Cover Picture Working with Functions

Working with Functions

TRIZ Power Tools: Working with Functions

2012, 2017 By Collaborative Authors--All rights reserved

This book is the work of collaborators.

Larry Ball (Primary Author)
David Troness
Kartik Ariyur
Jason Huang
Don Rossi
Petr Krupansky
Steve Hickman

Erika Ball
Larry Ball
David Troness
Paul Dwyer
S. Robert Lang

Larry Ball
David Troness

Other Authors, Theoreticians, Practitioners Whose Writings or Teachings have Impacted This Work

Genrich Altshuller
Ellen Domb
Roni Horowitz
John Terninko
Alla Zusman
Boris Zlotin
Lev Shulyak
Yuri Salamatov
Victor Fey
Eugene Rivin
Darrell Mann
Sergei Ikovenko 
Simon Litvin
Peter Ulan
Lane Desborough
Clayton Christensen
Renee Mauborgne
Kim Chan
Greg Yezersky

Functional Nomenclature
It is recognized that the proliferation of TRIZ terms is objectionable and makes it difficult for the new student to "translate" between different authors. Sometimes different terms are used to mean the same thing. In order for the reader to “translate” while reading this text, a consistent nomenclature will be established. It is hoped that this nomenclature will already be familiar to most readers.

Functional language is a convenient and compact way to describe what a system does.  Without the system function, the system objects are useless.  Functions are a shorthand way to describe the system processes.  A simple function can describe an entire process diagram.

A System is a collection of physical objects that deliver a function. Examples of a system might be a toaster or a car. Many different objects make up a system, and they all work together to deliver a function to the user which helps to perform a job or task. Objects in the system act upon each other. In function analysis, interactions between two objects are taken one at a time.

Below is a generic function diagram of a single function showing its parts. The physical element that is acted on will be referred to as the Product. (In other texts, it may be referred to as the object or artifact.) The object that acts on the Product is referred to as the Tool. What the tool does to the product will be referred to as the Modification. (In some texts, this is referred to as the Action). The modification is usually a verb. The use of the term “Modification” will be new to many readers; however it is used to stress the requirement that the action verb must describe a change or control of the attribute of the product. This is sometimes difficult for beginners to grasp.

1 Tool Modifies Product

Beginners and those who are confused by what modification to use are encouraged, to use a longhand form of the modification. The longhand form begins with “Changes” or “Controls.” For example, we can describe the action that occurs between a tool “liquid” and a product “thermometer” which is immersed in the liquid. The short form of the modification is “heats” or “cools.” The longhand form of the modification would be “changes the temperature.” The use of the term “modification” helps the beginner to understand that the tool and product must be physical elements. It also helps to correctly describe “confusing functions,” which we shall address later.

2 Short and Longhand form

Systems of Functions
By linking together functions, we can create systems of functions that describe a situation. We might want to describe the super-system or job that our system is helping to do. We might want to describe the system of functions between subsystem elements. In any case, when we start linking together functions, we will refer to this as a “function diagram”.

Let’s first depict the super-system with a function diagram. The super-system is composed of the functions related to a job that someone is trying to do. It also contains a few elements usually found in the environment where the job takes place. Our system is usually one functional element of the super-system. A functional element performs a discrete useful function in the function diagram. Because our system is part of the super-system it performs select functions within the job. In rare cases, it may perform all of the functions of the job. The part of the job that our system performs has likely evolved over time.  Changing what our system does can be a powerful way to meet user needs and desired experiences.

A special element of the super-system is called the system product. Our system acts directly on this system product to modify it.  Below is a function diagram for the job of cleaning clothes. We are looking at this job from the perspective of the super-system. All of the elements shown are elements of the super-system. Our system elements are shown in red. The rest of the elements are other super-system elements. The "dirt" is the system product which is another super-system element. We color it yellow to keep it as the focus of the system.

