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Modern sociotechnical systems exhibit dynamic and complex behavior, which can be difficult to anticipate, model and evaluate. The perpetually evolving nature and the emergent properties of such systems require a continuous re-evaluation of adopted safety and risk analysis methods to comply with arising challenges and ensure successful performance. One of the interesting methods proposed in recent years is the Functional Resonance Analysis Method (FRAM). FRAM adopts a systemic perspective to model sociotechnical systems characterizing non-linear relationships and quality of outcome arising from performance variability and functional resonance. This paper aims to further improve the framework and expand the spectrum of features provided by FRAM through the integration of fuzzy logic. Fuzzy logic offers adequate mathematical tools capable of quantifying qualitative concepts and uncertain information applying comprehensible inference systems based on human judgement. An example of a possible application scenario is included through a simulation of aircraft on-ground deicing operations. The preliminary results of this project present an approach to generate numerical indicators for the quality of outputs, which can allow for a more comprehensible representation of potential performance variability. The presented model, however, requires further validation and optimization work to provide more representative and reliable results.

The dominant view in science before and at the beginning of the 20th century was that of mechanistic reductionism, which considered any system to be reducible to its parts and understandable in terms of mechanisms [

Modern sociotechnical systems are open systems embedded in their environments [

The work environment of aircraft ground deicing/anti-icing operations forms such a complex sociotechnical system, in which man and machine collaborate to perform a specific task. The influential factors that affect the quality of the system’s performance are variable. Operations are conducted in a dynamic and fast-paced environment under strict temporal constraints and in harsh meteorological conditions [

As is the case in aviation generally, deicing operations are high-reliability organizations. Operational procedures are formulated and executed in a strict manner to ensure safe operations. The number of accidents and incidents is low in aviation in comparison to other systems. The trend in aviation over the years shows a continuous improvement in performance and safety measures. In Canada, most deicing operations at large airports nowadays take place in centralized deicing pads [

Improving a reliable system that really works well can be difficult, since the possibilities for things to go wrong are limited and not immediately obvious. High reliability translates into a limited amount of data for analysis due to the rarity of adverse events that can provide conclusions and data for analysis and evaluation. Despite the high safety standards and high reliability of such a system, the need to evaluate and improve does not diminish. The continuous developments of applied technologies and the evolving nature of complex systems necessitate a continuous evaluation of the state of the system to maintain desired reliability and safety levels. New perspectives become necessary to cope with changes and relying on traditional analysis methods solely could be insufficient. To the best of our knowledge, research in the area of aircraft deicing from a systemic perspective considering human factors (individual and organizational) is rare [

Adopting a systemic approach would require the consideration of the above-mentioned factors, which is easier said than done. First, the scope of the analysis must be wide enough to allow for a systemic evaluation, which increases the number of considerable variables and thus the complexity of the analyzed context. Secondly, such factors can hardly be measured quantitatively and are best represented in terms of qualitative linguistic values. The high reliability and the low number of accidents and incidents in aviation generally, and in deicing specifically, make the composition of quantitative analyses more difficult. Some evaluation parameters and factors in the deicing context can be difficult to quantify. Linguistic scales present only an approximate evaluation of the observed variables, which results in imprecise and uncertain analysis results. Humans can have different concepts of the same linguistic terms and might therefore evaluate the significance of the measured variables accordingly.

This study is part of a years-long research program [

Safety can be defined as “the system property or quality that is necessary and sufficient to ensure that the number of events that could be harmful to workers, the public, or the environment is acceptably low” [

As a consequence of the human need to be free of unacceptable risk, safety was defined as a “dynamic non-event” [

Safety-I takes a simple-system approach to analyzing systems. Simple systems are characterized by linear causal relationships and predictable behavior [

Complex systems are self-organized distributed systems, which are open to their environments [

Successful systemic performance depends on the level of understanding of the relationships among the components and the capability to manage variability. Focusing on one aspect or analyzing each aspect separately without considering the emergent and complex properties of a sociotechnical system would not provide a complete picture of the system status. Systems have become so complex nowadays that only the domain experts are still capable of understanding their aspects and behavior [

An alternative approach would be to focus additionally on “what goes right” i.e. the conditions of the system in question that ensures risk-free and optimal outcomes [

In summary, to avoid falling behind and cope with the growing complexity of modern sociotechnical systems, a shift in perspective is needed. Complex systems have to be considered as a whole to better understand the functional relationships of the systems in question. In addition to looking at what goes wrong (Safety-I), one should look at what goes right as well (Safety-II), especially in the case of highly reliable systems and the absence of statistics and sufficient data.

