Axiomatic design mainly deals with the ‘axioms’, which can be defined as “self-evident truths or fundamental truths for which there is no counter example or exceptions”. In this paper we try to understand how the axiomatic design technique works for any product, with the help of a case study. The product taken for the case study would be a coffee-maker. The principles of axiomatic design are implemented on the product considered and the feasibility of accommodating new features would be verified.

1. AXIOMATIC DESIGN
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2. AXIOMATIC DESIGN
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INTRODUCTION
Axiomatic design mainly deals with the ‘axioms’, which can be defined as “self-evident truths or fundamental
truths for which there is no counter example or exceptions”. In this paper we try to understand how the axiomatic
design technique works for any product, with the help of a case study. The product taken for the case study would
be a coffee-maker. The principles of axiomatic design are implemented on the product considered and the
feasibility of accommodating new features would be verified.
Understanding axiomatic design principles mainly deals with comprehending the building blocks of it. It mainly
deals with the two design axioms which in turn are associated with the four main components.
 The two design axioms
o The Independence Axiom
o The Information Axiom
 The components of Axiomatic design
o Functional Requirements(FR’s)
o Design Parameters(DP’s)
o Constraints(C’s)
o Process Variables(PV’s)
The definitions of all the above parameters are attached in the appendix for reference.
Keywords: Axioms, FR’s, DP’s, C’s
AXIOMATIC DESIGN FOR COFFEE-MAKER
The generally most used coffee-makers are of the following variants:
1. Vacuum brewers
2. Percolators
3. Water displacement drip coffeemakers
4. Electric drip coffeemakers
5. French press
We consider a water displacement drip coffee maker for our case study.
To implement axiomatic design for a coffee maker, we first need to be aware of its working & decide the design
parameters which are needed to fulfill the functional requirements. Care needs to be taken in the implementation
constraints appropriately for an optimal solution.
Working of a coffee-maker
In a water drip coffee maker, what we see is the hot water entering the faucet which facilitates collecting the
coffee in the jug, by passing the hot water through the powder which is placed in the filter of the faucet.
So, from the above description if we try to perceive the functions that need to be done to have a properly brewed
coffee at the output, we will have the following requirements to be fulfilled:
 Water input

3. AXIOMATIC DESIGN
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 Heating of the water to be done
 Pump the water up
 Collecting the hot coffee
But, we can sense that the above requirements are too vague for designing an object which is intended to
perform the desired functions at a controlled rate. This leads to the discussion of ‘Functional Requirements’.
Functional Requirements (FR’s) of a Coffee-maker
If we consider the working of a coffee-maker in a sequential approach we figure out the below mentioned are
the FR’s which need to be fulfilled.
 FR_1-Clean water input
 FR_2-Water storage
 FR_3-Water inlet to heating chamber
 FR_4-Water enters heating chamber
 FR_5-Heating of the water
 FR_6-Water passes out from heating chamber
 FR_7-Lifts up from bottom to top (faucet)
 FR_8-Pours out through faucet with coffee powder
 FR_9-Collects in the jug
 FR_10-Keep the jug warm
Water input
Heating of
water
Pump the
water up
Collecting the
hot coffee
CoffeeMaker
FR-1
FR-2
FR-3
FR-4
FR-5
FR-6
FR-7
FR-8
FR-9
FR-10

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As the ‘Functional Requirements’ are defined, the next step would be to find a solution to these FR’s. These can
be fulfilled with a proper design which should be addressing all the FR’s that need to be fulfilled. The ‘Design
Parameters’ would be the means to achieve the required outcomes.
Design Parameters (DP’s) of a Coffee-maker
The best approach to deal with ‘Design Parameters’ (DP’s) would be to logically check the possibility of a
technical or design method to fulfill the FR. This would even help in reducing the time spent on finding a
solution and also avoids the danger of generating a solution which might end up in no relation with the FR to be
satisfied.
With the proper consideration of FR’s to be satisfied, we decide the DP’s.
 DP_1-Water inlet port with a filter: This makes sure that clean water enters the machine, with all the
debris filtered if any.
 DP_2-Water reservoir: All the water which enters the machine directly need not go to the heating
chamber, but needs to enter the heating phase as per need. A reservoir keeps hold of the water and
releases as per need.
 DP_3-A one-way hole linking inlet to the heating chamber: The water is sent into the chamber as per
need and this is to be a controlled flow. This can be a hole linking reservoir & heating chamber, which
can be sensor controlled for the water to flow in or stop flowing. Care should be taken to avoid back
flow of water into the reservoir making it a one-way design.
 DP_4-A tube that carries the water to the heating area: The water which enters the heating chamber
needs to be carried to the heating area. This is enabled with the help of pipe like structure, which helps
in the transport of water.
 DP_5- Insulated heating element: After the water reaches the heating area, it is heating element plays a
very crucial role in making the water hot and to preserve heat necessary material which don’t absorb the
heat generated should be considered. Also as there will be flowing water in the vicinity of the element,
appropriate safety measures should be taken to avoid unforeseen circumstances.
 DP_6- A tube that carries the water away from the heating area: The heated water which after reaching
the desired temperature must be moved away from the heating area avoiding its evaporation. This heated
water now is to be carried to the faucet.
 DP_7- Bubbling pipe for rise of water: The use of bubbling pipe at this point would help the heated
water move up to the faucet level and helps in achieving the desired outcome.
 DP_8-Modular faucet- This enables to use coffee packs and even helps in the ease of cleaning the
faucet. The hot water will flow through the faucet and pass through the coffee powder kept in it to brew
the coffee.
 DP_9- Jug- The heated water passing through the faucet brews the coffee and a jug helps in collecting
the preparation.
 DP_10-Heating Plate- This can be used to keep the coffee warm even after sometime it is collected. This
feature can be accomplished by the providing multiple functioning to the heating element used as DP_5.

