Table 1 shows the main findings about the collection on the functional resonance analysis method (FRAM).

Figure 2 illustrates the annual scientific production associated with this subject matter. An annual percentage growth rate of 6.5% of publications was observed. The number of publications declined substantially between 2018 and 2019 before a high peak was observed in 2021. This increase corroborates the growing interest in using the FRAM methodology for the assessment of complex and dynamic socio-technical systems (environments characterized by high mishap hazard). These metrics infer that the annual number of papers published within the survey period is stable. Therefore, this research area is steady in respect of volume of publications (Afuye et al., 2021; Ellegaard & Wallin, 2015).

Table 2 shows the most relevant sources. Reliability Engineering and System

Safety ranks first with a total number of 8 publications followed by Safety Science and Cognition Technology and Work with respectively 6 and 4 publications as shows in Figure 3 depicting the source clustering through Bradford’s law. Figure 4 shows the Source growth.

Table 3 shows the most relevant authors. Costantino F., Di Gravio G., Patriarca R., and Hollnagel E. rank first followed by Kaya G.K. and Haddad A.N.

Table 4 shows the most cited authors. Hollnagel E. ranks first with 608 citations followed by Costantino F., Di Gravio G., Patriarca R. Figure 5 depicts the citation network, i.e., the citations within the collection of papers. It provides information about how authors relate to others in this specific field of research.

Figure 6 depicts the top-authors’ production over the time. A given line embodies an author timeline. The bubble at a particular year implies that the author published at least a paper in that year. The bubble size is proportional to the total number of papers that author published in that year. Finally, the color intensity is proportional to the total number of citations per year of the document published in that year.

Figure 7 illustrates the author productivity through Lotka’s law. The latter illustrates “the frequency of publication by authors in any given field. As the number of articles published increases, authors producing that many publications become less frequent” (Lotka, 1926). The general formula of Lotka’s law is expressed as follows: Y = C/Xⁿ (where X is the number of publications, Y the relative frequency of authors with X publications, and n and C are constants depending on the specific field (n ≈ 2). Only 3.30% of the authors have published four papers. Most of them (88.70%) have authored one paper.

The collaboration analysis provides information about how authors and countries interact to others in a particular domain of research. Figure 8 below depicts the author collaboration network (co-author network) classified in 4 clusters¹⁰. It

finds research groups of scholars and pivotal authors. The size of a link in the network depends on the relationship between the authors. The higher the relationship, the stronger the edge size. Figure 9 represents the authors’ bibliographic coupling categorized in four clusters. The relatedness of authors is established based on the number of references they shared or cited (“Bibliographic coupling occurs when two works reference a common third work in their bibliographies. It is an indication that a probability exists that the two works treat a related subject matter” (Martyn, 1964)). Figure 10 and Table 5 describe the

most relevant countries by corresponding authors nationalities. It shows the number of published papers in both Single Country Publications (SCP) and Multiple Country Publications (MCP). Brazil, Italy, and Turkey rank first with the largest number of papers. Documents published by SCP have a higher-trend productivity growth rate.

Table 6 depicts the most cited countries. Figure 11 illustrates their bibliographic coupling grouped in 3 clusters: CLUSTER 1: Canada, China, Denmark, Germany, Kazakhstan, Netherlands, Poland, South Korea, Spain, Turkey, United Kingdom; CLUSTER 2: Australia, Italy, Norway, Portugal, Sweden, CLUSTER 3: Brazil, United States. The citation analysis depicts the structure of the research area through the connections between countries. The timespan helps to explore the conceptual structures and analyze the evolution of themes over time. The collaboration networks show how countries relate to others in the research topic.

This section describes the word treemap and the clusters of most popular keywords. Figure 12 below depict the co-word network visualization of the co-occurrence analysis based on author’s keywords. The co-word networks describe the conceptual structure (i.e., the links between concepts) which characterizes the relationship between the keywords. The networks show the relationship among keywords within a document indicating themes or topics. Its node

corresponds to a keyword. Bigger is a link, greater is the relationship. This supports identify the intellectual domain of FRAM and provide research hotspots in this subject matter for future studies.

Information in Figure 13 and Figure 14 shows respectively the Tree-Mapfor the most pivotal Author’s Keywords (DE) and Keywords Plus (ID) associated with FRAM analyses. The Word Tree-Mapoutlines hot themes or the dynamic trends of major themes of the author (Cobo et al., 2011). It is key to studying hot themes within the sphere of research.

The Three-Fields Plot is depicted in Figure 15 using the items: Country (AU_CO), Authors (AU) and Author’s Keywords (DE). Appendix 1 shows the Three-Fields Plot for Keywords Plus (ID).

