Correlations among Fatigue Indicators, Subjective Perception of Fatigue, and Workload Settings in Flight Operations

: Conducting ﬂight operations at the pace of air trafﬁc relies on shift work, overtime work, work at night, work in different and numerous time zones, and unbalanced ﬂight crew schedules. Such 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. 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. This paper describes objectivation methods for data collecting processes regarding ﬂight crew fatigue, using an electronic system of standardized chronometric cognitive tests and subjective self-assessment surveys on the subjective perception of fatigue. The data collected were analyzed using statistical methods to identify and quantify elements that affect the appearance of fatigue. Finally, causal modeling methods were used to determine correlations among the measured ﬂight crew fatigue indicators, the subjective perception of fatigue, and the deﬁned workload settings. The results of this research reveal which elements strongly impact ﬂight crew fatigue. The detected correlations can help deﬁne improved measures for the mitigation of fatigue risk in future ﬂight operations.


Introduction
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].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 [3,4], 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].
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].
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].
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 objectivation of flight crew fatigue include subjective fatigue scales, psychomotor vigilance tests, actigraphy, predictive models, and sleep diaries [9,11].The subjective objectivation 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].
The first part of this study describes a method to measure the fatigue level of professional airline pilots using special psychodiagnostic equipment, i.e., tests.These tests are based on a chronometric approach to measuring cognitive functions [11].For the purpose of this study, an electronic Complex Reactionmeter Drenovac (CRD) [12] system of standardized chronometric cognitive tests is used.Personal (subjective) self-assessments of each subject's current state of fatigue were also used.The aim was to identify and quantify elements that affect the appearance of fatigue.
The second part of this study includes a statistical analysis of the results obtained with the CRD equipment and from the subjective fatigue scales.A statistical analysis was performed using the analysis of variance (ANOVA) function in the Statistica 10 software.
In the third and final part of this study, causal modeling methods are used to determine correlations among flight crew fatigue indicators, the subjective perception of fatigue, and the defined workload settings.Recent studies focusing on developing predictive safety management methodologies in aviation have revealed new possibilities.A conceptual model of predictive safety management methodology was developed in [13]; this approach defines the steps and tools of predictive safety management, i.e., the usage of predictive (forecasting) and causal modeling methods [14][15][16] to identify potential hazards in aviation, as well as their causal relations.This can help define efficient mitigation measures to prevent or reduce the number of future hazards from turning into adverse events.
Hence, the main objective of this research is to find the correlations among the measured flight crew fatigue indicators, indicators of the subjective perception of fatigue, and workload settings in flight operations.For the purpose of finding these correlations, the IBM SPSS Statistics 27 software [17] was used.

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].Personal factors are related to age, chronotype (morning type, evening type) [21], gender, genetic predisposition, and personality, which have an impact on tolerance to shift work [22].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].For the flight crew, work-related factors refer to shift work that includes early/late/night duties [25], 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].A small sleep debt is needed to fall asleep ("The probability of falling asleep means a combination of two opposing forces: our burden of sleep minus the level of excitement" [27]), 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].One study showed slow reaction time and poor performance of motorcycle driving [29] 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].
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].
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].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].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] 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].
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].
Within a FRMS, the most commonly used methods to measure and objectivate flight crew fatigue are [9,11]: Subjective fatigue scales (Samn Perelli, Karolinska); 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].The subjective objectification 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].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].Information regarding the instruments, methodology, measuring parameters, etc. used in such tests is provided in the CRD handbook [38].CRD series have been used for study on psychomotor disturbances in scuba divers [39].Another study showed differences between the working abilities of a driver, a train operator, and a dispatcher during day and night shifts [40,41].CRD series have also been used to evaluate the psychomotor abilities of military pilots [42] and in research regarding workloads and work efficiency over certain periods of time [43,44].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], studying new tools for use by pilots and the aviation industry to manage risks pertaining to workrelated stress and wellbeing [46], analyzing the workloads of aircraft pilots using Heart Rate Variability (HRV) and the NASA Task Load Index questionnaire [47], applying multimodal analyses of eye movements and fatigue in a simulated glass cockpit environment [48], studying work type influence on fatigue among air traffic controllers based on data-driven PERCLOS detection [49], identifying pilot fatigue status based on functional near-infrared spectroscopy [50], examining fatigue among different crew compositions on long-haul flights during the COVID-19 pandemic [51], and examining fatigue, work overload, and sleepiness on a sample of commercial airline pilots [52].
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][54][55], the causes and origins of human error [56], assumptions and methods for turning observations into causal knowledge [57], the human perception of the relationship between cause and effect [58], the role that human factors play in major aviation accidents [59], the use of causal models to control and manage aircraft accident risk [60], graphical causal models that can serve as powerful tools for detecting interrelations between variables [61], 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].
Against the described research background, this paper discusses the use of 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 collected data; causal modeling methods to detect correlations among the obtained fatigue indicators; and subjective self-assessment results and indicators of workload settings in flight operations.

Data Collection and Methods
This chapter presents the process of data collection regarding flight crew fatigue using objectivation methods, i.e., an electronic CRD system of standardized chronometric cognitive tests and subjective fatigue scales that capture the subjective perception of fatigue by flight crews.The statistical methods used to analyze the collected data are described, as well as the causal modeling methods used to detect correlations among the obtained fatigue indicators, subjective self-assessments, and workload settings.

Collecting Data on Flight Crew Fatigue-Objectivation Methods
The data collected for this study were obtained by using an electronic CRD system of standardized chronometric cognitive tests and subjective fatigue scales that capture the subjective perception of fatigue by flight crews.
The tasks in the CRD tests were based on the measurement of reaction times by CDR measuring instruments [34].These tests are intended for the chronometric measurement of the effectiveness of mental and psychomotor functions and to determine the dynamic features and functional disturbances in mental processing.The efficiency of task-solving in the CRD tests is shown by indicators expressed in time (milliseconds).
The individual mechanisms of the stimulus content processing system, as well as the actualization and management of psychomotor activity, comprise special procedures to extract and connect reaction time components with situational factors, which appear in each test.
Numerous studies regarding the CRD series test measurements have established to assess the following [38,[62][63][64][65]    Complex psychomotor reactions of different combinations of extremities (arms and legs) to different complex sets of light and sound signals.
When the motor response to the stimulus content is in the form of a movement, then the reaction time depends on the limb used to perform the movement.In the experiments, a difference in the speed of the same movement performed with the right or left hand was identified.
For sound, the required duration of the stimulus was shortened by 8.7%, and with light, by 10%, i.e., faster reaction times were observed for sound than for light [66].The longer latency time of sensory components to a light signal than a sound signal is a result of the different duration of the conversion of the signal into a stimulus (energy transformation of electromagnetic waves, chemical reactions of visual purpura on the retina, initiation and generation of the receptor potential).It takes 8 to 10 msec for sound stimulus, and 20 to 40 msec for light stimulus, to reach the cortex [66].
Reaction time is prolonged (slowed down) when the subject is tired [50].Mental fatigue, especially sleepiness, has the greatest influence [67].Sleep deprivation impacts in a similar way [28].However, besides causing slower reaction times, it also increases the likelihood of errors, for example, missing a response to stimulus.
Four CRD devices were used in this study.Additionally, five CRD tests were used, in the following order: In this study, all measurements were made anonymously with four male pilots of an average age of 42 years (+/− two years); all had been professional airline pilots for the last 11 years (standard deviation of 4.7 years) and had an average of 6305 flight hours (standard deviation of 2532 flight hours) [11].There was one captain and one co-pilot of a DH4-type aircraft and one captain and one co-pilot of a A319/A320-type aircraft.The pilots were familiarized with the methods used in the study, as well as with the CRD equipment and tests.Pilots underwent training before taking the actual tests in order to avoid the effect of learning how to do the tests, because the aim was to measure the drop in mental potential due to fatigue.
Measurements, during which pilots completed a full set of tests (i.e., the five CRD tests previously described) and filled out subjective surveys (self-assessment tables of emotional state, energy level, self-confidence, and anxiety level), were performed before or after a duty period.Tests were done in an improvised "CRD laboratory", i.e., a room in their base airport where pilots checked-in and checked-out (pre-flight and post-flight duty), as shown in Figure 1.The average duration of testing on the CRD consoles was about 15 min [11].All tests were recorded with a video camera.
A protocol was established with specific rules that were followed during the performance of all tests:

