Copyright © 2002 by Engineous Software, Inc.
Published by the Institute of Aeronautics
American Institute of Aeronautics and Astronautics
and Astronautics, Inc. with permission.
OPTIMIZING FOR SIX SIGMA QUALITY
Patrick N. Koch
Engineous Software, Inc.
2000 CentreGreen Way, Suite 100
Cary, North Carolina
Probabilistic design to address uncertainty and
variability has been approached from many different
angles, by different communities.
methods focus on probability of constraint satisfaction
or violation, robust design methods have focused
primarily on the level of performance variation, the
sensitivity of design objectives.
“Six Sigma” quality
concepts have arisen more recently from the
manufacturing arena, focusing on measuring and
All of these approaches deal with
some aspect of modeling uncertainty or variability and
measuring, improving, or controlling performance
For the case of six sigma, the term “
for Six Sigma (DFSS)
” has been coined and is the
current push in industry;
however, its implementation
often does not involve
In an engineering design context, the concepts and
philosophy of Six Sigma can be combined with methods
from structural reliability and robust design to formulate
a strategy to “
for six sigma” quality.
strategy is presented in this paper, a six sigma based
probabilistic design optimization formulation.
combining these concepts and approaches, variability is
incorporated within all elements of this probabilistic
optimization formulation – input design variable bound
formulation, output constraint formulation, and robust
This six sigma based
probabilistic design optimization formulation, as
implemented within the iSIGHT design framework, is
demonstrated in this paper for the structural design of a
Results presented illustrate the trade off
between performance and quality when optimizing for
six sigma quality.
Optimization without including uncertainty leads to
designs that cannot be called “optimal”, but instead are
potentially high risk solutions that likely have a high
probability of failing in use.
tend to push a design towards one or more constraints
until the constraints are active, leaving the designer with
a design for which even slight uncertainties in the
problem formulation or changes in the operating
environment could produce failed designs.
optimization problem formulations and solution
strategies are deterministic, very few real engineering
problems are void of uncertainty; variation is inherent in
material characteristics, loading conditions, simulation
model accuracy, geometric properties, manufacturing
precision, actual product usage, etc.
many uncertainties are removed through assumptions,
and others are handled through crude safety factors
methods, which often lead to over-designed products