Complicated systems. A complicated system has a high number of components with a fair degree of interrelationships and interdependencies between the components. By using current knowledge (e.g. by involving subject experts), we are able to understand the relevant system properties and to analyze it.
Complex systems. In a complex system, the behavior of at least some of the components or the interactions between them do not comply with the requirements of the Newtonian–Cartesian paradigm. A complex system cannot be adequately understood and analyzed by traditional approaches because the system is something more than a sum of its components.
Figure 2.7 System analysis and synthesis.
An emergent property is a system property that cannot be deduced from the properties of the system components. In many cases, emergent properties lead to unexpected system behavior that may be dangerous. A system is usually not designed or built to be complex, but may develop into a complex system through changes, coupling, and emergence.
There is a considerable disagreement about how to delimit the concept of emergence. Some authors interpret emergence very widely and say that “properties” such as reliability, quality, and safety are emergent properties of a system.
Simple and complicated systems can be studied based on the Newtonian–Cartesian paradigm, whereas complex systems cannot be adequately studied within this paradigm. A new worldview called the complexity paradigm is therefore being developed.
All the examples in this book are related to simple systems, but the theory and methods presented may also be applied to complicated systems and many aspects of complex systems. Complex systems as such are not studied in this book.
Remark 2.1 (Classical methods
Finally, you may wonder if the effort you make to learn the theory and methods described in this book is a waste of time when your study object is complex. According to Einstein and Infeld (1938), the development of new theory may be compared with climbing a mountain. When you have come to a certain height, you get a better overview, but you may realize that you need another strategy to reach the summit. To have reached the present height is an achievement that gives a good understanding of the further climbing efforts.
2.8 System Structure Modeling
An early step of a system reliability study is to establish a model of the system structure. The model defines the system boundary and the elements of the system (i.e. inside the system boundary) and the interactions between these elements. We also make assumptions about how the system is operated and the environmental conditions and constraints that may affect the system elements and their behavior. A range of system modeling techniques are presented in later chapters. Here, we delimit the presentation to a rather simple approach – reliability block diagrams.
2.8.1 Reliability Block Diagram
This section describes how a system function (SF) can be modeled by a reliability block diagram (RBD). An RBD is a success‐oriented graph with a single source (a) and a single terminal (b). The nodes of the RBD are called blocks or functional blocks. Each block represents a component function (or a combination of two or more functions). We assume that the blocks are numbered
Each block is either functioning or failed, but the terms up and down are also used. Intermediate states are not allowed. To block
(2.1)
Observe that
Blocks are drawn as squares or rectangles, as shown is Figure 2.8 for component function