FRAM was introduced by Erik Hollnagel in 2004 as a systemic accident investigation method. “The Functional Resonance Analysis Method describes system failures (adverse events) as the outcome of functional resonance arising from the variability of normal performance” [

• Equivalence of success and failure;

• Inevitability of approximate adjustments;

• Emergence of consequences;

• Functional resonance.

The reader is advised to consult the website of FRAM for a more detailed presentation of the features of FRAM (http://www.functionalresonance.com/).

The application of FRAM consists of five steps: Objective, Functions’ Identification, Variability Characterization, Functional Resonance and finally Variability Management. The five steps will be discussed briefly in the following subsections.

The objective of the FRAM application has to be determined, whether the objective is to perform an accident investigation (reactive) or a safety and performance assessment (proactive).

The functions that compose the system have to be defined and characterized. FRAM functions are objectives or tasks to be achieved by the system in question. They are characterized in terms of six aspects: input, preconditions, time, control, resources and output (

The performance variability of the functional outputs has to be identified. The basic FRAM model characterizes variability in terms of time and precision using a qualitative three-point scale for each attribute (

A specific analysis scenario or instantiation can be used to evaluate the influence of variable functions on other functions and the overlapping or resonance of those influences through functional couplings to result in adverse or successful outcomes (

The final step in FRAM is to identify countermeasures for variability management to design a more resilient system, ensure adequate performance and provide desired outcomes.

Characterization of Variability | |||
---|---|---|---|

Precision | Imprecise | Acceptable | Precise |

Timing | Too early | On time | Too late |

Since its introduction, FRAM’s usefulness was demonstrated through many applications in many fields as in construction [

FRAM is beneficial when dealing with contexts that are of qualitative nature, which can be difficult to quantify. The main advantage of FRAM remains the ability to account for complexity in the studied systems and to analyze nonlinear dynamic relationships among functions. Precise data for such contexts can be lacking due to their inherent complexity and the nature of the evaluated factors. The reliance on qualitative linguistic scales enables the analyst to evaluate contexts, in which data are missing or uncertain or the variables are hardly measurable numerically. However, one issue of this approach is that it does not provide a precise magnitude of the examined variables. The perceptions and definitions of the same linguistic scales as “imprecise” or “too late” can differ from one person to another. Adding quantification tools would allow for a more comprehensible representation of variability in terms of numerical values. As remarked by Hollnagel, in order to realize safety objectively and practically, it is important to validate the existence of safety through “intersubjective verification”, i.e. different parties should be able to confirm that their definitions and understanding of safety are matching [

The basic FRAM method evolved over the years and many improvements were proposed to provide more precise analysis results. Many studies addressed several limitations of FRAM related to the absence of quantification means. One of the first studies to propose an improvement to the framework of FRAM was conducted by Macchi [

Rosa et al. [

A recent and significant study for the evolution of FRAM was published by Patriarca et al. [

e j z = max { 1 ; ∑ k = 1 m S P C z k ⋅ b j k m } .

The variability for each coupling ( V P N i j z ) therefore was calculated as the product of the output’s variability (Timing Variability V j T & Precision Variability V j P ), the amplifying factor for each coupling ( a i j T & a i j P ) and the conditional variability e j z and the formula looked as follows:

V P N i j z = V j T ⋅ V j P ⋅ a i j T ⋅ a i j P ⋅ e j z .

To avoid misrepresenting the status and behavior of the system by using static scores, discrete probability distributions were instead utilized to provide a better representation of functional variability. Accordingly, the resulting product in the final formula above becomes through the Monte Carlo simulation a probability distribution as well. The developed methodology was then showcased through the application on a case study evaluating the Air Traffic Management (ATM) system. The proposed framework by Patriarca et al. marks an important development in the evolution of FRAM towards validation as a complementary tool to classical analysis methods. Rather than simply providing a simple numerical output, probability distributions are provided to assess variability. The applied Monte Carlo method relies on statistical data analysis to generate those distributions, which usually requires large data samples to run a large number of iterations. This makes the generation process of those values unidirectional since the sampling process is random.

