How are models built?
▪ Models are built by:
− Removing elements that are irrelevant – relevance depends on what you want to accomplish
− Abstraction of elements
− Defining relevant relations between those elements
Abstraction - Definition
An abstraction is an abstract idea or term. Abstract refers to something that is disassociated from any specific instance.
▪ Abstraction can be interpreted as forming an equivalence class
Equivalence class - Definition
An equivalence class is a set for which an equivalence relation holds between every pair of elements.
What is the equivalence class related to the question “What does it do (to something)?” called?
A function
Function - Definition
(1) A function describes the behavior of a system, often expressed as the action upon something (e.g. an object or a user) as an input-output relationship. It is the answer to the question “What does the system do (to sth.)?“
(2) A function is a task or purpose of a system, often expressed as the desired action upon something (e.g. an object or a user) as input-output relationship. It is the answer to the question “What is the system supposed to do to sth.?“
Definition (1) is of the type realized behavior. Definition (2) is of the type requirement / desired behavior.
What is a function model and what is its purpose?
Functions of a technical system and their relationships can be modeled in a function model. Function models are abstract representations of requirements on products and/or first concept ideas.
Purpose:
▪ Solution-neutral description of a product to be designed – by abstracting from the concrete problem.
▪ Look for alternative solutions / improvement of an existing solution – by abstracting from the existing solution.
What is the right situation to use Flow-Oriented Function Modelling?
▪ Early stages of product development process
▪ Development of a product that acts on another object, e.g., by processing, transporting, …
What is the input for Flow-Oriented Function Modelling?
▪ Design goal
▪ Requirements
What is the output for Flow-Oriented Function Modelling?
▪ Model of important functions that are necessary to reach the design goal
▪ Arrangement of modules and interfaces
What is the procedure for Flow-Oriented Function Modelling?
(*) may be omitted if obvious
What are the three types of elements in Relation-Oriented Function Modelling?
(1) Function of type task (FT): use imperative
(2) Function of type behaviour (FB): may be useful or harmful or neutral, use descriptive language
(3) Harmful function (HF): functions of type behavior that you clearly do not want, use descriptive language
What are the four types of relations in Relation-Oriented Function Modelling?
(1) was introduced for
(2) was introduced to prevent
(1) causes or may cause
(2) prevents or may prevent
„was introduced for“ does not mean that this is the only way to produce a desired behavior. In this sense, the originating FT is not necessary or required.
What is the input for Relation-Oriented Function Modelling?
▪Design goal / requirements / problem formulation
▪Optional: existing function models or product structure
What is the output for Relation-Oriented Function Modelling?
▪Model or relevant functions to be implemented to reach design goal (useful/harmful)
▪Arrangement of modules and interfaces
What is the right situation to use Relation-Oriented Function Modelling?
▪Structuring a design problem
▪First steps of solution generation
▪Restructuring and abstracting from an existing solution
What is the procedure for Relation-Oriented Function Modelling?
(1) Define important useful and/or harmful functions.
(2) Extend upstream to identify the means to realize or prevent functions
(3) Extend downstream to identify consequences of functions
(4) repeat for each new function until no reasonable extension possible
▪ Follow the compatibility rules, e.g., a HF cannot be introduced for an FT
What are some questions for upstream extension in Relation-Oriented Function Modelling? Name 2.
What are some questions for downstream extension in Relation-Oriented Function Modelling? Name 2.
What is the difference between Flow-oriented function models and Relation-oriented function models?
Flow-oriented function models
▪ Focus on processes
▪ Limited use for problem analysis
Relation-oriented function models
▪ Focus on conditions of success and consequences
▪ More useful for problem analysis
▪ Hidden assumptions may prevent alternative solutions
Graph - Definiton
A graph is a set of elements (or vertices, nodes) with relations (or edges, arcs) between pairs of these elements
▪ There are directed and undirected graphs
▪ The direction of edges is sometimes expressed by vertical positioning (hierarchy) and not shown on edges
Tree - Definition
A tree is a graph in which any two vertices are connected by exactly one path.
Polyhierarchy - Definition
A polyhierarchy can be represented by a directed graph without cycles along directed edges.
▪ In other words, elements may be connected to more than one element on the level above.
Matrix - Definition
A matrix is a rectangular array of expressions arranged in rows and columns.
▪ Every graph can be converted into a matrix by assigning each node one row and one column. The matrix itself represents the relations between nodes.
▪ For directed graphs, we use the convention: input is in rows, output in columns.
What are some examples for possible types of elements? Name 3.
▪ Design variables, attributes
▪ Functions
▪ Requirements
▪ Parts of the product / components
▪ States
▪ Tasks / process steps
▪ Individuals / groups / stakeholders