Future Sigma
The Axiomatic Component
Agenda
The DFLSS Alliance Team
Axiomatic Design
Domains
Mapping & Zigzagging
Design Axioms
Understand the use of Axiomatic Design in
DFLSS & LSS processes
Who are the partners in the
alliance?
What are the key elements of
our partnership?...
Execute Fast
Innovation
Tech Base &
SDD Project
Applications
Transform to Problem
Prevention
T&PD
Process
Discipline
Focus on the “Next Generation”
of Design for Lean Six Sigma
Training +
Hands-on
Workshops
The Mission: Fast Innovation
An alliance of 3 independent top experts are
partnering with and supporting the clients to
meet the following goals:
Increase the speed and performance of team based
innovation
Integrate our knowledge, experience, skills,
capabilities and intellectual capital to keep our clients
on the forefront of engineering capability and
competence
Transform from problem solving to problem
prevention through the new Alliance Team model of
Next-Generation DfLSS
What are the innovations that makes
this the “Next-Generation” of DFLSS?
! Traditional DFSS has been known to us for over 12 years… Dr. Haik & Creveling wrote the
1st & most used portfolio of practitioner & leadership books on the topic!
! As world leaders in DFSS & innovators in advancing new methods, we formed an alliance to
advance the state-of-the art in DFSS… here is what we created & integrated together:
Next-Generation DFLSS
Project Plan front-loaded w/DFLSS Tool-Task Alignment
DFLSS-enhanced Systems Engineering
Lean Product Development
Critical Parameter Management
Axiomatic Design
Traditional Brainstorming
TRIZ
Pugh Process
Probabilistic Design
Traditional Modeling
Statistical Monte Carlo Simulations
Traditional Reliability Methods
Robust Design
Traditional DOE
Transfer Function ID
DFMEA
What is an “AXIOM”?
An “axiom”, in mathematics and logic, is a general
statement accepted without proof as the basis for
logically deducing other statements (e.g. corollaries and
theorems), which later form a logical system of its own.
Axioms widely used are those related to engineering and
mathematical operations
Newton laws - Archimedes' Axiom
Euclidean geometry -Thermodynamics
Field Axiom - Probability Axioms (e.g. the associative
law and the commutative law of set theory)
An axiom , a postulate, is a self-evident statement without proof,
but the truth of the statement need not be readily evident.
What Is Axiomatic Design?
Axioms are general principles or self-evident truths that cannot
be derived or proven to be true except that there are no
counter-examples or exceptions to prove otherwise.
Axiomatic Design (AD) is a general principle for design
analysis and design synthesis developed by Prof. Nam
P. Suh of MIT.
“ The goal of axiomatic design is many fold: to make human
designers more creative, reduce the random search process,
minimize the iterative trial and error process, and determine the
best design among those proposed.”
Prof. Nam Suh
The Goal of Axiomatic Design
To improve quality and reliability both
conceptual and operational.
To establish a science base for design activity
to augment engineering knowledge and
experience.
To provide theoretical foundation based on
logical and rational thought process and tools.
To accelerate product development process.
To eliminate designer psychological inertia.
To minimize random search or trial and error design
solution process.
What is an “AXIOM”?
An “axiom”, in mathematics and logic, is a
general statement accepted without proof as the
basis for logically deducing other statements
(e.g. corollaries and theorems), which later form
a logical system of its own.
Axioms widely used are those related to
engineering and mathematical operations
Newton laws
- Archimedes' Axiom - Euclidean geometry
Thermodynamics - Field Axiom
- Probability Axioms
(e.g. the associative law and the commutative law of set theory)
An axiom , a postulate, is a self-evident statement without proof,
but the truth of the statement need not be readily evident.
Design is a mapping
process…
Customer Mapping Physical Mapping
FRs
FRs
CAs
FR1
FR1
FR11
DPs
PVs
DP1
PV1PV1
DP11
FR12
Process Mapping
DP12
PV11 PV12
PV12
PV11
FR11FR12
Functional Requirements
Domain
Customer Attributes Domain
Process Variables Domain
Design Parameters Domain
Design is a continuous mapping activity between 4 domains:
CAs"FRs"DPs"PVs
Example: Design Analysis of
Refrigerator
Level 1
FR1: Freeze food for long-term
preservation
FR2: Maintain food at cold
temperature for short-term
preservation
Zig
Zig
•
•
DP1: Freezer section
DP2: Refrigerator section
Zag
Zag
•
Zig
Level 2
•
•
•
FR11: Control the temperature of
the freezer in the range - 18 C
FR12:Maintain uniform
temperature at preset
temperature
FR13: Control humidity to
relative humidity 50%
Zig
Zig
•
•
DP11: Turn on and off the
compressor when the air
temperature is higher and lower
that the set temperature
DP12: Blow the air into the
freezer section and circulate it
uniformly throughout the freezer
section at all times
DP13: Condense the moisture in
the returned air when its dew
point is exceeded
Axiomatic Design
Axiom 1: The Independence Axiom
A good design comprises of Design Parameters
(DPs) that maintain the independence of
functional requirements (FRs)
Axiom 2: The Information Axiom
Among the designs that satisfy Independence
Axiom, the best design is one that requires the
least amount of “information” to achieve the
design goal.