A different approach to add quantification to FRAM can be achieved through the integration of fuzzy logic and the creation of a rule-based fuzzy inference system. The relationships between inputs and outputs can be characterized through the If-Then rules. Different weights and impacts can be associated with each quality class for each variable. The concept of fuzzy granulation and use of linguistic variables is a unique feature of fuzzy logic [

In this article, we explore a possibility to address this issue through the integration of fuzzy logic into FRAM as proposed by Hollnagel [

Fuzzy Logic is based on the Fuzzy Set Theory [

Let A be a fuzzy set and μ A is the membership function characterizing the fuzzy set A.

A then can be defined as: A = { x , μ A ( x ) | x ∈ A , μ A ( x ) ∈ [ 0 , 1 ] } with μ A : X → [ 0 , 1 ]

A fuzzy set A is therefore a collection of ordered pairs ( ( x , μ A ( x ) ) , where μ A ( x ) is the degree of membership of x in A.

Some basic operations of fuzzy sets are listed below as next:

Union of two fuzzy sets: C = A ∪ B = μ C ( x ) = max [ μ A ( x ) , μ B ( x ) ]

Intersection of two fuzzy sets: C = A ∩ B = μ C ( x ) = min [ μ A ( x ) , μ B ( x ) ]

Compliment of a fuzzy set A : A ′ = 1 − μ A (x)

The application of the fuzzy logic methodology consists of three steps: Fuzzification, Inference and Defuzzification [

A linguistic variable in fuzzy logic can belong with a certain degree of membership to a fuzzy set, which represents a label or a class of objects with specific characteristics [

The most used fuzzy inference processes are the Mamdani Inference model [

The final step of the fuzzy methodology is the defuzzification, which means transforming the fuzzy output into a crisp value. Many methods exist for defuzzification, from which one can be selected depending on the characteristics of the needed output (

C O G μ A ( x ) = ∫ μ A ( x ) ⋅ x d x ∫ μ A ( x ) d x (1)

Fuzzy logic can be an appropriate method to quantify uncertain and vague contexts, in which linguistic scales are the only possibility to measure the variables of interest [

The MTO classification of functions in FRAM distinguishes between three categories of functions: huMan, Technological and Organizational (MTO) functions [

Despite the drawbacks of this approach, it remains practical and useful. Capturing the precise nature of complex systems is difficult. Our perception of reality as humans is simplified and fuzzy. Simplifications are necessary for modeling reality and providing means of evaluation and control. Therefore, improvements to the current framework of FRAM could overcome the above-described issues without sacrificing the practical advantages of this approach. Fuzzy logic as a mathematical approach capable of computing with natural language and quantifying words can resolve the ambiguity of the outputs and present more comprehensible results. In the following section, we will present a detailed description of the integration of fuzzy logic into FRAM to present a possible approach for the addition of quantification.

The first two steps (step zero and step one) in FRAM remain unchanged: the identification of the analysis purpose and the identification and characterization of the functions. In step two, the performance variability has to be characterized. We can distinguish between two types of variability with respect to the identified functions: an exogenous variability, which is imposed on the function from external sources (other functions) through the functional couplings; and an indigenous or internal variability, which comes from within the function in question and depends on the characteristics and nature of that function [

The MTO classification method can be used here to determine which factors affect which functions. Originally, the quality of the CPC was evaluated on a three points scale: Adequate, Inadequate and Unpredictable [

Common Performance Conditions (CPC) | Human Functions | Technological Functions | Organizational Functions |
---|---|---|---|

Availability of resources | X | X | |

Training & competence | X | ||

Quality of communication | X | X | |

HMI and operational support | X | ||

Availability of procedures and plans | X | ||

Conditions of work | X | X | |

Number of goals and conflict resolution | X | X | |

Available time and time pressure | X | ||

Circadian rhythm and stress | X | ||

Team collaboration quality | X | ||

Quality and support of the organization | X |

present Common Performance Conditions (CPC). The range of the generated IVF will be between 0 and 1.5. Values between 0 and 1 account for negative variability that impairs performance, while values between 1 and 1.5 account for variability dampening and performance-enhancing impact (