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COUPLING OF FR’s & DP’s
After the DP’s and FR’s are figured out, the next task would be the coupling of these two. The coupling
between FR’s & DP’s is done with the ‘Design Matrix’ (DM) or ‘Sensitivity Matrix’. This can be expressed as:
{FR’s}= [DM]*{DP’s}
[
𝐹𝑅1
𝐹𝑅2
𝐹𝑅3
𝐹𝑅4
𝐹𝑅5
𝐹𝑅6
𝐹𝑅7
𝐹𝑅8
𝐹𝑅9
𝐹𝑅10]
=
[
𝑋 0 0 0 0 0 0 𝑋 0 0
𝑋 𝑋 0 0 𝑋 0 𝑋 0 0 0
0 0 𝑋 0 0 0 0 0 𝑋 0
0 0 𝑋 𝑋 0 0 𝑋 0 0 0
0 0 0 0 𝑋 𝑋 0 𝑋 0 𝑋
0 0 0 0 0 𝑋 0 𝑋 𝑋 0
0 𝑋 0 0 𝑋 0 𝑋 0 𝑋 0
0 0 0 0 0 0 0 𝑋 0 𝑋
𝑋 0 𝑋 0 0 0 0 0 𝑋 0
0 0 0 0 𝑋 0 𝑋 0 0 0] [
𝐷𝑃1
𝐷𝑃2
𝐷𝑃3
𝐷𝑃4
𝐷𝑃5
𝐷𝑃6
𝐷𝑃7
𝐷𝑃8
𝐷𝑃9
𝐷𝑃10]
From the above we see that it is a coupled design and to change it to a decoupled or uncoupled design, we
should implement the ‘constraints’ on the coupling of FR’s and DP’s. Apart from using the constraints, we can
impart the design improvements to get the optimal solution and also attain the customer satisfaction.
Constraints being implemented
 Water shouldn’t overflow from the reservoir.
 Controlled water flow to heating chamber.
 Heating rate to be optimal- Heat the water and even should be able to keep it warm.
 Single heat source for heating and keep the jug warm & relate the heating to be done to the plate with
the heating element.
 Reduce heat loss by using less heat absorbing couplers and interfaces.
Design Improvements
Apart from the general considerations of design of a coffee-maker, since the target is to have an improved
design the feasibility of either one or all of the new features mentioned should be
 Work with a preset timer, so that it works on an alarm trigger (Integrate with DP-1)
 Grind the beans before making coffee for a fresh taste (Integrate with DP-7 using sensors)
 Pours as much only required with a pause, which helps in brewing the coffee in large quantities for
many people and the quantity needed can be taken exactly. This would be useful in community
gathering or parties.(Integrate with DP-8)
With the integration of modifications & constraints, we have the modified coupling matrix to be a “decoupled
design”. (The units marked bold are the modified relations)