•
Each test was recorded with a camera;

•
Each test was preceded by a short practice task; • There were no breaks between tests;

•
The results and tactics of solving the task could be discussed with the subjects; • Every test started with the call "NOW"-"GET READY, WE BEGIN, NOW!" The protocol included training the subjects, i.e., familiarizing them with the tests.Training included 10 repetitions of the tests over a period of three to four days.The protocol included the instructions and a description of each test.A protocol was established with specific rules that were followed during the performance of all tests: • Each test was recorded with a camera; • Each test was preceded by a short practice task; • There were no breaks between tests;

•
The results and tactics of solving the task could be discussed with the subjects; • Every test started with the call "NOW"-"GET READY, WE BEGIN, NOW!" The protocol included training the subjects, i.e., familiarizing them with the tests.Training included 10 repetitions of the tests over a period of three to four days.The protocol included the instructions and a description of each test.
CRD 13 or "Spatial visualization test" examines the speed and accuracy of recognizing characters that appear in varying sizes and different positions in space.A signal panel is located in the upper part of the instrument.On that panel, in the central part, there are 12 signal lights arranged in three rows and four columns.In each task, a large number of signal lights that outline some kind of shape, are lit simultaneously, i.e., a line, a fork, a triangle, a quadrilateral, a pentagon, or others.The same characters in different tasks could be of different sizes and rotated differently in space.On the control panel, drawings of these characters are located below the answer keys.In the upper row, the characters are formed from open lines, and in the lower row, they are formed from geometric characters.The subject has to look at them carefully and try to remember where they are.The answer is given by pressing the button under which a given character is drawn.While solving the tasks, the subject has to try to recognize the character formed by a group of lit signal lights as quickly as possible, and quickly find and press the button above the drawing of the appropriate character among the answer keys.While solving the test, the importance of accuracy and speed is emphasized.The test contains 35 tasks.After correctly solving a task, a new task immediately appears.If a new task does not appear, it means that the correct answer was not provided.In such cases, the subject has to check where the error occurred and press the key with the correct answer before continuing to the next task.
CRD 241 or "Test of identifying progressive series of numbers" examines the speed and accuracy of assessing a series of 40 three-digit numbers ranging from 101 to 140, arranged in random order on the signal control panel.The task is to find the numbers in order from the smallest (101) to the largest (140).The position of an individual number on the signal control panel is indicated by pressing the button located below the respective number.If the position of a certain number is correctly found, a return sound signal "BIP" is obtained, but if the wrong key is pressed, the sound signal is absent.A single number CRD 13 or "Spatial visualization test" examines the speed and accuracy of recognizing characters that appear in varying sizes and different positions in space.A signal panel is located in the upper part of the instrument.On that panel, in the central part, there are 12 signal lights arranged in three rows and four columns.In each task, a large number of signal lights that outline some kind of shape, are lit simultaneously, i.e., a line, a fork, a triangle, a quadrilateral, a pentagon, or others.The same characters in different tasks could be of different sizes and rotated differently in space.On the control panel, drawings of these characters are located below the answer keys.In the upper row, the characters are formed from open lines, and in the lower row, they are formed from geometric characters.The subject has to look at them carefully and try to remember where they are.The answer is given by pressing the button under which a given character is drawn.While solving the tasks, the subject has to try to recognize the character formed by a group of lit signal lights as quickly as possible, and quickly find and press the button above the drawing of the appropriate character among the answer keys.While solving the test, the importance of accuracy and speed is emphasized.The test contains 35 tasks.After correctly solving a task, a new task immediately appears.If a new task does not appear, it means that the correct answer was not provided.In such cases, the subject has to check where the error occurred and press the key with the correct answer before continuing to the next task.
CRD 241 or "Test of identifying progressive series of numbers" examines the speed and accuracy of assessing a series of 40 three-digit numbers ranging from 101 to 140, arranged in random order on the signal control panel.The task is to find the numbers in order from the smallest (101) to the largest (140).The position of an individual number on the signal control panel is indicated by pressing the button located below the respective number.If the position of a certain number is correctly found, a return sound signal "BIP" is obtained, but if the wrong key is pressed, the sound signal is absent.A single number must not be skipped, because all answers after the skipped number would be considered errors.While solving the test, the importance of accuracy and speed was emphasized.
CRD 23 or "Test of complex convergent visual orientation" examines the speed and accuracy of complex navigation in space.In each task, three signal lights are lit simultaneously, which are combined to make two intersections of the columns and rows in which the answer keys are located.The task is to quickly determine the columns and rows that these lights define when the signal lights come on and to find the intersection of these columns and rows.The answer must be given by simultaneously pressing both buttons located in those places.It is important to press the answer keys simultaneously with both hands.The answer will not be valid if one key is pressed before the other.While solving the test, the importance of accuracy and speed was emphasized.The test contains 35 tasks.After correctly solving a task, a new task immediately appears.If a new task does not appear, it means that the previous task was not answered correctly.In this case, it is necessary to check that task, press the keys with the correct answer, and then continue to the next task.
CRD 324 or "Actualization of short-term memory" examines the speed and accuracy of operational memory, i.e., recall.The task consists of noticing the place where the light signal appears and finding the key to turn it off among the answer keys in the lower row.At the same time, the subject must remember a sequence of signal connections and answer keys.The position of the answer key can be vertically below, to the left, or to the right of the light.In this test, the signal lights are lit up in a random order, and the answers are given by alternately pressing the keys according to the principle "LEFT, RIGHT, RIGHT, DOWN".
CRD 422 or "Operative thinking with sound stimuli" involves the use of a main signalcontrol panel and connection elements, i.e., headphones (speakers) and pedals.The CRD 422 test measures operational thinking and coordinating the work of both hands and legs depending on an emitted pitch.In this test, one of the two predetermined sound signals is emitted.For a higher pitch, it is necessary to simultaneously press the large button in the left corner of the control panel with the left hand and the right foot pedal with the right foot.For a lower pitch, subjects must simultaneously press the large button in the right corner of the control panel with the right hand and the left foot pedal with the left foot.
The task design in the CRD series tests is based on the concept of reaction time measurement.These tests are intended for chronometric measurements of the efficiency of performing mental and psychomotor functions, as well as the determination of dynamic characteristics and functional interferences in the process of mental processing [38].
Independent variables (inputs) are related to: • Workload (flight hours, duty hours, rest periods, number of sectors); • Time of the day (when the CRD tests were performed; this was used to study the influence of circadian rhythm); • Subjective self-assessments (results of the subjective perception of fatigue, considered to be both independent and dependent variables).
Dependent variables (outputs/targets) are: • CRD fatigue indicators (results of the CRD tests); • Subjective self-assessments (results of the subjective perception of fatigue, considered to be both independent and dependent variables).
Independent variables are divided into the following seven groups: Subjective self-assessment (consisting of four indicators: Self-assessment of emotional state, Self-assessment of energy level, Self-assessment of self-confidence, and Selfassessment of anxiety level).
Independent variables represent the workload elements and the results of the subjective self-assessment scales, which are described in Table 1.For the purpose of detecting correlations among all variables, the independent variables (indicators) are designated with labels, i.e., Time of the day is X1, Start or end of the shift is X2, Number of F days in the previous 7 days is X3, Number of F days in the previous 28 days is X4, Number of individual F days in the previous 28 days is X5, Rest length is X6, Local night in a daily rest is X7, Number of local nights in the 48 h before flight duty is X8, Changes in the schedule is X9, Sectors in the previous 7 days is X10, Sectors in the previous 28 days is X11, Flight time in the previous 7 days is X12, Flight time in the previous 28 days is X13, Duty time in the previous 7 days is X14, Duty time in the previous 28 days is X15, Flight duty time is X16, Duty time is X17, Flight time in flight duty is X18, Average duration of a sector is X19, Average duration of aircraft ground handling is X20, Split duty is X21, Change of aircraft during flight duty period is X22, Multi-day shifts is X23, Self-assessment of emotional state is S1, Self-assessment of energy level is S2, Self-assessment of self-confidence is S3, and Self-assessment of anxiety level is S4.
The Number of errors (Nerr) measures the accuracy of mental processing; a lower value indicates a higher accuracy and vice versa.The Number of errors captures the coordination of speed and accuracy in mental processing.The Number of errors also provides information about the difficulty of the tasks.
Total test-solving time (Ttot) measures the total time required to solve a particular test (it includes ballast, i.e., lost time due to the effect of systematic and random factors on the speed of performing a certain mental activity).A lower value indicates a higher level of efficiency and vice versa.
Minimum test-solving time (Tmin) measures the speed of mental processing, i.e., the shortest task solving times in the individual tests.A lower value indicates a higher level of efficiency and vice versa.
Maximum test-solving time (Tmax) measures the longest time required to solve a particular task, i.e., an extremely long time to solve one or more tasks in a certain test.A lower value indicates a higher level of efficiency and vice versa.
Total ballast (Btot) measures total lost time due to fluctuations in the speed of solving similar tasks in individual tests; this represents the stability of mental processing, i.e., it is an indicator of individual stability as a dynamic feature of mental processing.Lower values indicate greater stability and vice versa.Btot is defined as the sum of the differences (Di) between the time required to solve each individual task (Ti) and the individually shortest time required to solve tasks in a certain test (Tmin), as shown in Figure 2. Di represents the blocks of partial ballast (D1 . . .Dn); it serves primarily to monitor the dynamics of change in the speed of mental processing as a function of the performance of a particular chronometric test, and cumulatively to derive the indicators of Initial ballast (Bin), and Final ballast (Bfin).In other words, it is the overall indicator of the stability of the mental processing of the test content by an individual.
Table 1.The elements of workload and the results of subjective self-assessment scales-the independent variables of CRD testing and subjective self-assessments.Initial ballast (Bin) represents the working speed or starting ballast.In the first half of the test, it contains information on the efficiency or interference of working speed.