Macchi [

The second type of variability is the external variability, which can be characterized through the couplings among functions. The outputs of the background functions are invariable, which means a stable output at 100% or one. The output of the foreground functions, which are the direct downstream functions to the background functions will receive only stable incoming aspects from the

background functions. The outputs will be classified into three classes relying on the classification method of Macchi [

Five classes were found to dampen variability (A to E) and four to increase or induce variability (F to I). At this stage of scientific developments, we need to limit the number of classes further to avoid the problem of rules explosion and present a simplified and practical model. Since highly controlled environments as aviation require high accuracy and all functions are to be executed as perfectly as possible, then we hypothesize and consider any dampening output as “Non-variable”, which shall account for positive or neutral impact. The outputs with low and medium variability will be combined and classified as “Variable”. The outputs with high variability will be classified as “Highly Variable”. This would simplify the classification of the outputs and limit the number of rules for the downstream functions significantly. The simplification is not an issue for the interpretation of the output’s quality, since an accurate numerical value for the output is provided (

Note that “Variable” in this context refers to the negative deviation of the output from the desired outcome, which is ideally one. A “Non-variable” label accounts for possibly positive impact on performance (

Then, a second higher-order fuzzy inference system relying on the rule base that characterizes the relationships between the incoming functional aspects in addition to the IVF of the function and the output is designed to produce the numerical output for the output’s quality of the function. The number of rules

Characterization of variability | Time | |||
---|---|---|---|---|

Too early | On time | Too late | ||

Precision | Precise | A: Dampening | B: Highly dampening | C: Low dampening |

Appropriate | D: Low dampening | E: Dampening | F: Slightly variable | |

Imprecise | G: Slightly variable | H: Variable | I: Highly variable |

Characterization of variability | Time | |||
---|---|---|---|---|

Too early | On time | Too late | ||

Precision | Precise | Non-variable | Non-variable | Variable |

Appropriate | Non-variable | Non-variable | Variable | |

Imprecise | Variable | Variable | Highly variable |

depends on the number of variables and respective classes. To keep the number of rules reasonable, many solutions can be adopted such as hierarchical fuzzy systems, or the use of genetic algorithms to design the rule base, etc. This would further complicate the design process and would make the application of FRAM difficult and exhaustive at this stage. In our case here, we tried to simplify the model to a degree that allows for the construction of a helpful model with reasonable effort. The simplification however shall not lead to the trivialization of the model. The rule base is helpful in overcoming another issue of FRAM, which is the assignment of weights to the different functional aspects. Different weights can be assigned to the rules depending on their significance and influence on the output. Additionally, weight scores can be assigned to the different labels in the antecedent part of the rule base to determine the implication of each rule and determine the respective consequent label. In our case, the applied implication method was the “MIN” method, and for aggregation, both the “MAX” and the “SUM” methods were applied.

The final step is to defuzzify the output to produce a numerical output. The applied defuzzification method in our case was the centroid method. The calculated numerical value presented a quantifier for the quality of the functional output. The fuzzy FRAM model is now ready for the simulation of deicing operations.

Looking at “work-as-imagined”, all performance conditions are optimal and the outputs of the functions are non-variable. To provide an application example in our case, a hypothetical scenario was constructed inspired by two deicing-related accidents, namely the Scandinavian Airlines flight 751 crash in 1991 [

• An international flight is scheduled to take off at a North American airport for a Trans-Atlantic flight provided by an international airliner;

• The pilots of the aircraft to be deiced are not very familiar with deicing procedures;

• Airliner instructions and guidelines provided for the flight crew do not specify clearly communication protocols and inspection procedures;

• The aircraft is to be taxied from the gate to the deicing pad, where two deicing trucks are positioned to perform the deicing operations;

• The weather conditions: temperature around 0˚C and snow showers were present;

• The flight crew was under temporal constraints: the flight was delayed due to weather conditions;

• The organizational performance conditions are not optimal, especially the provision of adequate training and instructions by the Airliner to its flight crew;

• The human or individual performance conditions for the flight crew are impaired: availability of resources, airliner procedures and plans, competence and time pressure.

The five steps for our FRAM model are then as follows.

The first step in FRAM is to identify the purpose of the analysis. Our objective is to present an example of a possible way to construct and run a FRAM model integrating fuzzy logic as a quantification method. The selected context for analysis is the context of aircraft deicing operations. The model will be of predictive nature and will not focus on simple basic activities such as move from point A to point B. Rather, the focus will be on more complex tasks to allow for a wide systemic perspective.