3 Washer Function Diagram

Let’s pretend that we make clothes washers, but not dryers so our system is the washer. We have design authority over the washer and its parts. Because we control the water, and have full authority over it (we can even replace it if we would like) we also consider the water part of our system. While we can recommend the soap that is to be used, the amount and type that is used is not under our control so we consider this to be a super-system element. The dryer is also a super-system element that is not under our control. Notice that it’s function is to move water which our system demands.

The system product is the stuff that needs to be removed from the clothes (stains, dirt, perspiration, etc which we will refer to as dirt for brevity). It may be a little confusing that our system is not actually designed to operate on clothes, but rather on the dirt. Again, think of the job as what we hire a clothes washer to do. We don’t hire the washer to modify the clothes. Our washer should be called a “dirt mover” rather than a “clothes washer”. The dirt is also a part of the super-system. We don’t have control over it. While our job is to eliminate the dirt, we do not have authority over how much is present.

In addition to the useful function of moving dirt, the water of our system also wrinkles the clothing which is showed as a harmful function. (The dryer also has this same harmful function). The person who is involved in washing the clothes is involved in moving them and dispensing the soap.

Even though we call our system a clothes washer, the clothes are not the system product. The clothes have a harmful function of holding or supporting the dirt. If the clothes were doing their job properly, they would not hold the dirt! Because we have no control over the clothes, and they are not directly part of the washer, they are an element in the super-system.

The process of creating this diagram teaches us a lot about the job of cleaning clothes. Each element in the system carries it’s burdens. For instance, the clothes have the burden of holding the dirt. The water and dryer wrinkle the clothes. The person has the job of moving clothing and detergent about. So much could be done to unburden the person who needs to take care of the clothes. This is covered in another book "Removing Burdens".

One surprising discovery is that the main job of the washer is move water!  This massive piece of machinery just moves water.  That discovery, alone, can prompt an innovative person to consider other ways to move water or eliminate it entirely.

Each of the above super-system elements can be broken down further into sub-system components. Our system, the clothes washer, is also composed of sub-system elements. Some, but not all, of these components operate on the system product. Let’s break down our system into functional sub-system components. We will continue to show the system product “dirt” but will not show all of the super-system elements for brevity.

4 Washer and Dryer

Each of the sub-system elements is shown in red. The elements of the washer are common components. Each of them can be broken down yet further. Which brings us to a point: all systems are elements of higher super-systems. All elements can be broken down into sub-systems to the point of sub-atomic particles. The modifications, themselves, are actually shorthand for processes that occur in time. Each modification verb can be broken down into process steps. What is important is that we are able to understand the system at the level that gives us sufficient insight into what we are considering. It takes experience to know how far to break the system down.

Knowing how to correctly write a function will help the problem solver at later stages when the function is being “fixed” or idealized. It is difficult to idealize or fix a function if it is not stated correctly.

Test 1: Are all of the Parts Present? One quality of a correctly stated function is that the tool, modification and product are all clearly shown. The product is the object being modified. The modification can be stated in long or short hand. The tool is the object that will modify the tool. The direction of modification or the causality should be correctly shown by the direction of the arrow.

5 All parts of the function

Test 2: Are the tool and product something you could drop on your foot? The tool and product are always physical objects when it comes to physical phenomena. However, when software and business problems are worked, there may be the need to consider virtual objects such as used in object oriented software.

6 Drop on Foot

Test 3: Does the modification describe a physical change or control of the product? If necessary, use the longhand form of the modification (Changes Or Controls) to avoid confusion. In this example, we have replaced the word “heats” with the words” changes temperature”. We are signifying that the temperature of the water is changing over time because functions denote what happens over time.

7 Pan Heats Water

If the system was being used to correct the temperature of the water over the course of time, we would have chosen the word “controls” instead of “changes”.

Test 4: Does the tool directly modify the product? This is not a hard and fast rule because sometimes brevity is required. However, it is important to understand the chain of physics that is involved, and if you do choose to be brief, it should be understood that this is a simplification and not a description of the actual physics. In this case, the pan is an intermediary for the heat to warm up the water. The flame does not directly affect the heating of the water.

