presented several innovative approaches regarding fatigue and its effects on various aviation employees, such as that conducted by Laovoravit and others in 2019, who used a photovoice technique, new tools to manage risks pertaining to work-related stress and wellbeing by Cahill and others in 2020, the use of heart rate or eye movement measuring equipment by Alaimo and others in 2020 and Naeeri and others in 2021, data driven detection techniques by Zhang and others in 2021, near-infrared spectroscopy by Pan and others in 2022, etc. Cognitive abilities that deteriorate as fatigue increases can be measured with a chronometric approach to measuring cognitive functions, i.e., an electronic CRD system of standardized chronometric cognitive tests, as defined by Drenovac in 2009. CRD series have been used in various studies. CRD series have been used to study psychomotor disturbances among practitioners in various fields. Some studies have used CRD series to evaluate psychomotor abilities and to determine workload and work efficiency during certain periods of time. Meanwhile, a few studies have shown how causal modeling methods can be used to identify causal relations among aviation hazards in order to define efficient mitigation measures to prevent future adverse events, such as research conducted by Roelen in 2008, Liou and others in 2008, Sloman in 2015, Rohrer in 2018, and Bartulović in 2022. Since fatigue is defined as one of the most important aviation hazards, the application of causal modeling techniques has been recognized and implemented in the present study. Hence, this used CRD tests to collect data regarding flight crew mental processing and psychomotor abilities and to detect the presence of fatigue in the defined workload settings. Subjective fatigue scales were used to additionally collect data on the subjective perception of fatigue by flight crews. Finally, to find correlations among defined sets of indicators, causal modeling techniques and methods were used. These methods use datasets of collected data and build models that show causal relations among them. Using causal models, specifically, detecting causal relations (impacts), it is possible to determine which variables should be modified to obtain the desired performance of targeted indicator(s). Against a research background related to the influence of fatigue on flight operations, the focus was to use multiple methods, i.e., objectivation methods such as CRD tests and subjective self-assessment fatigue scales to collect data on flight crew fatigue; statistical analysis methods to analyze the collected data; and causal modeling methods to detect correlations among the obtained fatigue indicators, subjective self-assessment results, and indicators of workload settings in flight operations. The first part of the study used objectivation methods to collect data on flight crew fatigue, i.e., an electronic system of standardized chronometric cognitive tests (CRD tests) and subjective self-assessment surveys on the subjective perception of fatigue (subjective fatigue scales). CRD measurements were conducted using five CRD tests, i.e., CRD 13, i.e., the Spatial visualization test, CRD 241, i.e., Identifying progressive series of numbers, CRD 23, i.e., Complex convergent visual orientation, CRD 324, i.e., Actualization of short-term memory, and CRD 422, i.e., Operative thinking with sound stimuli. Subjects underwent training before taking the actual tests in order to avoid the effect of learning, because the aim was to measure any drop in mental potential due to fatigue. The independent variables represent elements in the workload settings and the results of the subjective self-assessment fatigue scales. All tests were performed anonymously with four male subjects who had been professional airline pilots for the last 11 years. Tests were performed in an improvised CRD laboratory, i.e., in a room of their base airport, where they checked-in and checked-out (pre-flight and post-flight duty). The measurement produced a large database of information regarding the speed, reliability, and stability of each pilot’s mental processing and psychomotor capabilities. This database was used to conduct statistical analyses to examine whether the independent variables of workload settings and subjective states affected mental processing and, consequently, to determine the presence of fatigue. After collecting and normalizing the data, in the second part of the study, a statistical analysis was performed using the ANOVA of the Statistica 10 software. The main hypothesis, repeated for each independent variable, was that there would be no effect on the dependent variables (CRD measures), i.e., efficiency of mental processing. Most of the hypotheses were disproven, i.e., statistical analysis showed that the independent variables (workload settings and subjective states) had an effect on the dependent variables (CRD measures); in other words, workload settings and subjective states affect the appearance of fatigue. The results showed that CRD 422 (Operative thinking with sound stimuli) and CRD 13 (Spatial visualization test) were the most sensitive chronometric instruments in the study in terms of the number of dependent variables with statistical significance at a level of less than 0.05. The most statistically significant differences were recorded in the group of independent variables regarding cumulative workload, followed by the group associated with individual flight duties. The most statistically significant differences were recorded for the independent variables “Duty time in the previous 28 days”, “Flight time in the previous 28 days”, “Duty time in the previous 7 days”, “Sectors in the previous 28 days”, and “Changes in the schedule”. In the final part of the study, correlations were detected among measured flight crew fatigue indicators, indicators of the subjective perception of fatigue, and workload settings, using previously collected and analyzed data regarding flight crew fatigue. To identify correlations (causal links) among all indicators in the dataset, the temporal causal modeling tools in the IBM SPSS Statistics 27 software were used. The dataset used for this part of the study included 135 entries for 23 indicators concerning workload settings, four indicators concerning subjective self-assessments, and eight measured CRD indicators of mental processing, i.e., fatigue indicators. The setup was made in such a way that the independent variables, i.e., workload settings indicators, were the “inputs” in a temporal causal model and the dependent and independent variables were “both inputs and targets”. A temporal causal model of flight crew fatigue indicators, subjective self-assessments, and workload settings parameters was created, with an excellent evaluation of the model fit using the R-squared criterion (whose values ranged from 0.91 to 0.95). The Fatigue index is the quotient of the initial ballast and final ballast; it is derived indicator of the direction of changes in the speed (an acceleration or deceleration) of solving tasks in a particular test, i.e., it represents endurance, and consequently, fatigue. A value of this index greater than 1 indicates the presence of fatigue. Hence, in the temporal causal model, the focus was to observe which indicators correlated with this particular indicator. The results showed that the Fatigue index correlates with five workload settings indicators, namely “Number of individual days off in the previous 28 days”, “Rest length”, “Local night in daily rest”, “Changes in the schedule”, and “Sectors in the previous 7 days”. Additionally, it correlates with three subjective self-assessment indicators, i.e., “Energy level”, “Self-confidence”, and “Anxiety level”; and five other CRD indicators, namely, “Number of errors”, “Total test-solving time”, “Maximum test-solving time”, “Total ballast”, and “Final ballast”.