Define Function. There are three principal characteristics that govern how functions are identified and analyzed.
Functions are described using 2 words, an active verb, and a measurable noun.
The noun in the function description is generic. Products or "things" that are used for the noun describe an action or activity of a function. As an example; "enclose space" would be a function.
"Construct building" describes one way to "enclose space". Functions can be defined as basic or secondary. Basic functions describe the principal reason for the existence of a product, process, or structure. Failure of a basic function causes the loss of the market value of that item. Once a function is classified as "basic" that function cannot change. However, the manner in which that function is implemented is subject to innovative analysis. "Secondary" (or supporting) functions describe features, attributes, and the approach to implement the basic function(s). Unlike basic functions, secondary functions can be modified, combined, or eliminated if the objectives of the VE study are satisfied.

Analyze Function. There are a variety of ways to analyze functions, all of which have a common goal. That goal is to relate function to cost, which is an expression of value. Focusing on the function-to-cost relationship, rather than the cost of "things", allows the value analyst to break through the veneer of superficiality and cut to the heart of the issues.
(a) Random Function Determination. This basic method involves randomly selecting elements of the project under study and determining their functions. Once defined, the functions are classified as basic or secondary. Cost data is then allocated to the functions producing a function-to-cost ratio. This ratio identifies potential areas for improving value.
(b) FAST. The FAST process states that functions exist because they are dependent upon other functions for their existence the way components are dependent upon other components to make a system work.

FAST Methodology. FAST is a structured utilization of intuitive logic. FAST allows effective communication, across disciplines and technologies, to separate cause from effect in the resolution of root problems. The intuitive logic of FAST requires that functions be identified using an active verb and a measurable noun. The objective of the verb-noun definition, however, is not to provide answers but to help the team ask the correct questions, questions that will lead to creative opportunities that produce outstanding results. This approach stimulates understanding of the process under study, exposes non-value-added functions, and affects the use of a common language, all of which encourage teamwork.
(a) HOW and WHY. FAST accelerates understanding the process under study because the discipline of FAST requires that participants use the language of verb-noun to describe the performance requirements of functions that make up the process. This vocabulary, concentrating on HOW things happen and WHY they happen, allows participants to quickly assess the salient elements of the process. This common language cuts across all disciplines to become the key that opens understanding of how decisions or actions impact process functions. Finding the proper verb and noun that complies with the function definition is often tedious but rewarding.
For example -

A spring does not move parts, it "stores energy".
A screwdriver does not turn screws, it "transmits torque".
A supervisor does not control people, he/she "manages resources". 

A major strength of FAST is the technique of questioning and focusing on which functions must be performed to achieve the desired result, and how best to achieve those functions rather than merely accepting previous methods and activities. Each function is then identified as contributing or not contributing added value to the product or process to justify its contribution to cost and quality of performance. Those not contributing are exposed as valueless, marginal activity.
In the FAST model, function dependencies are determined by establishing "HOW" the function is performed, and "WHY" the function is performed. The lack of a specific and acceptable response to each question indicates the presence of valueless functions and, therefore, the presence of marginal activity.

Example: A number of functions can be selected from a list of components of an office building:
1. Enclose Space
2. Create Habitat
3. Condition Environment
4. Regulate Temperature
5. Manage Traffic
6. Protect Inhabitants
7. Ventilate Enclosure
If one were to select the function "Condition Environment" for analyses, the function "Create Habitat" would satisfy the WHY question, and "Enclose Space" would satisfy the HOW question. The orientation of these questions is to read HOW from left to right and WHY from right to left.

In the above example, reading the HOW direction the questions would be: How do you create habitat? By conditioning environment. And how would you condition the environment? By enclosing space. Reading in the WHY direction the questions would be: Why would you enclose space? To condition the environment.
And why would you condition the environment? To create a habitat. If the logic is correct, the model can be expanded in either direction.
The answers to these questions are also functions, which link to form a graphical illustration of the project under study. Reading the resultant FAST model in the HOW direction must satisfy the function logic.
Reading the model in the WHY direction must satisfy the project's system logic.
(b) WHEN. Although WHEN is not an intuitive logical question, it is used to identify cause and effect, or activities that result when a function is active. In this context, WHEN does not indicate time. Although time can be added to the model as part of the analyses, the function model focuses on function dependencies to satisfy the intuitive logic, not time. 
Graphically, WHEN is linked to the function in question in the vertical plane. As an example, in evaluating the function "Condition Environment" it could be said that " . . . when you condition the environment you must regulate temperature". This would be expressed graphically as follows:

"Regulate Temperature" is considered a function, rather than an activity, because the noun "temperature" is
generic. 
To test the WHEN dependency ask; "If I didn't have to "Condition Environment" would I still have to "Regulate Temperature"? If the answer is "no", "Regulate Temperature" is dependent on "Condition Environment". If the answer is "yes", "Regulate Temperature" is independent and would not be connected to the function in question.
(c) AND and OR. The use of AND and OR is graphically illustrated when more than one function is necessary to answer the intuitive logic questions (AND), or when a clear choice of functions exists that satisfy the intuitive logic questions (OR).
As an example, it can be argued that creating a habitat requires protecting the inhabitants as well as conditioning the environment. This would be expressed functionally as; "How do you Create Habitat"? by "Condition Environment" AND "Protect Inhabitants". This would be illustrated as follows:

As example of the use of OR would be in asking the question: "How do you regulate temperature"? By "Heating Air" OR "Cooling Air". This would be illustrated as follows:

We can continue the dialogue and expand the function model by agreeing that: " . . . When we "Enclose Space", we must "Ventilate Enclosure". Why? to "Evacuate Contaminants". Also, when we "Enclose Space" we must "Manage Traffic". Notice that ventilation, in this model, is not dependent on the air temperature but on evacuating contaminants that collect in an occupied enclosed space.
Putting it all together thus far, the function model would appear as shown in Figure