2.5.4 Functional Modeling and Analysis
The objectives of a functional analysis are to
1 Identify all the functions of the item.
2 Identify the functions required in the various operating modes of the item.
3 Provide a hierarchical decomposition of the item functions (see Section 2.5.5).
4 Describe how each function is realized and provide the associated performance requirements.
5 Identify the interrelationships between the functions.
6 Identify interfaces with other systems and with the environment.
Functional analysis is an important step in systems engineering (Blanchard and Fabrycky 2011), and several analytical techniques have been developed. We briefly mention two of these techniques: Function trees and SADT / IDEF 0.
2.5.5 Function Trees
For complicated systems, it is sometimes beneficial to illustrate the various functions as a tree structure called a function tree. A function tree is a hierarchical functional breakdown structure starting with a system function or a system mission and illustrating the corresponding necessary functions on lower levels of indenture. The function tree is created by asking how an already established function is accomplished. This is repeated until functions on the lowest level are reached. The diagram may also be developed in the opposite direction by asking why a function is necessary. This is repeated until functions on the system level are reached. Function trees may be represented in many different ways. An example is shown in Figure 2.4.
Figure 2.4 Function tree (generic).
A lower level function may be required by a number of main functions and may therefore appear several places in the function tree.
2.5.6 SADT and IDEF 0
A widely used approach to functional modeling was introduced by Douglas T. Ross of Sof Tech Inc. in 1973, called the structured analysis and design technique (SADT). The SADT approach is described, for example, in Lambert et al. (1999) and Marca and McGowan (2006). In the SADT diagram each functional block is modeled according to a structure of five main elements, as shown in Figure 2.3
Function. Definition of the function to be performed.
Inputs. The energy, materials, and information necessary to perform the function.
Controls. The controls and other elements that constrain or govern how the function is carried out.
Resources. The people, systems, facilities, or equipment necessary to carry out the function.
Outputs. The result of the function. The outputs are sometimes split in two parts; the wanted outputs from the function, and unwanted outputs.
The output of a functional block may be the input to another functional block, or may act as a control of another functional block. This way the functional blocks can be linked to become a functional block diagram. An illustration of an SADT diagram for subsea oil and gas stimulation is shown in Figure 2.5. The diagram was developed as part of a student project at NTNU (Ødegaard 2002).
Figure 2.5 SADT diagram for subsea oil and gas stimulation.
When constructing an SADT model, we use a top‐down approach as shown in Figure 2.6. The top level represents a required system function. The functions necessary to fulfill the system function are established as an SADT diagram at the next level. Each function on this level is then broken down to lower level functions, and so on, until the desired level of decomposition has been reached. The hierarchy is maintained via a numbering system that organizes parent and child diagrams.
Figure 2.6 Top‐down approach to establish an SADT model.
The functional block in Figure 2.3 is also used in the Integrated definition language (IDEF), which is based on SADT and developed for the US Air Force. IDEF is divided into several modules. The module for modeling of system functions is called IDEF 0 (e.g. see U.S. Air Force 1981; U.S. DoD 2001; Marca and McGowan 2006).
For new systems, SADT and IDEF 0 may be used to define the requirements and specify the functions and as a basis for suggesting a solution that meets the requirements and performs the functions. For existing systems, SADT and IDEF 0 can be used to analyze the functions the system performs and to record the mechanisms (means) by which these functions are accomplished.
2.6 System Analysis
The term analysis means to break down – or decompose – a system or problem into its constituent components in order to get a better understanding of it. In a system analysis, all the constituent components are studied individually. The word “analysis” comes from an ancient Greek word that means “breaking up.” To be able to analyze a system, the system must comply with the Newtonian–Cartesian paradigm (see box).
2.6.1 Synthesis
A synthesis is an opposite process of an analysis and is concerned with the combination of components and their properties to form a connected whole (i.e. a system).
In a system reliability study, we usually need to apply both analysis and synthesis to obtain a sufficient understanding of the system and its reliability.
The processes of system analysis and synthesis are illustrated in Figure 2.7.
2.7 Simple, Complicated, and Complex Systems
Most modern books on reliability theory and analysis seem to be concerned with “complex systems,” but (almost) none of them define what they mean by the term complex. In our understanding, we may classify a system into one out of three categories:
Simple systems. A simple system is easy to understand and can be analyzed by following a defined procedure or algorithm. Most simple systems have a rather small number of components. Simple systems can generally be modeled by a series–parallel RBD (see Section 2.8).The Newtonian–Cartesian ParadigmA paradigm is a worldview underlying the theories and methodologies of a scientific subject. For system reliability, the Newtonian–Cartesian paradigm has been, and still is, the most essential. The basis for this paradigm was