Clusters identified through the co-word analysis above are deemed as themes that can be classified according to their density and centrality in a two-dimensional diagram (Cobo et al., 2011; Aria & Cuccurullo, 2017). Themes can be analyzed according to the quadrant wherein they are positioned. Figure 16 depicts the thematic map encompassing seven clusters identified through the analysis of the centrality and density ranking of Keywords Plus. The cluster in the motor themes (first quadrant with the highest centrality and the highest density)¹¹ connoting that these themes is well-developed and significant for the

shaping of the research area. It contains Keywords Plus “human”, “functional resonance analysis method”, “health care”, “delivery of health care”, “health care personnel”, “semi structured interview”, and “controlled study” as the most co-occurring words. The cluster straddling between the motor themes and the basic themes, with a good centrality and density, includes words: “functional resonance analysis method”, “ferroelectric ram”, “risk assessment”, “safety engineering”, “sociotechnical systems”, “resilience engineering”, “performance variability”, “safety management” being the most recurring words. The cluster in the highly developed and isolated themes or niche themes (second quadrant with low centrality and high density) includes the single word “complex processes” implying that it has low reputation for the subject matter. The two clusters in the emerging or declining themes denoting they are weakly studied(third quadrant with low centrality and low density) encompasses words “oil spills”, “urban transportation” as the most repetitive words. The cluster in the basic and transversal themes relating to general and various research areas (fourth quadrant with high centrality and low density) incorporates words “accident prevention”, “accident analysis”, “aircraft accidents”, “air traffic control”, “roads and streets”, “advanced traffic management systems”, “air transportation”, “automation”, “behavioral research”. Lastly, the cluster straddling between the motor themes and the highly developed and isolated themes, with a good centrality and high density, includes the only word: “uncertainty analysis”.

There is a rising appeal in utilizing the FRAM methodology for the assessment of what precisely is happening in complex and dynamic socio-technical systems in practical high hazard environments (for e.g.: de Vries, 2017; De Carvalho, 2011; Adriaensen et al., 2019; Aguilera et al., 2016; Albery et al., 2016; Anvarifar et al., 2017; Belmonte et al., 2011; Bjerga et al., 2016; Buikstra et al., 2020; Clay-Williams et al., 2015; Costantino et al., 2018; Duan et al., 2015; Falegnami et al., 2019; Praetorius et al., 2015; Ferreira & Cañas, 2019; França et al., 2019; Gattola et al., 2018; Smith et al., 2020; Jensen & Aven, 2017; Furniss et al., 2016; Gao et al., 2019). The FRAM is a relatively new performance appraisal tool for risk assessment or accident investigation, in line with the thinking of the resilience engineering (RE) and reflects the “Safety II” theory rather than the traditional “Safety I” theory toward everyday operations or “events” (Hollnagel, 2012, 2014). The “Safety I” thinking (such as in Failure Mode and Effects Analysis, FMEA) focuses on what goes wrong (how a component may fail), while the “Safety II” thinking concentrates on what goes right (define the functions that are mandatory for the system to attain its objective). The FRAM approach enables practitioners to describe a complex and dynamic socio-technical system in the matter of the functions and the interactions among functions forming this system. Thus, performance variability can be investigated to understand where it may occur then disseminate all over the system (functional resonance) i.e., in what manner functional variability can deteriorate into unforeseen and undesirable outcomes. The RE, an attitude that has constantly advocated that safety is beyond the absence of failures, tackles how the socio-technical system may adjust to withstand disturbance within the mandatory parameters then maintain performance in required parameters (for e.g., Cabrera et al., 2014).

The outcomes of “how functions become coupled” and how “everyday performance variability may resonate” are the main objectives of the FRAM approach. The latter is a method rather than a model (Hollnagel, 2012). Accordingly, it neither formulates hypotheses about potential causes and cause/consequence relationships nor regarding how the system under probe is organized or structured. It is based on four comprehensive principles in line with the RE approach, namely:

· the principle of equivalence of success and failure¹²,

· the principle of approximate adjustments¹³,

· the principle of emergence¹⁴,

· the principle of functional resonance¹⁵.

Figure 17 describes the four core steps of the FRAM approach (Hollnagel, 2012).

First and foremost, Step 0 (preliminaries) is a requirement for defining the

analysis objective. Two analyses purposes are possible: 1) risk assessment (system descriptions, for e.g. Rosa et al., 2015) or 2) accident investigation (probe of the causes of the accident and draw the relevant conclusions, for e.g. De Carvalho, 2011; Herrera & Woltjer, 2010).

The first step (Step 1: Identify and Describe the Functions) focuses on identifying the functions (i.e. activities or set of activities) that are required for a given system or organisation to produce a certain outcome. Functions may be accomplished by technological systems or human operators, individually or cooperatively. Six aspects, namely Intput (I), Output (O), Preconditions (P), Recourses (R), Time (T), Control IC), describe a function as illustrated graphically by a hexagon in Figure 18. Thus, activities are identified, described and classified in term of how they are accomplished everyday rather than how they are imagined, facilitating to enhance insight of how variability may arise and propagate. Functions are classified either foreground, i.e., functions whose variability might influence the result of the assessment, or background, i.e., functions that are relatively stable and have less influence on the result of the assessment. Function-coupling is characterized as the interaction among functions. Function can be upstream (arising before another one) or downstream (arising after another one). This requires appropriate acknowledgement of the system.