Violation
of
Axiom 1
Violation
of
Axiom 2
Over 40 corollaries and theorems were derived
from these two axioms.
Axiomatic Design develops CONCEPTUAL IMMUNITY
Example of Independence Axiom
Functional Requirements
Design Parameters
DP1:Angle of valve 1
Which Design is Independent?
DP2: Angle of valve 2
FR1:Control the flow of water
FR2: Control the temperature
of water
Hot water
Cold water
Hot water
Cold water
DP
DP!
DP
DP!
Source: El-Haik, B., “Axiomatic Quality & Reliability”, John Wiley & Sons, Inc., New York, April, 2005.
Example of Independence Axiom
(cont’d)
Coupled Design
(DP’s create conflicting functions)
Hot water
Uncoupled Design
(DP’s maintain independence of functions)
Cold water
Hot water
Cold water
DP
DP!
DP
DP!
' FR 1 $ - A 11
&
#. +
2
FR
%
" , A 21
A 12 * ' DP 1 $
&
#
A 22 () % DP 2 "
' FR 1 $ - A 11
&
#. +
2
FR
%
" , 0
0 * ' DP 1 $
&
#
A 22 () % DP 2 "
In El!Haik, B., “Axiomatic Quality & Reliability”, John Wiley & Sons, Inc., New York, April, 2005.
Axiom 2: The Information
Axiom
Among the designs that satisfy Independence Axiom,
the best design is the one that requires the least
amount of “information” to achieve the design goal.
Provide a quantitative means to select the best design among
various design alternatives.
Among the designs that satisfy Independence Axiom, the best
design is the one that has the highest probability of success to
achieve the design goal.
A system is called complex if the probability of success is low;
that is a complex system requires more information (e.g., machining
precision, control environment, etc.) to make the system function.
Axiomatic Quality Concept Selection is based on Axiom 2.
Axiom 2: Definition of
Information Content
target
I & log' (1) & 0
Design Intent
system capability
Common region
CR
Pr ob( success) &
SR
% SR "
I & log' #
$ CR !
Functional Requirement
• The common region between the design intent and the system
capability is the probability of success of achieving the intended
FR.
• The information content, I = logv(system range/common range)
• v = 2 (e)
I in bits (nats)
DFLSS and Axiomatic Design
Conceptual
Quality
Do we have the
RIGHT concept?
+
Operational
Quality
Do we develop the
concept RIGHT?
Axiomatic Design is develops CONCEPTUAL IMMUNITY
LSS and Axiomatic Design
Axiomatic
Design
1.
2.
3.
4.
CTQ Flow
Down
Stakeholder
matrix
RACI matrix
Team
Matrix
Define
1.
2.
3.
Coupling
Measureme
nt
CTQ Flow
Down
Cause &
Effect Matrix
Measure
1.
2.
3.
4.
5.
FMEA
5 Why’s
Constraint
Analysis
Conflict
Matrix
FTA
Analyze
1.
2.
3.
FMEA
Multi-response
DOE
Mistake
Proofing
Improve
1.
Control Plans
Control
Axiomatic Design provides:
• A general framework to assess the conceptual and operational “quality”
• Design axioms provides assessment of the capability and limitation of Six Sigma
capability potential
Questions?
References
! El-Haik, B., “Axiomatic Quality & Reliability”,
John Wiley & Sons, Inc., New York, April, 2005.
! El-Haik, B. and Roy, D.,” Service Design for Six
Sigma”, John Wiley & Sons, Inc., New York,
June, 2005.
! El-Haik, B. and Alaomar, R.,” Simulation-based
Lean Six Sigma and Design for Lean Six
Sigma”, John Wiley & Sons, Inc., forthcoming,
July, 2006.
! Yang, K. & El-Haik, B. (2003). Design for Six
Sigma: A Roadmap for Product Excellence.
McGraw Hill, New York.