Book,
A Formulation of Multidimensional Growth Models for the Assessment and Forecast of Technology Attributes: PhD Thesis
(2006)
Abstract
Developing technology systems requires all manner of investment|engineering tal-
ent, prototypes, test facilities, and more. Even for simple design problems the in-
vestment can be substantial; for complex technology systems, the development costs
can be staggering. The pro¯tability of a corporation in a technology-driven industry
is crucially dependent on maximizing the effectiveness of research and development
investment. Decision-makers charged with allocation of this investment are forced
to choose between the further evolution of existing technologies and the pursuit of
revolutionary technologies. At risk on the one hand is excessive investment in an
evolutionary technology which has only limited availability for further improvement.
On the other hand, the pursuit of a revolutionary technology may mean abandon-
ing momentum and the potential for substantial evolutionary improvement resulting
from the years of accumulated knowledge. The informed answer to this question,
evolutionary or revolutionary, requires knowledge of the expected rate of improve-
ment and the potential a technology o®ers for further improvement. This research
is dedicated to formulating the assessment and forecasting tools necessary to acquire
this knowledge.
The same physical laws and principles that enable the development and improve-
ment of speci¯c technologies also limit the ultimate capability of those technolo-
gies. Researchers have long used this concept as the foundation for modeling techno-
logical advancement through extrapolation by analogy to biological growth models.
These models are employed to depict technology development as it asymptotically ap-
proaches limits established by the fundamental principles on which the technological
xviii
approach is based. This has proven an e®ective and accurate approach to modeling
and forecasting simple single-attribute technologies. With increased system complex-
ity and the introduction of multiple system objectives, however, the usefulness of this
modeling technique begins to diminish.
With the introduction of multiple objectives, researchers often abandon technology
growth models for scoring models and technology frontiers. While both approaches
possess advantages over current growth models for the assessment of multi-objective
technologies, each lacks a necessary dimension for comprehensive technology assess-
ment. By collapsing multiple system metrics into a single, non-intuitive technology
measure, scoring models provide a succinct framework for multi-objective technology
assessment and forecasting. Yet, with no consideration of physical limits, scoring
models provide no insight as to the feasibility of a particular combination of system
capabilities. They only indicate that a given combination of system capabilities yields
a particular score. Conversely, technology frontiers are constructed with the distinct
objective of providing insight into the feasibility of system capability combinations.
Yet again, upper limits to overall system performance are ignored. Furthermore, the
data required to forecast subsequent technology frontiers is often inhibitive.
In an attempt to reincorporate the fundamental nature of technology advancement
as bound by physical principles, researchers have sought to normalize multi-objective
systems whereby the variability of a single system objective is eliminated as a result
of changes in the remaining objectives. This drastically limits the applicability of
the resulting technology model because it is only applicable for a single setting of all
other system attributes. Attempts to maintain the interaction between the growth
curves of each technical objective of a complex system have thus far been limited to
qualitative and subjective consideration.
This research proposes the formulation of multidimensional growth models as
an approach to simulating the advancement of multi-objective technologies towards their upper limits. Multidimensional growth models were formulated by noticing
and exploiting the correlation between technology growth models and technology
frontiers. Both are frontiers in actuality. The technology growth curve is a frontier
between capability levels of a single attribute and time, while a technology frontier is
a frontier between the capability levels of two or more attributes. Multidimensional
growth models are formulated by exploiting the mathematical signi¯cance of this
correlation. The result is a model that can capture both the interaction between
multiple system attributes and their expected rates of improvement over time. The
fundamental nature of technology development is maintained, and interdependent
growth curves are generated for each system metric with minimal data requirements.
Being founded on the basic nature of technology advancement, relative to physical
limits, the availability for further improvement can be determined for a single metric
relative to other system measures of merit. A by-product of this modeling approach
is a single n-dimensional technology frontier linking all n system attributes with time.
This provides an environment capable of forecasting future system capability in the
form of advancing technology frontiers.
The ability of a multidimensional growth model to capture the expected improve-
ment of a speci¯c technological approach is dependent on accurately identifying the
physical limitations to each pertinent attribute. This research investigates two poten-
tial approaches to identifying those physical limits, a physics-based approach and a
regression-based approach. The regression-based approach has found limited accep-
tance among forecasters, although it does show potential for estimating upper limits
with a speci¯ed degree of uncertainty. Forecasters have long favored physics-based
approaches for establishing the upper limit to unidimensional growth models. The
task of accurately identifying upper limits has become increasingly di±cult with the
extension of growth models into multiple dimensions. A lone researcher may be able
to identify the physical limitation to a single attribute of a simple system; however, as
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system complexity and the number of attributes increases, the attention of researchers
from multiple ¯elds of study is required. Thus, limit identi¯cation is itself an area of
research and development requiring some level of investment. Whether estimated by
physics or regression-based approaches, predicted limits will always have some degree
of uncertainty. This research takes the approach of quantifying the impact of that
uncertainty on model forecasts rather than heavily endorsing a single technique to
limit identi¯cation.
In addition to formulating the multidimensional growth model, this research pro-
vides a systematic procedure for applying that model to speci¯c technology architec-
tures. Researchers and decision-makers are able to investigate the potential for addi-
tional improvement within that technology architecture and to estimate the expected
cost of each incremental improvement relative to the cost of past improvements. In
this manner, multidimensional growth models provide the necessary information to
set reasonable program goals for the further evolution of a particular technological
approach or to establish the need for revolutionary approaches in light of the con-
straining limits of conventional approaches.