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[
𝐹𝑅1
𝐹𝑅2
𝐹𝑅3
𝐹𝑅4
𝐹𝑅5
𝐹𝑅6
𝐹𝑅7
𝐹𝑅8
𝐹𝑅9
𝐹𝑅10]
=
[
𝑋 0 0 0 0 0 0 0 0 0
𝑋 𝑋 0 0 0 0 0 0 0 0
0 𝑿 𝑋 0 0 0 0 0 𝟎 0
0 0 𝑋 𝑋 0 0 𝑋 0 0 0
0 0 0 0 𝑋 0 0 0 0 𝟎
0 0 0 0 0 𝑋 0 𝑋 0 0
0 𝑋 0 0 𝑋 0 𝑋 0 0 0
0 0 0 0 0 𝑿 0 𝑋 0 𝟎
𝑋 0 𝑋 0 0 0 0 0 𝑋 0
0 0 0 0 𝑋 0 𝑋 0 0 𝑋] [
𝐷𝑃1
𝐷𝑃2
𝐷𝑃3
𝐷𝑃4
𝐷𝑃5
𝐷𝑃6
𝐷𝑃7
𝐷𝑃8
𝐷𝑃9
𝐷𝑃10]
INDEPENDENCE AXIOM
The independence axiom as in the name has its focus on the maintaining the independence of the Functional
Requirements (FR’s).
For example: If we consider a water tap which has a provision for both cold & hot water at outlet, it is undesirable
from the user’s perspective to have the temperature depending on the flow rate. (When flow is high, water is cold
& when flow is low, water is cold)
The independence axiom helps in keeping the relation between FR’s and DP’s very simple. This allows the user
to manipulate the design parameters without drastically affecting the FR’s. Here by saying simple, we refer to the
above discussion of decoupled and uncoupled designs, which maintain a one-one relation or a sequential method
of solving the relations to arrive at a solution.
We see the method of solving the coupling relations basically depends on the level of understanding of a problem
by the designer. This approach of solving a problem cannot be judged as a positive or a negative aspect of this
approach. As the design is driven with the total intuitive of the designer, which might or might not be with the
consideration of the overall factors such as market study, previous cases where the similar problem occurred etc.
the results cannot be totally reliable when the design is done only with respect to independence axiom.
The main advantage of axiomatic design is the frame work in which it can accommodate different design
methodologies at various levels of the design but the crucial point is when the transformation of a design has to
occur. The axiomatic design unlike TRIZ methods doesn’t suggest a specific method in which the design
transformation (coupled-decoupled or decoupled-uncoupled) should occur. As this aspect plays a key role in
creative design, it should be given importance which also stands a draw-back of axiomatic design. Unlike MFD
and QFD, the axioms don’t possess the flexibility of iterations, i.e. in the deployment techniques we have an
option to get back to the rated matrices when we find the user needs and technical solutions can be improvised
for a better result. This might be corresponded to the already existing interrelations of FR’s and DP’s. Not only
with iterations, but also the throughout improvement phenomenon which is possible in techniques like FMEA
with the help of stage-wise focus on the problem and generating appropriate solutions is not possible with this
approach. For example, if a decoupled matrix is considered the relations can be modified for the optimal solution
but the design parameters itself cannot be improved targeting an optimal outcome.

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CONCLUSIONS
Most of the decision techniques basically start with a customer feedback and the results are totally driven in that
direction with main intention of modification of existing design to meet the customer needs. It is a true fact that
customer’s opinion should be given the higher priority, working without any innovation drives the total concept
of design in a wrong direction. The axiomatic design has given the designer a freedom to think, but not a
procedural approach how to implement it on a design problem. The axioms set defined target values for the
designer, in terms of what is to be achieved at the final phase for getting an optimal solution. For instance, if we
refer to independence axiom, it deals with attainment of decoupled or uncoupled design of any design problem
and information axiom deals with minimizing the information on any design problem. This provides an idea of
what is to be achieved but now how, which needs to be addressed with help of maybe another axiom. A new
axiom if can be proposed with a set of driving principles for the existing axioms, so that they land up at the
targeted result would be the most desired transform in axioms. This also helps to take decision with a solid base
rather than moving forward with only the intuition of the designer or purely based on market study without giving
space to innovation. So, the need of accommodating innovation by addressing demand along with the defined
constraints should be an open arena to explore in this area.
Experts figure out the common errors made by designers when dealing with axiomatic design is not creating a
robust design and not minimizing information content through elimination of bias and reduction of variance.
Apart from that the concentration is mainly on symptoms rather than on the cause, which needs the establishment
of importance of FR in a design and recognizing a decoupled design must be done with good intuition.
At times when the physical integration comes to play in any design, it might stand opposite to the assumptions of
independence axiom which depends on total independence of Functional Requirements (FR’s). This point might
be posing as a violation of the axioms but on a defensive note the functional requirements are not unified but the
unification is only in terms of physical being of any product. Like in the case of a bottle opener with a can opener,
which is misunderstood in most cases as a violation of independence axiom but actually is not. This can be linked
to the ‘concept of best design’, which exists basically on a simplifying the physical parameters and increasing the
functions of any design. (Example: Swiss knife). The recent research in this area is concentrated on showing the
conventional connectors to be a violation to independence axiom and by proposing a woven connector as a
solution to it, in a hope to address the modifications needed to be done for axioms.
REFERENCES
Engineering design – a systematic approach by Pahl, Beitz, Feldhusen & Grote.
Axiomatic design lecture notes by Dr. Georges Fadel
Ch10_axiomaticdesign_mit.pdf
APPENDIX
“Functional requirements (FR’s) are a minimum set of independent requirements that completely characterizes
the functional needs of the product (or software, organizations, systems, etc.) in the functional domain. By
definition, each FR is independent of every other FR at the time the FR’s are established”

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“Design parameters (DP’s) are the key physical (or other equivalent terms in the case of software design, etc.)
variables in the physical domain that characterize the design that satisfies the specified FR’s”
“Constraints (Cs) are bounds on acceptable solutions. There are two kinds of constraints: input constraints and
system constraints. Input constraints are imposed as part of the design specifications. System constraints are
constraints imposed by the system in which the design solution must function”
“Process variables (PV’s) are the key variables (or other equivalent term in the case of software design, etc.) in
the process domain that characterizes the process that can generate the specified DP’s”.

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