8 Directly Heats Water With FlameTest5: Is the correct function symbol used? It is possible to use other symbols or colors to denote the type of function, as long as you are consistent. Using such notation makes it easier to locate problem areas when a function diagram is built. A function can be useful, harmful, useful but insufficient or excessive. Useful functions can be distinguished by a solid line between the tool and the product. Harmful functions use a wavy line. Insufficient functions use a dashed line and excessive functions use two lines.  When a function is performed excessively, it usually brings further burdens to the system.

9 Different Kinds of Functions

Test 6: Does it describe what is really happening? Be Careful with Confusing Functions. Look at what you are trying to describe and think in terms of the actual physics rather than describing what is happening in sentences. In the case of a clothes dryer, the function of the clothes dryer is not to act on the clothes, but rather the moisture that is in the clothes. Hangers and irons operate on clothing. Dryers operate on moisture.

10 Dryer Drys Clothes Incorrect

Following is a description of the method for describing a problem using functional language. 

Step 1: Break the system down into functional elements. At this point, do not include super-system elements. (This will be discussed in the next step).

13 System Elements

Step 2: Add Super-System elements and the system product. The system product is the element that the system modifies. Super-system elements are a part of the job and reside in the environment. The system product may be a special type of super-system element that the system serves or it may be a part of the system. The system modifies the system product.  In this case, we have colored the system product yellow to indicate that it is special.

14 Add super system elements

Step 3: Introduce Modification Links including useful, flawed and harmful links. Verify that all rules for forming functions have been followed. It is possible to discover system problems during this process because we consider the possibility of interactions between every element. Harmful and useful but flawed modification links should be included.

9 Different Kinds of Functions

Example—Acid Container
Metallic Test cubes are immersed in hot acid for long periods of time to test the corrosive resistance of the metals. The cubes are placed in a corrosion resistant container which is then placed in an oven. The action of the acid is sufficient to corrode the cubes, but there is a problem. The container that contains the cubes and acid is eventually corroded and has to be replaced. Replacing the container is very expensive since it is made from a very expensive material.

16 Picture of Acid Oven

Step 1: Break the system down into functional elements. At this point, do not include super-system elements. The functional elements of the cube corrosion system include the acid, oven and pan.  We have control over all of these elements.

17 Pan Acid Oven Elements

Step 2: Add Super-System elements and identify the system product. 
The Super-System elements in this case are the table, earth and cubes. The cube is the system product. The cubes are what the system modifies by corroding them.  In this case, the cubes are a part of our system since we actually do have some degree of control over them.

18 Cubes and SS Elements Added

Step 3: Introduce Modification Links including useful, flawed and harmful links.

19 Acid Corrosion Links Added

Note that this time we have included the harmful function of pan corrosion.

Example – Dispensing Tape
The cost to manufacture a common tape dispenser is too high to be competitive. What can be done to reduce the cost of manufacture?

20 Tape dispenser Picture

Step 1: Break the system into functional elements. 
The functional elements of “tape dispensing” include the spindle, base, blade and person.

21 Tape Dispenser Elements

Step 2: Add Super-System elements and the system product.  Again, we have control over the tape so that technically it is a part of the system.

22 Tape Dispenser Product Added

Step 3: Introduce Modification Links. Include useful, flawed and harmful links.

23 Tape Dispenser Links Added

You can see the modification links in the figure below, e.g. the table supports the base, the spindle supports the tape and the person cuts the tape, though inconsistently.

One curious function is that the tape holds itself. Recall that the tape adheres to itself as it comes off of the roll. While this might not seem clever, actually, it may have resolved a very difficult conflict at one time. Consider that an adhesive is fixed to one side of the tape. How do we move the tape about without it becoming stuck to everything in sight? How do we keep it from becoming contaminated with dust and dirt? A mediator is required to keep the tape safe. This mediator could have been supplied by some “foreign” material, but the idea of allowing the tape to protect itself satisfied the requirements, so long as the adhesive did not stick well to the opposite side of the tape. Additionally, this provides a convenient means of positioning the tape for the purpose of tearing.