Independent
Final ballast (Bfin) represents fatigue, i.e., it contains information about the transfer of experience from the initial to the final part of the test.
Fatigue index (Bfin/Bin) is the quotient of Initial ballast (Bin) and Final ballast (Bfin); it represents a derived indicator of the direction of changes in the speed (an acceleration or a deceleration) of solving tasks in a particular test, i.e., it represents endurance and, consequently, fatigue.Values of this indicator greater than 1 indicate the presence of fatigue.
Table 2 shows an overview of all dependent variables, including the full name, label, acronym, a short description, and meaning of each CRD fatigue indicator.The variables of subjective self-assessments represent the subjective results of selfassessments regarding emotional state, energy level, self-confidence, and anxiety level.
The subjective self-assessment scale of emotional state comprises a ranking from 1 to 10, as shown in Table 3, where the worst was 1, i.e., "I am completely depressed, and everything is black", and the best was 10, i.e., "I feel unusually joyful and energetic".Initial ballast (Bin) represents the working speed or starting ballast.In the first half of the test, it contains information on the efficiency or interference of working speed.
Final ballast (Bfin) represents fatigue, i.e., it contains information about the transfer of experience from the initial to the final part of the test.
Fatigue index (Bfin/Bin) is the quotient of Initial ballast (Bin) and Final ballast (Bfin); it represents a derived indicator of the direction of changes in the speed (an acceleration or a deceleration) of solving tasks in a particular test, i.e., it represents endurance and, consequently, fatigue.Values of this indicator greater than 1 indicate the presence of fatigue.
Table 2 shows an overview of all dependent variables, including the full name, label, acronym, a short description, and meaning of each CRD fatigue indicator.The variables of subjective self-assessments represent the subjective results of selfassessments regarding emotional state, energy level, self-confidence, and anxiety level.
The subjective self-assessment scale of emotional state comprises a ranking from 1 to 10, as shown in Table 3, where the worst was 1, i.e., "I am completely depressed, and everything is black", and the best was 10, i.e., "I feel unusually joyful and energetic".
The subjective self-assessment scale for energy level comprises a ranking from 1 to 10, as shown in Table 4, where the worst was 1, i.e., "I'm completely exhausted, unable to make the least effort", while 10 was the best, i.e., "I feel great energy and see no obstacles".The subjective self-assessment scale of self-confidence comprised a ranking from 1 to 10, as shown in Table 5, where the worst was 1, i.e., "I am unable to muster the strength to do anything", while 10 was the best, i.e., "Nothing is impossible for me, I can accomplish anything I want".I think that I am capable and that I have the knowledge to meet the demands placed on me.7 It seems to me that my knowledge and abilities are greater than the demands placed on me.8 I am completely confident in my knowledge and abilities.9 I am confident in my abilities to perform important and responsible tasks.10 Nothing is impossible for me, I can accomplish anything I want.
The subjective self-assessment scale of anxiety level comprised a ranking from 1 to 10, as shown in Table 6, where the worst was 1, i.e., "I'm completely freaked out, scared", while 10 was the best, i.e.,: "I am completely calm and peaceful".A sample of the collected data regarding flight crew fatigue, i.e., independent and dependent variables obtained using the described objectivation methods, is presented in Appendix A.

Statistical Analysis of Collected Data on Flight Crew Fatigue
After the measurements were completed and the chronometric data had been collected, a statistical analysis of the data was conducted.Before the statistical analysis began, it was necessary to convert the original results of the CRD measurements expressed in time indicators (milliseconds) into standard statistical measures (T scale) for the purpose of normalizing the data.
The need to transpose the original measures into the standardized measures stems from the fact that chronometric data are asymmetrically distributed, and the normalization of their distribution is necessary, because statistical analysis assumes a normal distribution of data.This procedure also eliminated the individual differences among subjects.To this end, we converted Ttot, Tmin, Tmax, Btot, Bin, and Bfin data, which were originally expressed in milliseconds; meanwhile, the total number of errors (Nerr) and the fatigue index (Bfin/Bin) retained the original values.
At the same time, it is necessary to emphasize that shorter times in the aforementioned variables indicate a higher degree efficiency of mental processing and vice versa, which means that a lower value on the T scale also represents a higher degree of efficiency of mental processing and vice versa.Dependent variables Nerr and Bfin/Bin are expressed in their original values in further analysis, whereby a lower number of errors indicates greater accuracy of mental processing, while for Bfin/Bin, i.e., the fatigue index, values greater than 1 (when Bfin is greater than Bin) indicate the presence of fatigue.
Conversion to the T scale consists of two steps, as follows.
Step I: conversion of the original measurement results (values) into Z values according to the formula: Z value = (average of original value)/(standard deviation of original value). ( Step II: conversion of the Z value into the T value according to the formula: A sample of the Ttot, Tmin, Tmax, Btot, Bin, and Bfin indicators converted into T scale values, i.e., TtotZ, TminZ, TmaxZ, BtotZ, BinZ, and BfinZ, is shown in Table 7.After the normalization of the collected data, a statistical analysis was performed using ANOVA in the Statistica 10 software.The results are presented in Chapter 4 and accompanying appendices.

Causal Modeling Methods
The aim of this research was to detect correlations among flight crew fatigue indicators, subjective self-assessments (the subjective perception of fatigue), and workload parameters.It is possible to improve the flight crew planning processes in flight operations and mitigate the risk of fatigue by identifying causal links among flight crew fatigue indicators, subjective self-assessments, and workload settings, collected via the CRD testing.
IBM SPSS Statistics is an analytics software [17] that can be used to analyze all data in one or more datasets and identify causal links among variables (indicators).The SPSS Statistics 27 version of the software was used for this study.
Causal models can be generated once a dataset has been prepared correctly using the function called "Create Temporal Causal Model".The Temporal Causal Model (TCM) detects causal links among all indicators (variables) in a dataset-in this case, among flight crew fatigue indicators, subjective self-assessments, and workload settings-and presents them in a circular or impact diagram.The causal modeling results are presented in Chapter 4.

Results
Correlations among flight crew fatigue indicators, subjective self-assessments, and workload settings were detected, based on the CRD measurements, statistical analyses of the collected data, and the causal modeling of the relevant dataset.The obtained results are presented in this chapter.