The functions of the model are to be identified. To keep the number of functions, variables and respective rules reasonable, the scope of the analysis will be limited to the deicing activities conducted by the deicing service provider at the deicing pad. The functions will be identified based on knowledge gained through a literature review of deicing reports and research work conducted by our team over the previous years. The background functions will form the boundaries of the model and will provide invariable outputs. The foreground functions will be the focus of the analysis and can produce therefore variable outputs. Totally, there are four background functions and 13 foreground functions.

The variability of the functions is to be characterized. We start by characterizing the internal variability for each function using the CPC list as explained above.

No. | Function Name | Type | Description |
---|---|---|---|

1 | Review Meteorological Data | Background | Review of weather conditions for preflight planning and inspections |

2 | Aircraft Specifications | Background | Aircraft technical and operational information provided mainly by manufacturer |

3 | Regulations and Supervision | Background | Supervision and regulations provided by governmental agencies |

4 | ATC Supervision | Background | Clearances provided by the ATC to navigate aircraft on the airport grounds |

5 | Resources and Equipment | Organizational | Resources and equipment provided for the inspection and deicing operations |

6 | Training | Organizational | Training provided to the deicing personnel |

7 | Airliner Instructions & Guidelines | Organizational | Guidelines provided by the airliner for the flight crew and deicing personnel |

8 | DSP Instructions & Guidelines | Organizational | Guidelines provided by the Deicing Service Provider (DSP) to its personnel |

9 | Preflight Planning | Human | Flight planning performed by the pilot and the flight dispatcher |

10 | Flight Crew Supervision | Human | Supervision provided by the pilot and flight crew to monitor and control operations |

11 | Deicing Tower Control | Human | Supervision provided by the deicing tower or the bay-lead to monitor and control operations |

12 | Pre-deicing Inspection | Human | Inspection of the aircraft to decide if deicing/anti-icing is required |

13 | Taxi Aircraft to Deicing Pad | Human | Taxi aircraft from gate to the deicing pad |

14 | Deicing | Human | The application of deicing fluids and removal of contamination |

15 | Post-deicing Inspection | Human | Inspection after deicing to ensure all surfaces are clean |

16 | Anti-icing | Human | The application of anti-icing fluid to keep aircraft clean until take-off |

17 | Taxi to Runway | Human | Taxi aircraft from deicing pad to runway for takeoff within the specified holdover time |

Each CPC is evaluated on a scale between zero and ten to plot its membership to the fuzzy sets “adequate” or “inadequate”. The detailed assignment of scores to each performance condition is listed in

No. | Function Name | Conditions of work | Number of goals & Conflict resolution | Quality & support of the organization | IVF |
---|---|---|---|---|---|

1 | Resources and Equipment | 9 | 9 | 9 | 0.969 |

2 | Training | 7 | 9 | 5 | 0.859 |

3 | Airliner Instructions & Guidelines | 8 | 9 | 4 | 0.845 |

4 | DSP Instructions & Guidelines | 8 | 8 | 9 | 0.93 |

No. | Function Name | Availability of Resources | Goals & conflict resolution | Quality of Communication | Availability of procedures and plans | Training & Experience | Available time | Circadian Rhythm and Stress | Team Collaboration | IVF |
---|---|---|---|---|---|---|---|---|---|---|

1 | Preflight Planning | 9 | 10 | 8 | 8 | 8 | 8 | 9 | 10 | 0.985 |

2 | Flight Crew Supervision | 6 | 10 | 6 | 6 | 6 | 6 | 9 | 10 | 0.815 |

3 | Deicing Tower Control | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 1.25 |

4 | Pre-deicing Inspection | 8 | 10 | 8 | 8 | 8 | 8 | 9 | 10 | 0.985 |

5 | Taxi Aircraft to Deicing Pad | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 1.25 |

6 | Deicing | 10 | 10 | 7 | 7 | 7 | 7 | 10 | 10 | 0.891 |

7 | Post-deicing Inspection | 10 | 10 | 7 | 7 | 7 | 7 | 10 | 10 | 0.891 |

8 | Anti-icing | 10 | 10 | 8 | 8 | 8 | 7 | 10 | 10 | 0.968 |

9 | Taxi to Runway | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 1.25 |

assigning the numerical score. For example, the CPC “conditions of work” can include a list of factors that define what constitutes adequate or inadequate conditions. The internal FIS is used to produce the IVF for each function.