Business Example—Year End Review
The yearly performance review process is very time-consuming, especially when you have a large number of direct reports.

24 Year End Review Picture

Step 1: Break the system down into functional elements.
The functional elements of the year-end review system include the manager, approval system reminder system and recording system.

25 Year End Review Elements

Step 2: Add super-system elements and the system product.
No super-system elements will be mentioned. The system product is the employee.  In this case, the review system has little control over this element, so it is considered a super-system element.

26 Employee Added

Step 3: Introduce Modification Links. Include useful, flawed and harmful links.
The modification links are shown below.

27 Year End Review Links

Human systems often have a number of interesting and surprising functions.  Transaction systems, such as a checkout at a grocery store, are particularly interesting because they involve functions that we take for granted. When we ask what gets modified, it is often related to changed concepts in the mind such as who owns what. At a checkout line for a grocery store, for instance, the question of who owns the item changes from the store owning the item to the buyer owning the item. We say that we bought the item, but in reality the item never changes; only our concept of who owns it changes, both in the mind of the buyer and seller. In the case of the year end review, information is exchanged between the manager and the employee. Note that the employee and manager perform functions on themselves.  We say that they inform each other. Both must contemplate, both before and after the review. This contemplation changes their perception of what has happened during the year and what is expected to happen the next year. In effect, both the manager and the employee change themselves. We could say that the manager motivates or de motivates the employee, but this would be misleading. The manager does not have direct power to do this. Information flows, and the employee then changes the “motivated” or “de-motivated” register in his or her mind. Creating this diagram reminds us that motivating the employee is the primary function of the system. We show these functions as flawed, harmful, useful or excessive depending on the specific situation at hand. In this case, we are showing an interview where the employee is poorly motivated. This could have been shown as a harmful or flawed function. Here it is shown as a flawed “contemplation” function.

As a matter of practicality, it is important that the modification be properly described to ensure clear thinking. The modification must directly change some attribute of the product. For instance, the attribute that is modified could be the density, position, color or smell of the product. In the shorthand form, the modification is a verb. This cannot be just any verb, but only verbs that describe a change or control of the product.

The selection of the verb can often be confusing. This is particularly true when it comes to creating modifications from common English descriptions of functions. For instance, we may say that “a bottle lid seals the bottle”. This is an example of a confusing function. We might be tempted to think that the lid is actually doing something to the bottle. If we are applying the above tests, we see that test #3 is failed. The verb “seals” does not actually modify or change the bottle whatsoever. If we write out all of the elements which are involved, we notice that we have a bottle, a lid and the contents. If we ask how each modifies the other we get a better picture of what is happening. What is really happening has more to do with keeping the contents of the bottle inside or what is outside from coming into the bottle. We could state this in English is a less confusing fashion. “The lid constrains the content of the bottle” and/or “the lid constrains the outside gases” (not shown). Less related is the function that the bottle performs on the lid by positioning it.

11 Confusing Lid Seals Bottle

If we include the exclusion of items outside of the bottle, we get the following function diagram:

46 Bottle Functions

If there is confusion, one should consider using the longhand form of the modification. This starts with the words “Change” “Control” or “Create”, thus making it clear that some physical parameter of the product must be physically influenced. We may say that paint protects the wood. While the word “Protects” is a verb, it is not a modification, as it does not describe a change or controlling of the wood. Insistence on using the word “protects” will hamper the problem solver in later steps. The longhand form encourages the student to correctly break the forgoing function into a small system of functions. Once the longhand form is firmly entrenched, the student can usually revert back to the short form of the modification for brevity.  In the first function shown below, "Protects" is a confusing and incorrect modification. Beginners often write: “paint-->protect-->wood”.  The diagram below shows the correct description in short and longhand form.