Statistical Analysis Results of Flight Crew Fatigue Indicators
After the normalization of the collected data, a statistical analysis was performed for the independent variables outlined in Table 1, Section 3.1, using the ANOVA of the Statistica 10 software.
Independent variables, as previously described, are divided into the following groups: • Time of day when the measurement was made, i.e., how the time of day when the measurement was conducted affects the dynamics of mental processing;

•
The beginning or the end of the shift, i.e., the dynamics of mental processing at the beginning or end of the shift; As described previously, based on CRD tests, data were collected.The total number of conducted tests was 1182, which produced a large database of information.The tests were conducted in a period of about one year.Parallel to conducting each test, subjects filled out the subjective fatigue tests to provide information about their subjective perception of fatigue.Subjects also filled out questionnaires regarding their workloads prior to taking the tests.The workload settings data and results of the subjective fatigue tests were defined as independent variables, while the CRD measures were defined as dependent variables.The aim of the statistical analysis was to examine whether the independent variables affected the dependent variables, i.e., CRD measures.The main hypothesis which was repeated for each independent variable assumed that these have no effect on the dependent variables, i.e., efficiency of mental processing.
Samples of the conducted statistical analysis of the CRD dependent variables are presented in Appendix B, showing also an analysis of the independent variable "Average duration of a sector", while in Appendix C, and analysis of the independent variable "Subjective self-assessment of the anxiety level" is provided.
The overall results of the statistical analysis are presented in the following table and graphs.
Table 8 shows the dependent variables of the CRD tests, i.e., the number of measurements when the difference was statistically significant (statistical significance at a level of less than 0.05), which totaled in 268 instances.According to our statistical analysis, CRD 422 and CRD 13 were the most sensitive chronometric instruments in this study in terms of the number of dependent variables, with statistical significance at a level of less than 0.05, as shown in Figure 3.The dependent variable with the most statistical significance at a level of less than 0.05 was Total test time, i.e., Ttot, while the least was Maximum test-solving time, i.e., Tmax, as shown in Figure 4.The most statistically significant differences were recorded in the group of independent variables for cumulative workload, followed by the group for individual flight duties, as shown in Figure 5.The most statistically significant differences were recorded in the group of independent variables for cumulative workload, followed by the group for individual flight duties, as shown in Figure 5.The most statistically significant differences were recorded for the independent variable "Duty time in the previous 28 days", and the least for "Sectors in the previous 7 days".Most (55.2%) of the statistically significant differences were recorded at the end of the shift (Check-Out-CO), as shown in Figure 6.The most statistically significant differences were recorded for the independent variable "Duty time in the previous 28 days", and the least for "Sectors in the previous 7 days".Most (55.2%) of the statistically significant differences were recorded at the end of the shift (Check-Out-CO), as shown in Figure 6.
Figure 7 shows the dependent variables in relation to the grouped CRD variables regarding speed, stability, and reliability, according to the number of statistically significant differences.CRD variables regarding speed include Total test-solving time (Ttot), Minimum test-solving time (Tmin), and Maximum test-solving time (Tmax).CRD variables regarding stability include Total ballast (Btot), Initial Ballast (Bin), and Final ballast (Bfin).The CRD variable regarding reliability is Number of errors (Nerr).Regarding the CRD indicators measuring speed, most of the statistically significant differences were found for the indepen-dent variables "Duty time in the previous 7 days" and "Duty time in the previous 28 days".For the CRD indicators measuring stability, most of the statistically significant differences were found for the independent variables of "Changes in the schedule", "Sectors in the previous 28 days", "Duty time in the previous 28 days", and "Flight time in the previous 28 days".For the CRD indicator measuring reliability, most of the statistically significant differences were found for the independent variables "Sectors in the previous 28 days", "Duty time in the previous 7 days", and "Self-assessment of emotional state".The most statistically significant differences were recorded for the independent variable "Duty time in the previous 28 days", and the least for "Sectors in the previous 7 days".Most (55.2%) of the statistically significant differences were recorded at the end of the shift (Check-Out-CO), as shown in Figure 6.CRD indicators measuring speed, most of the statistically significant differences were found for the independent variables "Duty time in the previous 7 days" and "Duty time in the previous 28 days".For the CRD indicators measuring stability, most of the statistically significant differences were found for the independent variables of "Changes in the schedule", "Sectors in the previous 28 days", "Duty time in the previous 28 days", and "Flight time in the previous 28 days".For the CRD indicator measuring reliability, most of the statistically significant differences were found for the independent variables "Sectors in the previous 28 days", "Duty time in the previous 7 days", and "Self-assessment of emotional state".

Correlations Among Fatigue Indicators, Subjective Self-assessments, and Workload Settings Using Temporal Causal Modeling
In this part, the aim was to create a causal model of a defined dataset of previously described indicators in order to detect correlations among fatigue indicators, subjective self-assessments, and workload settings.Detecting correlations among indicators implies detecting the impacts (causes or effects) of indicators upon one another, which, in turn,

