4 Approaches to understand, model and analyse complex systems
The present thesis is essentially about the problem of analysing risks in and vulnerabilities of complex systems. In order to do that, we must explore different ways of making sense of such systems. In the research literature there are several approaches and suggestions available. In this section an overview of three general and broad approaches will be given, which have been influential to the research presented here. The three approaches are:
¾ Systems theory and the systems movement,
¾ Complexity theory and the theory of complex adaptive systems,
¾ Network theory and analysis.
matters in an orderly and coherent corpus of knowledge” (Boulding, 1956). What was also observed by the “systems pioneers” was the high degree of isomorphism between different scientific disciplines. In systems theory, therefore, some researchers try to identify “universal” laws which are applicable to many different disciplines. The utility of such laws is that they can provide hypotheses about phenomena in disciplines other than from which the laws were derived. The “laws”
thus can give suggestions of how to study phenomena and where to look for the answers (Ashby, 1957); however, they do not “give” the answers since they are based on inductive inferences (Weinberg, 1975). Making such analogies between different types of disciplines or systems is one fundamental aspect of systems theory.
Another part of systems theory, perhaps the most significant, is the discipline that is concerned with applying systems thinking to practical problem-solving, labelled
“systems practice” by Checkland (1993). What are of interest to “system practitioners” are problems in the real-word with all its complexity. Since the concern is problem-solving, systems practice is very close akin to engineering in general. In the field of systems practice, methodologies, frameworks and guidelines have been developed in order to facilitate problem-solving. Systems engineering, systems analysis, systems dynamics and decision aids from decision theory are examples of developments in this field. Furthermore, methods and techniques for performing risk and reliability analyses can also be said to be a part of the development in the field of systems practice, and have largely been influenced by systems theory, which will be seen in chapter 5 where the foundations of risk and vulnerability analysis is addressed.
4.1.1 Distinguishing the real-world system and the system model
Central to systems theory is the existence of a real world system of some type (e.g.
technological, socio-technical, biological) that someone wants to make sense of, or solve a problem with regards to, e.g. an electric power distribution system or a municipality. Prima facie it might be easy to conclude that the system is ‘the thing in reality that is being studied’. However, as Ashby points out, there are fundamental disadvantages with such an approach, because “every material object contains no less than an infinity of variables and therefore of possible systems”
(Ashby, 1957). It is impossible to include all facts and aspects of the real phenomena when studying it. The pragmatic (the only!) way to proceed, which is adopted in systems theory and in the present thesis, is that the investigator selects the factors that are relevant in a certain situation and “those which are relevant may change with changes in the purpose of the research” (Ackoff, 1971). The chosen
factors, variables and properties are then incorporate in the “system” being studied, as such, a system is essentially a “human-made model” (Ropohl, 1999). The models can be specified in various ways, from formal mathematical or logical models to graphical representations of the real system of interest. But these models have in common that they stem from a mental representation of the real system of interest (Cook and Ferris, 2007). Due to the fact that the system is a model of the
‘real thing’ the system definition and description is somewhat dependent on the person making the description; the investigator chooses the factors to include and which factors that are relevant in a specific context depends on the purpose of making the description. This characteristic is captured by Weinberg when he defines a system as “a point of view” (Weinberg, 1975). However, although the system definition is somewhat subjective it is not relative in the sense that it is impossible to judge the appropriateness of the description, only that there might exist many definitions that are equally valid in the sense that they define the real phenomenon from different perspectives. This view is also supported by Haimes when talking about models in risk analysis: “more than one mathematical or conceptual model is likely to emerge; each of these focus on a specific aspect of the system, yet all may be regarded as acceptable representations of the system”
(Haimes, 1998). As a rough guideline regarding which factors to include in the system description, Weinberg’s rule of thumb can be used: “simplicity is what determines the right set of factors “ (Weinberg, 1975).
In the simplest form, a system can be defined as “a set of elements and a set of relations between these elements” (Ropohl, 1999). In this interpretation, a system is a structural concept; however, Ropohl argues that it is also possible to interpret a system as a functional concept, where the system transforms some input to some output. In practice, these interpretations complement each other. The former interprets the system concept as a “white box” where the internal elements and relations can be studied, while the latter interprets the system concept as a “black box”, where the inputs, functions and outputs are of interest. In the present thesis, these two definitions are amalgamated and a system is therefore seen as a set of element, their internal relations that taken together perform specific functions by transforming some inputs to some outputs.
4.1.2 Some systems concepts
In any application of systems concepts it is important to clarify which elements that the system is comprised of. This can be done by specifying the system boundaries, i.e. distinguishing between what is part of the system and part of the environment. Indirectly the system boundaries can be specified by “listing the variables that are to be taken into account” (Ashby, 1957), which is Ashby’s suggestion of how to define the system. Ackoff argues that the “system’s
environment consists of all variables which can affect its state” (Ackoff, 1971).
Simon makes the same distinction between a system and its environment but uses the words inner and outer environment (Simon, 1996). Systems can have different relationships to their environment and consequently be classified as open, closed or isolated. Open systems are systems that interact with (receive input from and yield output to) their environment (Skyttner, 1996). A closed system only exchanges energy with its environment, whereas isolated systems are hermetically closed, i.e.
they have no environment. The systems that are of interest here are predominantly open systems, which imply that it is not sufficient to only consider the system, it is also important to study its context.
Another important concept in systems theory is state variables. A state variable7, u, is used to describe different elements of the system. If considering a human being, for example, the state variables can be body temperature, heart rate, breath rate etc.
Each of these variables can take on different states, which often vary over time; the heart rate, for example, naturally increases when a person is exercising. The system’s overall state, U, can then be defined as the states of each of the variables (u1, u2…., un) of which the system is composed (Ashby, 1957). All possible states of a system can be represented in the state space8 of the system, thus each point in a state space corresponds to a unique system state, U. Furthermore, in order to represent a system’s dynamical behaviour, the concept of trajectories can be used. A trajectory can be defined as the succession of states that a system is taking on over time (U1, U2…., Uk) when transformations are taking place in the system. All these concepts will be relevant for the subsequent discussion of risk and vulnerability in chapter 5.