The second step (Step 2: identification of variability) characterizes both the potential variability and the expected actual variability of the functions to determine the variation in the functional output instead of the change in the function. The potential variability refers to the model, while the expected actual variability refers to an instantiation of the model (“the FRAM model represents the set of functions that together account for the activity being analysed and the potential couplings among functions. An instantiation describes the couplings that existed or may exist for a given scenario or a set of conditions, and thus represents a realisation of the model” (Hollnagel, 2012)). This determines how each individual function can be influenced by internal (endogenous) or external (exogenous) performance variability.

The third step (Step 3: aggregation of variability) focuses on the combination of variability (i.e., functional resonance). It supports to identify which functions

may encounter potential performance variability and how the outcome may spread through the system. Once the functions are coupled, the interaction among them comes to be evident. The potential variability appraisal enables to recognize how upstream function variations impact downstream functions by up-down coupling. Thus, the true interest of the evaluation is to grasp the variation in the outcome of the function more willingly than the variation in the function itself; (“since a FRAM model does not stand for any specific situation, it can only represent the potential performance variability. The range of this can be estimated based on established scientific knowledge as well as practical experience from a domain. An instantiation represents a concrete instance of the model for given (actual or assumed) circumstances and set(s) of conditions, and the details provided by the instantiation makes it possible to be more precise about whether and how the potential variability can become actual variability. It is, however, not enough to know what the actual variability may be for individual functions. It is also necessary to know how variability may combine and thereby lead to outcomes that are either unexpected or out of scale—or both. In other words, it is necessary to know how functional resonance can come about. This is done by using the idea of function upstream-downstream coupling” (Hollnagel, 2012)).

The fourth step (Step 4: consequences of the analysis) aims at managing and controlling performance variability as well as encouraging effective outcomes (rather than only weakening undesirable outcomes). As soon as unforeseen or unwanted outcomes arise, safety measures should allow useful actions to be taken. In addition to the well-established methods such as safety prevention (barriers or defense), eliminating the hazards at the source if known, protection, etc., the FRAM methodology recommends two further solutions, namely monitoring (performance indicators) and dampening, in line with the four principles of underlying the FRAM. Therefore, the answer is to manage performance variability, typically by attempting to dampen the variability in order to diminish resonance influences (Hollnagel, 2012).

The RE and the FRAM idea recognize that things succeed and fail in fundamentally the similar way (i.e., the equivalence of successes and failures). The Principle of Approximate Adjustments means that adjustments are omnipresent and beneficial. This principle elucidates why resources like workforce, time, information, are not infinite and require recurrent approximate adjustments rather than exact. Indeed, organizations recurrently adapt and adjust their performance¹⁶. For e.g., an organization setting of objectives and priorities as well as actions to be undertaken against uncertainties of the environment such as supervisory requirements and legal liabilities, challenges of talents acquisition and their retention in the workplace, uncertainty in worldwide markets deregulation, technological innovation and technological obsolescence, constantly rising customer demands. Likewise, challenges are the current uncertain business context caused by the coronavirus disease pandemic, natural disasters, terrorist attacks and major cyberattacks (Diop et al., 2021). Subsequently, numerous socio-technical systems are problematic. The occupational conditions never entirely agree with what has been predetermined or suggested. The subsequent performance variability is the explanation why things either succeed or fail. However, the explanations that make the adjustments essential also imply that they are approximate rather than exact. The reason why things generally succeed or sometimes fail is attributable to approximate adjustments. In other words, outright failures, malfunctioning or errors for instance, do not mostly cause things to go wrong. Instead, the daily performance variabilities sum up or combine in an unforeseen way (i.e., the principle of functional resonance) causing something to fail. On one hand, normal performance variabilities hardly lead to possible safety concerns or failures since many of them are rarely significant to be the cause of mishaps or breakdowns, but on the other hand, despite actions

taken up to now, countless tragedies and human lives losses still occur every single day. For instance, recent disasters such as the deadly explosion in 2020, during test operations of Fortesa’s Gadiaga-2 Gas Field located in the village of Gadiaga, north of Dakar in Senegal, actualize the issue of onshore and offshore safety. A vicious fire broke out at one of the wells of the gas field operated by Fortesa International (AODL: Africa Onshore Drilling LTD). Likewise, for e.g., the MV Le Joola disaster, the second-worst non-military tragedy in maritime history. This roll-on/roll-off ferry was belonging to the Senegalese government. It capsized off in 2002 with 1863 losses in human life and 64 survivors.

These consequences can be explained by the combination in unexpected manners of multiple functions performance variability. Indeed, both normal performance and failures are emergent instead of the outcome of events or phenomena (i.e., the principle of emergence). In fact, risk should be seen as a developing attribute of complex and dynamic socio-technical systems. Therefore, it is urgent to investigate thoroughly at these kinds of disturbance to fully grasp all the connotations and ascertain the real needs that call for a response at strategic level.

This section carries out an evaluation of some of the most established methods used for risk assessment and management that may constitute an alternative or a complementary method to the FRAM process namely, the AcciMap, the Systems-Theoretic Accident Model and Processes (STAMP), the Management Oversight and Risk Tree (MORT), the Failure Mode and Effect Analysis (FMEA), the Root-Cause Analysis (RCA), the Human Reliability Assessment (HRA). Table 7 depicts these non-exhaustive assessment processes.