Correlations among Fatigue Indicators, Subjective Self-assessments, and Workload Settings Using Temporal Causal Modeling
In this part, the aim was to create a causal model of a defined dataset of previously described indicators in order to detect correlations among fatigue indicators, subjective self-assessments, and workload settings.Detecting correlations among indicators implies detecting the impacts (causes or effects) of indicators upon one another, which, in turn, provides a possibility to improve the planning of future actions that may help mitigate fatigue risk in flight operations.
To identify causal links among indicators, the IBM SPSS Statistics function "Create Temporal Causal Modeling" was used.Table 9 shows all of the indicators in the observed dataset, with their labels, names, and allocated roles.Fatigue index Independent and dependent variables (input/target, i.e., both) * * These indicators were initially determined to be dependent variables, but in the context of causal impacts, it was concluded that they can also be independent variables influencing other variables, and hence, their role was determined to be "both input and target" for the process of generating causal models.
For the purpose of detecting correlations among the defined indicators, a sample dataset was used due to software limitations.The dataset used for this study included 135 entries for 23 indicators of workload settings (Xs), four indicators of subjective self-assessments (Ss), and eight measured CRD indicators regarding mental processing, i.e., fatigue indicators (Ys).The setup was made in such way that the independent variables, i.e., workload settings indicators (Xs), were set as "inputs" in a temporal causal model, and the dependent and independent variables, i.e., Ss and Ys, were set as "both inputs and targets".Variables X16 (Flight duty time), X17 (Duty time), X18 (Flight time in flight duty), X19 (Average duration of a sector), X20 (Average duration of aircraft ground handling), X21 (Split duty), and X22 (Change of aircraft during flight duty period) were excluded due to the fact that their values were constant, i.e., equal to 0, or there were too many missing values.The sample dataset is presented in Figure 8. due to the fact that their values were constant, i.e., equal to 0, or there were too many missing values.The sample dataset is presented in Figure 8. Table 10 shows statistics for the causal models generated for each of the twelve target indicators, obtained using the IBM SPSS Statistics function "Create Temporal Causal Modeling".Model quality (model fit) for all of the the built models was evaluated using the R-squared criterion, which can be explained as the proportion of the variation in the dependent variable which is predictable from an independent variable or variables.Different criteria can be used to do the "best fit" evaluation (RMSE-Root Mean Squared Error, RMSPE-Root Mean Squared Percent Error, AIC-Akaike Information Criterion, BIC-Bayesian Information Criterion, R-squared).In this case, R-squared was selected, as it is the default in the software; the larger the R-squared value, the better the model.Table 10 shows the fit statistics for all causal models of each target indicator in the observed dataset.Table 10 shows statistics for the causal models generated for each of the twelve target indicators, obtained using the IBM SPSS Statistics function "Create Temporal Causal Modeling".Model quality (model fit) for all of the the built models was evaluated using the R-squared criterion, which can be explained as the proportion of the variation in the dependent variable which is predictable from an independent variable or variables.Different criteria can be used to do the "best fit" evaluation (RMSE-Root Mean Squared Error, RMSPE-Root Mean Squared Percent Error, AIC-Akaike Information Criterion, BIC-Bayesian Information Criterion, R-squared).In this case, R-squared was selected, as it is the default in the software; the larger the R-squared value, the better the model.Table 10 shows the fit statistics for all causal models of each target indicator in the observed dataset.
Figure 9 shows the "overall model quality", which shows the distribution of model quality for all of the built models (from Table 10).As shown in Figure 9, the models were of excellent quality, because 100% of them had R-squared values in the top interval (0.88. 1). Figure 9 provides confirmation that the applied TCM was of excellent quality, with R-squared values ranging from 0.91 to 0.95; this means that the correlations detected in the built TCM were strong.
Figure 10 shows the overall causal model system (TCM) of all causal links among the flight crew fatigue indicators, subjective self-assessments, and workload settings parameters, obtained using the causal modeling functions of the IBM SPSS Statistics 27.For example, TCM shows that indicator S2 (Self-assessment of the energy level) correlates with X2 (Start or end of the shift (Check In/Check Out-CI/CO)), X3 (Number of days off in the previous 7 days), X5 (Number of individual days off in the previous 28 days), X15 (Duty time in the previous 28 days), S3 (Self-assessment of self-confidence), Y1 (Number of errors or accuracy of mental processing), Y2 (Mental processing speed or total time required to solve a test), and Y5 (Total ballast or total lost time due to fluctuations in the speed of solving similar tasks).Figure 9 shows the "overall model quality", which shows the distribution of model quality for all of the built models (from Table 10).As shown in Figure 9, the models were of excellent quality, because 100% of them had R-squared values in the top interval (0.88. 1). Figure 9 provides confirmation that the applied TCM was of excellent quality, with Rsquared values ranging from 0.91 to 0.95; this means that the correlations detected in the built TCM were strong.Figure 11 shows the direct impacts of target indicator Y8, i.e., Fatigue index.Figure 11a shows the correlations (links) with statistical significance values less than or equal to 0.05, while Figure 11b shows all of the detected correlations (impacts) of Y8. Figure 11a shows all the links with statistical significance values less than or equal to 0.05.As shown in these results, Y8 correlates with five workload settings indicators, namely X5 (Number Figure 11 shows the direct impacts of target indicator Y8, i.e., Fatigue index.Figure 11a shows the correlations (links) with statistical significance values less than or equal to 0.05, while Figure 11b shows all of the detected correlations (impacts) of Y8. Figure 11a shows all the links with statistical significance values less than or equal to 0.05.As shown in these results, Y8 correlates with five workload settings indicators, namely X5 (Number of individual days off in the previous 28 days), X6 (Rest length), X7 (Local night in daily rest), X9 (Changes in the schedule), and X10 (Sectors in the previous 7 days).Additionally, this correlates with three subjective self-assessment indicators, i.e., S2 (Self-assessment of energy level), S3 (Self-assessment of self-confidence), and S4 (Self-assessment of anxiety level), as well as with five other CRD indicators, namely, Y1 (Number of errors or accuracy of mental processing), Y2 (Mental processing speed or total time required to solve a test), Y4 (Maximum mental processing speed, i.e., the longest task-solving time), Y5 (Total ballast or total lost time due to fluctuations in the speed of solving similar tasks), and Y7 (Final ballast or final lost time due to fluctuations in the speed of solving similar tasks).Figure 13 shows an impact diagram of all indicators affected by Y8, i.e., Fatigue Index.These include S1 (Self-assessment of emotional state), S2 (Self-assessment of energy level), S3 (Self-assessment of self-confidence), S4 (Self-assessment of anxiety level), Y1 (Number of errors or accuracy of mental processing), Y2 (Mental processing speed or total time required to solve a test), Y3 (Minimum mental processing speed, i.e., the shortest task-solving time), Y4 (Maximum mental processing speed, i.e., the longest task-solving time), Y5 (Total ballast or total lost time due to fluctuations in the speed of solving similar tasks), and Y7 (Final ballast or final lost time due to fluctuations in the speed of solving similar tasks).
As previously mentioned, the focus of this study was to find correlations among flight crew fatigue indicators, the subjective perception of fatigue, and workload settings.Using causal modeling techniques, correlations were detected.Figure 14 shows all of the detected correlations with specific emphasis on correlations regarding workload settings, i.e., those labeled with Xs.In Figure 14a, these are clearly marked in red squares; in Figure 14b, the same ones are marked in red squares, while additional ones are marked in orange squares.Those include X5 (Number of individual days off in the previous 28 days), X6 (Rest length), X7 (Local night in daily rest), X9 (Changes in the schedule), and X10 (Sectors in the previous 7 days).The reason why these are of particular interest is because they represent the independent variables which are susceptible to modification.Hence, finding indicators of workload settings that impact the flight crew fatigue opens up the possibility to modify them in order to mitigate fatigue risk.Figure 13 shows an impact diagram of all indicators affected by Y8, i.e., Fatigue Index.These include S1 (Self-assessment of emotional state), S2 (Self-assessment of energy level), S3 (Self-assessment of self-confidence), S4 (Self-assessment of anxiety level), Y1 (Number of errors or accuracy of mental processing), Y2 (Mental processing speed or total time required to solve a test), Y3 (Minimum mental processing speed, i.e., the shortest task-solving time), Y4 (Maximum mental processing speed, i.e., the longest task-solving time), Y5 (Total ballast or total lost time due to fluctuations in the speed of solving similar tasks), and Y7 (Final ballast or final lost time due to fluctuations in the speed of solving similar tasks).As previously mentioned, the focus of this study was to find correlations among flight crew fatigue indicators, the subjective perception of fatigue, and workload settings.Using causal modeling techniques, correlations were detected.Figure 14 shows all of the detected correlations with specific emphasis on correlations regarding workload settings, i.e., those labeled with Xs.In Figure 14a, these are clearly marked in red squares; in Figure 14b

Discussion
Due to the severity of fatigue risk in flight operations, it is necessary to constantly seek and improve mitigation measures.As discussed in our review of the available literature, fatigue issues in flight operations have been frequently addressed.Various methods had been adopted to address fatigue related issues.

Discussion
Due to the severity of fatigue risk in flight operations, it is necessary to constantly seek and improve mitigation measures.As discussed in our review of the available literature, fatigue issues in flight operations have been frequently addressed.Various methods had been adopted to address fatigue related issues.Hence, this paper 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 of this paper was to use multiple methods, i.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).One indicator in the dataset was of particular interest in this study: the Fatigue index (or Y8 in the dataset).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".
The most interesting correlations were those related to the independent variables of workload settings, i.e., the impacts of number of individual days off in the previous 28 days, rest length, local night in a daily rest, changes in the schedule, and sectors in the previous 7 days, on fatigue.The reason why these were of particular interest is because they may be modified.Detecting correlations among indicators showed the impacts (causes or effects) of indicators upon one another, which, in turn, provides a foundation to improve the planning of future actions that may help mitigate fatigue risk in flight operations.

Conclusions
The aim of this paper was to find correlations among the measured flight crew fatigue indicators, indicators of the subjective perception of fatigue, and workload settings in flight operations.Detecting correlations could help define improved mitigation measures regarding fatigue risk in flight operations.
We described the objectivation methods used to collect data on flight crew fatigue, i.e., with an electronic system of standardized chronometric cognitive tests (CRD tests) and subjective self-assessment surveys on the subjective perception of fatigue (subjective fatigue scales).Additionally, the various applied procedures were described.
A statistical analysis was performed using the ANOVA of the Statistica 10 software.The main hypothesis was 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., our statistical analysis showed that the independent variables (workload settings and subjective states) had an effect on the dependent variables (CRD measures), or in other words, workload settings and subjective states affected the appearance of fatigue.
The final part of the study aimed to detect correlations among measured flight crew fatigue indicators, indicators of the subjective perception of fatigue, and workload settings using previously collected and analyzed data on flight crew fatigue.Correlations were detected showing the impact of specific workload and other elements; these could be used to define improved mitigation measures regarding fatigue in flight operations.