12 Confusing Paint Protects Wood

Note that in both cases, the English phrase would tempt us to form a function with only two objects. In reality, more objects were required to describe what was really going on.

This section provides exercises to strengthen the skill of writing functions, especially when the situation is confusing. Answers are given following the exercises. Please note that your answers may be correct and still not match the answers given due to the fact that the functional elements can be broken down into sub-systems and displayed differently, similar to what was shown in the clothes washer explanation above.

By the end of the exercises for confusing functions, it is hoped that the reader will have a new appreciation for how much the perception and understanding of the problem solver can be changed by simply forming a function diagram!

Exercise—“The Ball Breaks the Glass”28 Picture Ball Hitting Window 
Shown is a window being broken with a baseball. This is not generally a good situation so we will consider this to be harmful. Create a functional description of the English phrase. There are several ways to describe the modification. Hint: First draw all of the substance elements (that you could drop on your foot) and then make the functional links. The answer is given further on.

Exercise—“The Bearing Holds the Rod”29 Picture Bearing Holding Rod
Shown is a picture of a bearing and a rod. The bearing positions the rod so that it can freely rotate. The positioning is vertical and horizontal, yet it allows free rotation. Create a functional description of the English phrase. There are several ways to describe the modification. Hint: First draw all of the substance elements (that you could drop on your foot) and then make the functional links. The answer is given further on.

Exercise—“The Pipe Conducts the Liquid”30 Picture Water Flowing in Pipe
Shown is a picture of a cut-away of a pipe with a liquid flowing inside. Create a functional diagram from the English phrase. We are progressing to functions that may be more difficult. Hint: In this case, the English phrase is not too bad. Try writing out the long-hand form if you are not sure what to write. The answer is given further on.

Exercise—“The Wire Conducts Electricity”31 Picture of Insulated Wire
Shown is shown a copper electrical wire with insulation. This wire conducts electricity. Create a functional diagram from the English phrase. Hint: This is very similar to the problem of conducting liquids in a pipe. The thing that may make this more fuzzy has to do with the term electricity. Try and convert this to an object that you could drop on your foot, even if it is very tiny.

Exercise—“The Lightning Rod Protects the House”32 Picture Lightening Striking House
A lightening rod is used to keep lightning from directly striking a house. The rod is usually higher than the house and has a sharp point. The sharp point creates a high field gradient at the tip which ionizes the air and makes a great attractor for lightning. Create a function diagram from the English phrase. Hint: This is a confusing function because the English phrase does not properly describe what is going on.

Exercise—“The Thermometer Measures the Temperature”33 Picture Thermometer in Liquid
The picture shows a cylinder filled with liquid. A mercury thermometer is used to measure the temperature of the liquid. Create a function diagram from the English phrase. Hint: This is a confusing function because the English phrase does not properly describe what is going on.

Exercise—“The Toothbrush Brushes the Teeth”34 Picture Toothbrush and Teeth
Shown is a toothbrush in the act of brushing teeth. Create a function diagram from the English phrase. Hint: This is a confusing function because the English phrase does not properly describe what is going on.

Exercise—“The Oil Lubricates the System”35 Picture of Piston
Shown is a piston for an internal combustion engine or a compressor. The piston moves up and down in the bore. Oil is used to lubricate the piston and keep the bore and piston from wearing. Create a functio diagram from of the English phrase. Hint: This is a confusing function because the English phrase does not properly describe what is going on.

Exercise—“The Gold Improves the Reliability”36 Picture of Electrical Connector
Shown is an electrical pin connector. The connector is the combination of a male pin that slips into a female “socket” and makes electrical contact. There is usually some mechanism to cause a load between the surfaces. (Components are flexing). Putting gold on the surface keeps the pin from corroding and thus makes it more reliable. Create a functional description of the English phrase. Hint: This is a confusing function because the English phrase does not properly describe what is going on.

Exercise Answers

Answer—“The Ball Breaks the Glass”
In this case, the English phrase correctly describes the function. Notice that both the shorthand (break) and longhand (changes # pieces) is used. This could have been described several ways.