The functional resonance is to be determined. The numerical outputs of the upstream functions will serve as incoming aspects for the downstream functions. The incoming aspects will be fuzzified in addition to the internal IVF and their impact on the downstream functions will be determined through the output’s Fuzzy Inference System (FIS) of each function (

The final step would be to analyze the received results according to the selected scenario and examine what measurements can be taken to improve the quality and resilience of the examined system (

The modelling of the system’s functions in the FMV happens in the form of tables characterizing the purpose of the defined functions and their aspects

No. | Function Name | Output’s Score | |
---|---|---|---|

1 | Review Meteorological Data | 1.0 | |

2 | Aircraft Specifications | 1.0 | |

3 | Regulations and Supervision | 1.0 | |

4 | ATC Supervision | 1.0 | |

5 | Resources and Equipment | 1.08 | |

6 | Training | 0.885 | |

7 | Airliner Instructions & Guidelines | 0.867 | |

8 | DSP Instructions & Guidelines | 1.0 | |

9 | Preflight Planning | 0.916 | |

10 | Flight Crew Supervision | 0.933 | |

11 | Deicing Tower Control | 1.18 | |

12 | Pre-deicing Inspection | 0.925 | |

13 | Taxi Aircraft to Deicing Pad | 1.22 | |

14 | Deicing | 0.932 | |

15 | Post-deicing Inspection | 0.689 | |

16 | Anti-icing | 0.849 | |

17 | Taxi to Runway | 0.866 |

according to the FRAM structure. The FMV enables the generation of a graphical representation of the designed model depicting a sort of a map of the system. This graphical representation provides an illustration of the relationships among functions, which allows for understanding how the functions affect each other and how variability can combine throughout the system. The numerical values of the IVF (representing the potential variability of the functions) and the outputs (representing the combined impact of internal and external variability on the output’s quality) were plotted in the graphical representation for illustrative purposes.

The formulated assumptions in our case here present a scenario, in which the airliner did not provide adequate training and adequate instructions to its flight crew. The flight was delayed due to weather conditions and a stressed flight schedule. This impacted negatively the performance conditions for the functions: Training, Airliner Guidelines and Instructions, Planning, Flight Crew Supervision, Pre-deicing Inspection, Deicing, Post Deicing Inspection, Anti-icing and Taxi to Runway. The functions with an output’s quality of one or higher are not variable in an adverse manner and have the potential to dampen variability in the downstream functions. The maximum output that can be achieved is 1.25 due to the selected defuzzification method i.e. the center of gravity method. The minimum quality output is 0.25. The numerical outputs showed a negative deviation from the ideal value (one or more) for the above-mentioned functions. The

lowest result was received for the output of the function “Post-deicing Inspection” due to the principle of resonance of variability.

Based on the characterized functions and performance conditions, the analyst would be able to construct a map of the system in question. The relationships and dependencies between the performance conditions and the quality of the outcome can be described to identify which conditions promote success and which ones impair performance. This map describes how the functions are linked and how they can possibly affect each other’s performance. The numerical outputs can provide a more precise and intersubjective representation of the variability magnitude. Using this map, the analyst would be able to locate potential sources for variability within the system. It is then possible to propose and implement measures to strengthen weak points and enforce conditions that ensure successful outcomes.

The application of FRAM can provide interesting and helpful results to keep up with the fast pace of technological developments and the dynamic nature of complex sociotechnical systems. This is not to say that FRAM can replace traditional analysis tools; rather, FRAM is complementary to the established methods and can present a different perspective on safety management and performance evaluation [

In contrast to retrospective analyses, in which events and their consequences can be described in a more precise manner, proactive or predictive studies lack certainty. Through the integration of fuzzy logic into the framework of the classical FRAM, the advantages of both approaches can be utilized for the provision of systemic analyses. Applying probabilistic methods relying on statistical data analysis may not always be possible. Fuzzy logic can be more suitable in the absence of sufficient quantitative data or the presence of vagueness and information imprecision [