Limitations and Future Research
There were some limitations to this study.It did not consider all possible elements of workload settings that could impact the appearance of fatigue.Additionally, the study was performed on the four male pilots of similar age and experience, and hence, it could not be determined whether characteristics such as age, gender, or experience affected the appearance of fatigue.Even though large number of tests were performed over a long period of time, collecting data on a larger number (more than four) of pilots, as well as on female and male pilots, with different ages, experience levels, and other characteristics, might provide a better database to detect parameters affecting the appearance of fatigue.
In future, more extensive testing should be performed, and more elements concerning the work environment and personal factors should be examined to obtain more information regarding the presence of fatigue in flight operations.Finding indicators of workload settings that impact flight crew fatigue opens up the possibility of modifying them in order to mitigate fatigue risk.Further research will focus on simulating such modifications of workload settings based the correlations defined in this study.The aim is to establish improved workload settings that will have the least impact on fatigue, i.e., to mitigate fatigue risk by preventing the conditions that lead to its appearance.

Appendix B
The main hypothesis states: "Mental potential does not depend on the results of the subjective self-assessment of the anxiety level".
For the purpose of answering this hypothesis, the statistical analysis of an independent variable "Subjective self-assessment of the anxiety level" (at the end of the shift) and obtained dependent variables, was performed by using ANOVA variance analysis of Statistica 10, as presented below.
The results of subjective self-assessment of the anxiety level are divided into four main groups: 1.
I am sure of myself, and nothing disturbs me; 3.
I am cool, self-confident and do not get excited.

CRD 13-Statistical Analysis
Table A2 shows the frequency of the independent variable "Subjective self-assessment of the anxiety level" divided among four defined groups.The data is collected using the CRD 13 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A3.There were no statistically significant differences recorded.

CRD 23-Statistical Analysis
Table A4 shows the frequency of the independent variable "Subjective self-assessment of the anxiety level" divided among four defined groups.The data is collected using CRD 23 test.
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A5.The ANOVA variance analysis showed statistically significant differences in the mental efficiency at the promile level for the Bfin/Bin variable, i.e., Fatigue index.
Figure A1 shows One-way ANOVA analysis of a dependent variable Bfin/Bin and independent variable "Subjective self-assessment of the anxiety level".In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A5.The ANOVA variance analysis showed statistically significant differences in the mental efficiency at the promile level for the Bfin/Bin variable, i.e., Fatigue index.
Figure A1 shows One-way ANOVA analysis of a dependent variable Bfin/Bin and independent variable "Subjective self-assessment of the anxiety level".Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Table A6.

CRD 241-Statistical Analysis of Results
Table A7 shows the frequency of the independent variable "Subjective self-assessment of the anxiety level" divided among four defined groups.The data is collected using CRD 241 test.
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A8.The ANOVA variance analysis showed statistically significant differences in the mental efficiency at the level less than 0.05 for a Tmin variable.
Figure A2 shows One-way ANOVA analysis of a dependent variable Tmin and independent variable "Subjective self-assessment of the anxiety level".
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Table A9.Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Table A9.

CRD 324-Statistical Analysis of Results
Table A10 shows the frequency of the independent variable "Subjective self-assessment of the anxiety level" divided among four defined groups.The data is collected using CRD 324 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A11.There were no statistically significant differences recorded.

CRD 324-Statistical Analysis of Results
Table A10 shows the frequency of the independent variable "Subjective self-assessment of the anxiety level" divided among four defined groups.The data is collected using CRD 324 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A11.There were no statistically significant differences recorded.

CRD 422-Statistical Analysis of Results
Table A12 shows the frequency of the independent variable "Subjective self-assessment of the anxiety level" divided among four defined groups.The data is collected using CRD 422 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A13.The ANOVA variance analysis showed statistically significant differences in the mental efficiency at the level less than 0.05 for a Btot variable, and at the promile level for Bfin and Nerr variables.
Figure A3 shows One-way ANOVA analysis of a dependent variable Nerr and independent variable "Subjective self-assessment of the anxiety level" (Figure A3a), and One-way ANOVA analysis of dependent variables Btot and Bfin and an independent variable "Subjective self-assessment of the anxiety level" (Figure A3b).
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Table A14.way ANOVA analysis of dependent variables Btot and Bfin and an independent variable "Subjective self-assessment of the anxiety level" (Figure A3b).Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Table A14.

Appendix C
The main hypothesis states: "The average duration of a sector does not affect the dynamics of mental processing".
For the purpose of answering this hypothesis, the statistical analysis of an independent variable "Average duration of a sector" (at the end of the shift) and dependent variables, was performed using the ANOVA variance analysis of the Statistica 10, as presented below.
The average duration of a sector is divided into four groups: 5. Duration of a sector from 00:40 to 01:01 h;

Appendix C
The main hypothesis states: "The average duration of a sector does not affect the dynamics of mental processing".
For the purpose of answering this hypothesis, the statistical analysis of an independent variable "Average duration of a sector" (at the end of the shift) and dependent variables, was performed using the ANOVA variance analysis of the Statistica 10, as presented below.
The average duration of a sector is divided into four groups:

CRD 13-Statistical Analysis
Table A15 shows the frequency of the independent variable "Average duration of a sector" divided among four defined groups.The data is collected at the end of the shift, using CRD 13 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A16.There were no statistically significant differences recorded.

CRD 23-Statistical Analysis
Table A17 shows the frequency of the independent variable "Average duration of a sector" divided among four defined groups.The data is collected at the end of the shift, using CRD 23 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A18.The ANOVA variance analysis showed statistically significant differences in the mental efficiency at the level less than 0.05 for Nerr variable.
Figure A4 shows the One-way ANOVA analysis of a dependent variable Nerr and an independent variable "Average duration of a sector".
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Table A19.The ANOVA variance analysis showed statistically significant differences in the mental efficiency at the level less than 0.05 for Nerr variable.
Figure A4 shows the One-way ANOVA analysis of a dependent variable Nerr and an independent variable "Average duration of a sector".Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Table A19.Table A19.Post-hoc analysis of a Nerr and an "Average duration of a sector" using the Fisher LSD test.Table A20 shows the frequency of the independent variable "Average duration of a sector" divided among four defined groups.The data is collected at the end of the shift, using CRD 241 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A21.There were no statistically significant differences recorded.

CRD 324-Statistical Analysis of Results
Table A22 shows the frequency of the independent variable "Average duration of a sector" divided among four defined groups.The data is collected at the end of the shift, using CRD 324 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A23.The ANOVA variance analysis showed statistically significant differences in the mental efficiency at the level less than 0.05 for Nerr and Bfin/Bin variables.
Figure A5 shows the One-way ANOVA analysis of a dependent variable Nerr and an independent variable "Average duration of a sector" (Figure A5a), and One-way ANOVA analysis of a dependent variable Bfin/Bin (Fatigue index) and an independent variable "Average duration of a sector" (Figure A5b).
The ANOVA variance analysis showed statistically significant differences in the mental efficiency at the level less than 0.05 for Nerr and Bfin/Bin variables.
Figure A5 shows the One-way ANOVA analysis of a dependent variable Nerr and an independent variable "Average duration of a sector" (Figure A5a), and One-way ANOVA analysis of a dependent variable Bfin/Bin (Fatigue index) and an independent variable "Average duration of a sector" (Figure A5b).Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Tables A24 and A25.Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statistica 10, as shown in Tables A24 and A25.

