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Function model

Function model is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Function model rather than just read about it. In short: In systems engineering, software engineering, and computer science, a function model or functional model is a structured representation of the functions (activities, actions, processes, operations) within the modeled system or subject area. A function model, similar to the activity model or process model, is a graphical representation of an enterprise's function within a defined scope.

Function model — main illustration
Function model — illustration

Key takeaways

  • Function model belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Function model to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Function model from memory before moving on to harder problems.

Reference excerpt

In systems engineering, software engineering, and computer science, a function model or functional model is a structured representation of the functions (activities, actions, processes, operations) within the modeled system or subject area. A function model, similar to the activity model or process model, is a graphical representation of an enterprise's function within a defined scope. The purposes of the function model are to describe the functions and processes, assist with discovery of information needs, help identify opportunities, and establish a basis for determining product and service costs.

History The function model in the field of systems engineering and software engineering originates in the 1950s and 1960s, but the origin of functional modelling of organizational activity goes back to the late 19th century. In the late 19th century the first diagrams appeared that pictured business activities, actions, processes, or operations, and in the first half of the 20th century the first structured methods for documenting business process activities emerged. One of those methods was the flow process chart, introduced by Frank Gilbreth to members of American Society of Mechanical Engineers (ASME) in 1921 with the presentation, entitled “Process Charts—First Steps in Finding the One Best Way”. Gilbreth's tools quickly found their way into industrial engineering curricula. The emergence of the field of systems engineering can be traced back to Bell Telephone Laboratories in the 1940s. The need to identify and manipulate the properties of a system as a whole, which in complex engineering projects may greatly differ from the sum of the parts' properties, motivated various industries to apply the discipline. One of the first to define the function model in this field was the British engineer William Gosling. In his book The design of engineering systems (1962, p. 25) he stated:

A functional model must thus achieve two aims in order to be of use. It must furnish a throughput description mechanics capable of completely defining the first and last throughput states, and perhaps some of the intervening states. It must also offer some means by which any input, correctly described in terms of this mechanics, can be used to generate an output which is an equally correct description of the output which the actual system would have given for the input concerned. It may also be noted that there are two other things which a functional model may do, but which are not necessary to all functional models. Thus such a system may, but need not, describe the system throughputs other than at the input and output, and it may also contain a description of the operation which each element carries out on the throughput, but once again this is not. One of the first well defined function models, was the functional flow block diagram (FFBD) developed by the defense-related TRW Incorporated in the 1950s. In the 1960s it was exploited by the NASA to visualize the time sequence of events in a space systems and flight missions. It is further widely used in classical systems engineering to show the order of execution of system functions.

Functional modeling topics

Functional perspective In systems engineering and software engineering a function model is created with a functional modeling perspective. The functional perspective is one of the perspectives possible in business process modelling, other perspectives are for example behavioural, organisational or informational. A functional modeling perspective concentrates on describing the dynamic process. The main concept in this modeling perspective is the process, this could be a function, transformation, activity, action, task etc. A well-known example of a modeling language employing this perspective is data flow diagrams. The perspective uses four symbols to describe a process, these being:

Process: Illustrates transformation from input to output. Store: Data-collection or some sort of material. Flow: Movement of data or material in the process. External Entity: External to the modeled system, but interacts with it. Now, with these symbols, a process can be represented as a network of these symbols. This decomposed process is a DFD, data flow diagram.

In Dynamic Enterprise Modeling a division is made in the Control model, Function Model, Process model and Organizational model.

Functional decomposition Functional decomposition refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed from those parts by function composition. In general, this process of decomposition is undertaken either for the purpose of gaining insight into the identity of the constituent components, or for the purpose of obtaining a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of modularity. Functional decomposition has a prominent role in computer programming, where a major goal is to modularize processes to the greatest extent possible. For example, a library management system may be broken up into an inventory module, a patron information module, and a fee assessment module. In the early decades of computer programming, this was manifested as the "art of subroutining," as it was called by some prominent practitioners. Functional decomposition of engineering systems is a method for analyzing engineered systems. The basic idea is to try to divide a system in such a way that each block of the block diagram can be described without an "and" or "or" in the description. This exercise forces each part of the system to have a pure function. When a system is composed of pure functions, they can be reused, or replaced. A usual side effect is that the interfaces between blocks become simple and generic. Since the interfaces usually become simple, it is easier to replace a pure function with a related, similar function.

Functional modeling methods The functional approach is extended in multiple diagrammic techniques and modeling notations. This section gives an overview of the important techniques in chronological order.

Function block diagram

A functional block diagram is a block diagram, that describes the functions and interrelationships of a system. The functional block diagram can picture:

… excerpt ends here. Continue reading the full article.

Illustrations

Function model: Example of a function model of the process of "Maintain Reparable Spares" in IDEF0 notation.
Example of a function model of the process of "Maintain Reparable Spares" in IDEF0 notation.
Function model: Example of functional decomposition in a systems analysis.
Example of functional decomposition in a systems analysis.
Function model: Functional block diagram of the attitude control and maneuvering electronics system of the Gemini spacecraft. June 1962.
Functional block diagram of the attitude control and maneuvering electronics system of the Gemini spacecraft. June 1962.
Function model: Functional flow block diagram format.[13]
Functional flow block diagram format.[13]
Function model: An expanded IPO Model.
An expanded IPO Model.

Worked examples

Example 1 — a first encounter with Function model

Start with the simplest possible case. Write down what Function model claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Function model before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Function model ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Function model

In research
Function model appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Function model in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Function model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Modeling languages, Software architecture, Software design, so understanding it makes those chapters shorter.
In everyday life
Look for Function model outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Function model in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Function model means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Function model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Function model in simple terms?

In systems engineering, software engineering, and computer science, a function model or functional model is a structured representation of the functions (activities, actions, processes, operations) within the modeled system or subject area. A function model, similar to the activity model or process…

Why does Function model matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Function model?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Function model.

Tags

  • Modeling languages
  • Software architecture
  • Software design
  • Systems analysis
  • Systems engineering

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