37 Ball Breaks Glass Function 2

Answer—“The Bearing Holds the Rod”
In this case, the English phrase correctly describes the function. Notice that both the shorthand (holds) and longhand (controls position) is used. This could have been described several ways.

38 Bearing Holds Rod Function 2

Answer—“The Pipe Conducts the Liquid”
Once again, the English phrase correctly describes the function. Notice that both the shorthand (conducts) and longhand (controls path) is used. This could have been described several ways.

39 Pipe Conducts Liquid Function 2

Answer—“The Wire Conducts Electricity”
Once again, the English phrase correctly describes the function. However, we needed to change the term “electricity” to charges or electrons.

40 Wire Conducts Charges Function 2

Answer—“The Lightning Rod Protects the House”
The temptation is to write

Lightning Rod-->Protects-->House

But notice that the verb “protect” does not modify anything having to do with the house. Once again, the lightning rod directly affects the charges or electrons. Without the rod, the electrons would more easily damage the house. With the rod, the damage from the electrons to the house is minimized. This is shown by a line through the harmful function of “Damage”. Notice also that there is a harmful function that the rod may attract the charges. Setting up lightning rods is tricky business. A more effective approach is to repel the charges.

41 Lightening Rod Functions 3

Answer—“The Thermometer Measures the Temperature”
The temptation is to write:


This is a very confusing function. The thermometer is truly involved in the system, but notice that the thermometer does not change the liquid. The liquid changes the thermometer. This is true in all measurement (informing) functions. The thing that is being observed (subject) always changes the thing that needs to measure it (observer). Also notice that “measures” does not change anything and “temperature” is not something that can be dropped on your foot. A lot of rules were violated. The safe way to write any function is to first identify the material objects in the system. Notice that the liquid, glass, mercury and observer are all material objects. Then we determine the functional links between each, making sure that the direction of the arrows is correct.

An alternate system would be for the liquid to change the temperature of a whole thermometer which would then inform the observer. In this case, the thermometer was broken down to two sub-systems, the glass and the mercury.

One other thing to notice is that most measurement systems disturb what they are trying to measure. The act of putting the thermometer into the liquid changes the temperature of the liquid. This is shown as a harmful function. The glass changes the temperature of the liquid.

42 Thermometer Functions 2
Answer—“The Toothbrush Brushes the Teeth”
The temptation is to write:


This would violate a couple of rules. First, the verb “brushes” does not describe a modification to anything. Secondly, it is not the teeth that need to be modified, but rather the plaque and the food particles. Creating such a functional diagram is actually very illuminating. Notice that the only useful function that the teeth perform is to guide the brush. Other than that, it has a harmful function of controlling the position of the plaque and food particles. Once again. The best approach is to write down all of the substance objects involved and then determine the functional links between each of them. 

43 Toothbrush Functions 2 

Answer—“The Oil Lubricates the System”
The temptation is to write:


But notice that the verb “lubricates” does not actually indicate a change to the piston. Another temptation is to believe that the piston is guided by the wall and the oil reduces the wear. If the piston was actually touching the wall very much, the life would be quite short. In reality, the contact between the piston and the cylinder is quite rare and usually happens when the engine starts. Another way to say this is if the oil is doing its job, the piston and cylinder never touch. If this is the case, then the oil is the only thing left to guide the piston. The oil does create some drag on the piston which is shown as a harmful function. Also, notice that the piston smears the oil around and thus controls its position. One could also argue that the bore is involved in positioning the oil. This is not shown on the diagram.

44 Oil Functions 2

Answer—“The Gold Improves the Reliability”
The temptation is to write:


“Improves” describes a modification, but it is a very imprecise description. Worse, “reliability” is not something that you can drop on your feet. It was given that the reason the reliability improved was because the corrosive effects of things coming from the atmosphere are reduced. The diagram indicated two substances: water and oxygen. That is the function of the gold, to deflect damaging objects in the atmosphere.

45 Gold Functions 2

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