CRD 422-Statistical Analysis of Results
Table A26 shows the frequency of the independent variable "Average duration of a sector" divided among four defined groups.The data is collected at the end of the shift, using CRD 422 test.In the next step, the ANOVA variance analysis of Statistica 10 was used to test the significance of statistical differences in CRD dependent variables.The results of that analysis are shown in Table A27.There were no statistically significant differences recorded.
day Local time of testing at the beginning of the shift (Check In-CI) or at the end of the shift (Check Out-CO) Start or end of the shift X2 Start or end of the shift (Check In/Check Out-CI/CO) Start of 'shift or Check In-CI, or end of shift or Check Out-CO Days off X3 Number of F days in the previous 7 days Number of days off (F) in the previous 7 days, at the beginning of the shift (CI) or at the end of the shift (CO) X4 Number of F days in the previous 28 days Number of days off (F) in the previous 28 days, at the beginning of the shift (CI) or at the end of the shift (CO) X5 Number of individual F days in the previous 28 days Number of individual days off (F) in the previous 28 days, at the beginning of the shift (CI) or at the end of the shift (CO) Rest X6 Rest length Rest length before flying duty, at the start of a shift (CI) or at the end of a shift (CO) X7 Local night in a daily rest Whether the rest before flight duty includes a local night X8 Number of local nights in the 48 h before flight duty How many local nights included rest 48 h before flight duty X9 Changes in the schedule Changes in the schedule of crews in the previous 7 days by more than 1 h Cumulative workload X10 Sectors in the previous 7 days Number of sectors (flights) completed in the previous 7 days X11 Sectors in the previous 28 days Number of sectors (flights) performed in the previous 28 days X12 Flight time in the previous 7 days Total flight time (includes only flight time, not the time of aircraft ground handling) in the previous 7 days X13 Flight time in the previous 28 days Total flight time (includes flight time only, not the time of aircraft ground handling) in the previous 28 days X14 Duty time in the previous 7 days Total duty time (includes all time on duty-from CI to CO and duties on the ground) in the previous 7 days X15 Duty time in the previous 28 days Total duty time (includes all time on duty-from CI to CO and duties on the ground) in the previous 28 days Individual flight duty X16 Flight duty time Flight duty time for individual flight duty period (FDP) X17 Duty time Duty time for individual flight duty period (FDP) X18 Flight time in flight duty Flight time (Block Time) during the individual flight duty period (FDP) X19 Average duration of a sector Average duration of an individual sector (flight) of self-confidence Subjective self-assessment of self-confidence (scale from 1 to 10) S4 Self-assessment of anxiety level Subjective self-assessment of anxiety level (scale from 1 to 10) shortest time required to solve tasks in a certain test (Tmin), as shown in Figure 2. Di represents the blocks of partial ballast (D1 … Dn); it serves primarily to monitor the dynamics of change in the speed of mental processing as a function of the performance of a particular chronometric test, and cumulatively to derive the indicators of Initial ballast (Bin), and Final ballast (Bfin).In other words, it is the overall indicator of the stability of the mental processing of the test content by an individual.

Figure 2 .
Figure 2. Derivation of ballast Di from reaction time Ti.

Figure 2 .
Figure 2. Derivation of ballast Di from reaction time Ti.

Figure 3 .
Figure 3.The number of CRD tests with statistical significance (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 3 .
Figure 3.The number of CRD tests with statistical significance (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 4 .
Figure 4.The number of dependent variables with statistical significance (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 4 .
Figure 4.The number of dependent variables with statistical significance (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 5 .
Figure 5.The number of statistically significant differences for each group of independent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 5 .
Figure 5.The number of statistically significant differences for each group of independent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 5 .
Figure 5.The number of statistically significant differences for each group of independent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 6 .
Figure 6.The number of statistically significant differences for each of the independent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 7 Figure 6 .
Figure 7 shows the dependent variables in relation to the grouped CRD variables regarding speed, stability, and reliability, according to the number of statistically significant differences.CRD variables regarding speed include Total test-solving time (Ttot), Minimum test-solving time (Tmin), and Maximum test-solving time (Tmax).CRD variables regarding stability include Total ballast (Btot), Initial Ballast (Bin), and Final ballast (Bfin).The CRD variable regarding reliability is Number of errors (Nerr).Regarding theFigure 6.The number of statistically significant differences for each of the independent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 7 .
Figure 7.The number of statistically significant differences per independent variable and per group of CRD dependent variables (speed, stability, and reliability) (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 7 .
Figure 7.The number of statistically significant differences per independent variable and per group of CRD dependent variables (speed, stability, and reliability) (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Figure 8 .
Figure 8. Sample of the dataset used to create a causal model of the observed flight crew fatigue indicators (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 8 .
Figure 8. Sample of the dataset used to create a causal model of the observed flight crew fatigue indicators (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 9 .
Figure 9. Overall model quality (Source: Own elaboration using IBM SPSS and dataset from the Appendix A).

Figure 10
Figure 10 shows the overall causal model system (TCM) of all causal links among the flight crew fatigue indicators, subjective self-assessments, and workload settings parameters, obtained using the causal modeling functions of the IBM SPSS Statistics 27.For example, TCM shows that indicator S2 (Self-assessment of the energy level) correlates with X2 (Start or end of the shift (Check In/Check Out-CI/CO)), X3 (Number of days off in the previous 7 days), X5 (Number of individual days off in the previous 28 days), X15 (Duty time in the previous 28 days), S3 (Self-assessment of self-confidence), Y1 (Number of errors or accuracy of mental processing), Y2 (Mental processing speed or total time required to solve a test), and Y5 (Total ballast or total lost time due to fluctuations in the speed of solving similar tasks).Figure11shows the direct impacts of target indicator Y8, i.e., Fatigue index.Figure11ashows the correlations (links) with statistical significance values less than or equal to 0.05, while Figure11bshows all of the detected correlations (impacts) of Y8.Figure11ashows all the links with statistical significance values less than or equal to 0.05.As shown in these results, Y8 correlates with five workload settings indicators, namely X5 (Number

Figure 9 .
Figure 9. Overall model quality (Source: Own elaboration using IBM SPSS and dataset from the Appendix A).

Figure 10 .
Figure 10.Temporal causal model of flight crew fatigue indicators, subjective self-assessments, and workload settings parameters (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 11 .
Figure 11.Direct impacts of target indicator Y8 (Fatigue index): (a) Links with statistical significance values less than or equal to 0.05; (b) All links (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 12
Figure 12 shows an impact diagram of all indicators related to Y8, i.e., Fatigue index.These include X2 (Start or end of the shift (Check In/Check Out)), X5 (Number of

Figure 10 . 44 Figure 10 .
Figure 10.Temporal causal model of flight crew fatigue indicators, subjective self-assessments, and workload settings parameters (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 11 .
Figure 11.Direct impacts of target indicator Y8 (Fatigue index): (a) Links with statistical significance values less than or equal to 0.05; (b) All links (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 12
Figure 12 shows an impact diagram of all indicators related to Y8, i.e., Fatigue index.These include X2 (Start or end of the shift (Check In/Check Out)), X5 (Number of

Figure 11 .
Figure 11.Direct impacts of target indicator Y8 (Fatigue index): (a) Links with statistical significance values less than or equal to 0.05; (b) All links (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 12
Figure 12 shows an impact diagram of all indicators related to Y8, i.e., Fatigue index.These include X2 (Start or end of the shift (Check In/Check Out)), X5 (Number of individual

Figure 12 .
Figure 12.Impact diagram: causes of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 12 .
Figure 12.Impact diagram: causes of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 13 .
Figure 13.Impact diagram: effects of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Figure 13 .
Figure 13.Impact diagram: effects of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS and dataset from Appendix A).
, the same ones are marked in red squares, while additional ones are marked in orange squares.Those include X5 (Number of individual days off in the previous 28 days), X6 (Rest length), X7 (Local night in daily rest), X9 (Changes in the schedule), and X10 (Sectors in the previous 7 days).The reason why these are of particular interest is because they represent the independent variables which are susceptible to modification.Hence, finding indicators of workload settings that impact the flight crew fatigue opens up the possibility to modify them in order to mitigate fatigue risk.

Figure 13 .Figure 14 .
Figure 13.Impact diagram: effects of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS and dataset from Appendix A).
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

Figure 14 .
Figure 14.Direct impacts of workload setting on flight crew fatigue (Y8): (a) Links with significance values less than or equal to 0.05; (b) All links (Source: Own elaboration using IBM SPSS and dataset from the Appendix A).
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.
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.This research implemented a combination of fatigue objectivation methods, statistical analysis tools, and causal modeling techniques to determine correlations among flight crew fatigue indicators, indicators of the subjective perception of fatigue, and workload settings in flight operations.Determining correlations among indicators provides useful information on causal factors that trigger the appearance of fatigue in flight crews, making it possible to modify those factors and define improved mitigation measures.

Figure A1 .
Figure A1.One-way ANOVA analysis of a dependent variable Bfin/Bin and independent variable "Subjective self-assessment of the anxiety level"-CRD 23.