The construction of the simulated model (characterization of functions, relationships, selection of membership functions, etc.) and the analysis were performed based on knowledge gained from studying deicing operations. Additionally, the characterization of the simulated deicing functions was performed relying as well on literature findings, accident reports and technical reports published by governmental agencies around the world. Through the formulation of some assumptions over performance conditions, a proactive analysis model was constructed. The simulation was run in the FRAM Model Visualizer and in MATLAB using the Fuzzy Logic Designer to demonstrate a possible approach for the realization of a fuzzy-logic-based FRAM model. The evaluation scale was selected between zero and ten, which can be used either as a discrete or as a continuous scale. However, it is important to note that human judgement can be less accurate on a continuous scale. While different scales may be more suitable for different applications, the test-retest reliability for rating scales with 11 response categories or more tends to decline in comparison to a 7-point, 9-point or 10-point scale [

The aggregated numerical output does not translate into a definite membership into one class of quality. Rather, the numbers can be seen as indicators for the potential of positive or negative variability based on the designed functions and their respective membership functions, quality classes and performance conditions. The model is flexible i.e. the functions can be re-defined and re-characterized if needed, new functions can be added or existing ones subtracted and relationships can be redefined as deemed appropriate. The influence of the different CPCs and the different functional aspects on the output can be weighted in the rule base. Each function depending on its nature can be examined separately to determine the weights in the rule base and account for the different influences on the output. In our case study, same weights were attributed to the different aspects and to all rules in the rule base of each function, which simplified the construction process of the rule base and allowed for a more efficient and feasible execution of the simulation. After all, the objective is to demonstrate how such an application can be executed and the focus is mostly directed to the theoretical aspect. Applying this approach to a real case study must be done with caution, since the proposed model at this stage is still a prototype in need of further improvements.

Admittedly, the simulation in the proposed case is a simplification of reality. The representation of influential conditions and the characterization of functions were simplified to facilitate the simulation process, which requires high computing resources. To avoid the “rules explosion” problem, the number of inputs was limited to a maximum of six. A higher number is possible of course; however, the size of the rule base would increase exponentially with each added variable, which can amount to a very exhaustive process. The validity and reliability of the numerical outputs depend greatly on the defined model characteristics for this simulation and the formulated assumptions. This means that the results are not necessarily generalizable to other contexts, which is not the point of this simulation anyway.

The continuous improvement of safety in aviation and the declining number of accidents year after year make it difficult to collect sufficient data to generate meaningful statistics [

To keep up with the fast pace of evolving modern sociotechnical systems, a continuous re-evaluation of applied safety and risk management tools is advised. A paradigm shift in the way we look at adversity is needed, namely the shift from a SAFETY-I to a SAFETY-II perspective. In addition to looking at what goes wrong and aiming at simply identifying causes and errors, looking at what goes right becomes necessary, especially when there is a lack of sufficient or precise data. The Functional Resonance Analysis Method (FRAM) is proposed in this paper as an adequate method to address these challenges in addition to classical assessment methods. The principles of FRAM allow for a fresh and different perspective on system analysis characterizing nonlinearity, complexity and performance variability. The main objective of this paper was to propose a possible improvement to the framework of FRAM through the integration of fuzzy logic as a quantification tool. In an effort to produce more intersubjective results, a fuzzy-FRAM model of the aircraft ground deicing operations was constructed relying on literature and findings of our research team over recent years. The context of deicing operations was simulated in the FRAM Model Visualizer and in MATLAB to present a first application of the proposed model. The preliminary results are promising and allow for a more comprehensible representation of potential performance variability. The presented model is still at this stage a prototype and requires further validation and optimization work going forward to provide more representative and reliable results.

The authors thank the Arbour Foundation and the National Sciences and Engineering Council of Canada (NSERC) for funding this study. The authors also thank Rees Hill, the developer of the software “FRAM Model Visualizer (FMV)”, which was applied in this study to develop and visualize the FRAM model.

The authors declare no conflicts of interest regarding the publication of this paper.

Slim, H. and Nadeau, S. (2019) A Proposal for a Predictive Performance Assessment Model in Complex Sociotechnical Systems Combining Fuzzy Logic and the Functional Resonance Analysis Method (FRAM). American Journal of Industrial and Business Management, 9, 1345-1375. https://doi.org/10.4236/ajibm.2019.96089