Figure A1 .
Figure A1.One-way ANOVA analysis of a dependent variable Bfin/Bin and independent variable "Subjective self-assessment of the anxiety level"-CRD 23.

Figure A2 .
Figure A2.One-way ANOVA analysis of a dependent variable Tmin and independent variable "Subjective self-assessment of the anxiety level"-CRD 241.

Figure A3 .
Figure A3.One-way ANOVA analysis of: (a) A dependent variable Nerr and an independent variable "Subjective self-assessment of the anxiety level"; (b) Dependent variable Btot and Bfin and an independent variable "Subjective self-assessment of the anxiety level".

Figure A3 .
Figure A3.One-way ANOVA analysis of: (a) A dependent variable Nerr and an independent variable "Subjective self-assessment of the anxiety level"; (b) Dependent variable Btot and Bfin and an independent variable "Subjective self-assessment of the anxiety level".
at the level of 0.05.

Figure A4 .
Figure A4.One-way ANOVA analysis of a dependent variable Nerr and an independent variable "Average duration of a sector"-CRD 23.

Figure A4 .
Figure A4.One-way ANOVA analysis of a dependent variable Nerr and an independent variable "Average duration of a sector"-CRD 23.

Figure A5 .
Figure A5.One-way ANOVA analysis of: (a) A dependent variable Nerr and an independent variable "Average duration of a sector"; (b) A dependent variable Bfin/Bin and an independent variable "Average duration of a sector".

Figure A5 .
Figure A5.One-way ANOVA analysis of: (a) A dependent variable Nerr and an independent variable "Average duration of a sector"; (b) A dependent variable Bfin/Bin and an independent variable "Average duration of a sector".
results of the CRD measurement include the CRD measures and fatigue indicators.

Table 2 .
Overview of the CRD fatigue indicators.
The quotient of Bfin and Bin Values greater than 1 indicate fatigue

Table 2 .
Overview of the CRD fatigue indicators.
The quotient of Bfin and Bin Values greater than 1 indicate fatigue

Table 3 .
Self-assessment scale of emotional state.
6 I'm not in a particularly good mood, I almost feel fine.7 I am fine and feel a slight positive excitement.8 I feel very well.9 I am in a very positive mood, I feel great.10 I feel unusually joyful and energetic.

Table 4 .
Self-assessment scale of energy level.

Table 5 .
Self-assessment scale of self-confidence.
RankDescription of Self-Confidence 1 I am unable to muster the strength to do anything.2 I feel unhappy and sad, tired, and incompetent.3 I am broken and not capable of taking action.4 It seems to me that I am not capable of anything.5 It's as if my knowledge and abilities are insufficient to meet the demands placed on me.6

Table 6 .
Self-assessment scale of anxiety level.

Table 7 .
Sample of the original values for the CRD fatigue indicators converted into T scale values.
Days off, i.e., the influence of the number of days off on the dynamics of mental processing; • Rest, i.e., the influence of fatigue on the dynamics of mental processing; • Cumulative workload, i.e., the impact of cumulative workload on the dynamics of mental processing; • Individual flight duty, i.e., the influence of the elements of individual flight duty on the dynamics of mental processing.
• Subjective scales of self-assessment (scales of the energy level, emotional state, selfconfidence, and anxiety level), i.e., the dynamics of mental processing in relation to a subject's subjective self-assessment; • • Speed indicators: Ttot, Tmin and Tmax; • Stability indicators: Btot, Bin, Bfin and Bfin/Bin; • Reliability indicator: Nerr.

Table 8 .
The number of measurements that were statistically significant as per each CRD test and the dependent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Table 8 .
The number of measurements that were statistically significant as per each CRD test and the dependent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).
Figure 3.The number of CRD tests with statistical significance (Source: Own elaboration based on Statistica 10 ANOVA analysis).

Table 9 .
Variables of the observed dataset (collected data) of fatigue indicators, subjective selfassessments, and workload settings (Source: Own elaboration using dataset from Appendix A).

Table 10 .
Fit statistics for the causal models of each target indicator in the dataset (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Table 10 .
Fit statistics for the causal models of each target indicator in the dataset (Source: Own elaboration using IBM SPSS and dataset from Appendix A).

Table A1 .
Sample of CRD measurements (collected data).

Table A3 .
One-way ANOVA variance analysis of CRD 13 results for "Subjective self-assessment of the anxiety level".

Table A5 .
One-way ANOVA variance analysis of CRD 23 results for "Subjective self-assessment of the anxiety level".

Table A5 .
One-way ANOVA variance analysis of CRD 23 results for "Subjective self-assessment of the anxiety level".Statistical significance at the promile level.

Table A6 .
Post-hoc analysis of the Bfin/Bin and "Subjective self-assessment of the anxiety level" using the Fisher LSD test.

Table A7 .
Frequency of "Subjective self-assessment of the anxiety level"-test CRD 241.

Table A8 .
One-way ANOVA variance analysis of CRD 241 results for "Subjective self-assessment of the anxiety level".
* Statistical significance at the level of 0.05.

Table A9 .
Post-hoc analysis of a Tmin and "Subjective self-assessment of the anxiety level" using the Fisher LSD test.
Figure A2.One-way ANOVA analysis of a dependent variable Tmin and independent variable "Subjective self-assessment of the anxiety level"-CRD 241.

Table A9 .
Post-hoc analysis of a Tmin and "Subjective self-assessment of the anxiety level" using the Fisher LSD test.

Table A10 .
Frequency of "Subjective self-assessment of the anxiety level"-test CRD 324.

Table A10 .
Frequency of "Subjective self-assessment of the anxiety level"-test CRD 324.

Table A11 .
One-way ANOVA variance analysis of CRD 324 results for "Subjective self-assessment of the anxiety level".

Table A12 .
Frequency of "Subjective self-assessment of the anxiety level"-test CRD 422.

Table A13 .
One-way ANOVA variance analysis of CRD 422 results for "Subjective self-assessment of the anxiety level".
* Statistical significance at the level of 0.05.*** Statistical significance at the promile level.

Table A14 .
Post-hoc analysis of a Btot and "Subjective self-assessment of the anxiety level" using the Fisher LSD test.

Table A14 .
Post-hoc analysis of a Btot and "Subjective self-assessment of the anxiety level" using the Fisher LSD test.

Table A16 .
One-way ANOVA variance analysis-Differences in "the mental processing efficiency" on CRD 13 for "Average duration of a sector".

Table A17 .
Frequency of "Average duration of a sector"-test CRD 23.

Table A18 .
One-way ANOVA variance analysis-Differences in "mental processing efficiency" on CRD 23 for "Average duration of a sector".

Duration of a Sector 1. Duration of a Sector from 00:40 to 01:01 h 2. Duration of a Sector from 01:03 to 01:23 h 3. Duration of a Sector from 01:25 to 01:45 h 4. Duration of a Sector from 01:46 to 03:35 h F p
* Statistical significance at the level of 0.05.

Table A20 .
Frequency of "Average duration of a sector"-test CRD 241.

Table A21 .
One-way ANOVA variance analysis-Differences in "the mental processing efficiency" on CRD 241 for "Average duration of a sector".

Table A22 .
Frequency of "Average duration of a sector"-test CRD 324.

Table A23 .
One-way ANOVA variance analysis-Differences in "the mental processing efficiency" on CRD 324 for "Average duration of a sector".

Duration of a Sector 1. Duration of a Sector from 00:40 to 01:01 h 2. Duration of a Sector from 01:03 to 01:23 h 3. Duration of a Sector from 01:25 to 01:45 h 4. Duration of a Sector from 01:46 to 03:35 h F p
* Statistical significance at the level of 0.05.

Table A24 .
Post-hoc analysis of a Nerr and an "Average duration of a sector" using the Fisher LSD test.

Table A25 .
Post-hoc analysis of a Bfin/Bin and an "Average duration of a sector" using the Fisher LSD test.

Table A26 .
Frequency of "Average duration of a sector"-test CRD 422.

Table A27 .
One-way ANOVA variance analysis-Differences in "the mental processing efficiency" on CRD 422 for "Average duration of a sector".