E N G I N E E R S + A Researching Futureseecore.org/d/20121009_ResearchingFuture.pdf · KUCHARAVY...
Transcript of E N G I N E E R S + A Researching Futureseecore.org/d/20121009_ResearchingFuture.pdf · KUCHARAVY...
Researching Futuremethodology (RFM) for long‐term technological forecast
Dmitry KUCHARAVY, [email protected]
LICIA / LGECO ‐ Design Engineering LaboratoryINSA Strasbourg24 bd de la Victoire, 67084 STRASBOURG, France
May, 2010 – October 2012
INSTITUT NATIONAL DES SCIENCES APPLIQUÉES DE STRASBOURGNATIONAL INSTITUTE OF APPLIED SCIENCE (INSA) OF STRASBOURG
E N G I N E E R S + A R C H I T E C T S
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:35 1
questions to be answered
1. Why do we need a reliable forecast?
2. Why is it difficult to forecast?
3. What are the existing approaches?
4. What is suggested?
5. Why do we apply logistic S‐curve?
6. How to improve reliability of forecast?
…The righter we do the wrong thing,
the wronger we become…
Russel Ackoff (2003)
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two gentlemen storySir Christopher and Sir James are walking along the
Thames. Suddenly they see a child in the water calling for help. Sir Christopher jumps into the river and saves the child. As soon as he gets back to the shore he hears another child crying for help. The gentleman jumps back to the river and keeps saving the children as the situation repeats several times.
Finally, Sir Christopher feels absolutely exhausted and asks Sir James why he doesn't help him save the children as he can barely keep on water having saved the children for some time. Sir James looks at him and replies that he thinks he'd better go up the current and see who throws children into the river.
Why do we need a reliable forecast?
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How do we get things?
WasteJunk
·Ore, ·Coal, ·Sand, ·Wood, ·Oil, ·Rock,
·Plants
·Metals, ·Chemicals, ·Paper, ·Cement,
·Fibers
BULK MATERIALS
·Crystals, ·Alloys, ·Ceramics, ·Plastics, ·Concrete, ·Textile
·Products, ·Devices,
·Machines, ·Structures
MineDrill
Harvest
ExtractRefine
Process
ROW MATERIALS
ProcessENGINEERING MATERIALS
DesignManufacturing
Assembly
PerformanceService
UseDispose
RecycleENERGY
ENERGY
ENERGY
ENERGY
ENERGY
ENERGY
ENERGY
Original presentation source: “Materials and Man’s Needs,” National Academy of Sciences, Washington D.C., 1974
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earth and human (socio‐technical systems and environment)
source: LIVING PLANET REPORT 2008 (http://wwf.panda.org/about_our_earth/all_publications/living_planet_report/ )
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Why do we need forecast?
• We delay to recognize and to be agree about
problems and threats.
• We delay to solve problems and to be agree about
solutions.
• We delay to implement a potential solution and
recognize its limitations.
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ecological debtor and creditor countries (1961)
source: LIVING PLANET REPORT 2008 (http://wwf.panda.org/about_our_earth/all_publications/living_planet_report/ )
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ecological debtor and creditor countries (2005)
source: LIVING PLANET REPORT 2008 (http://wwf.panda.org/about_our_earth/all_publications/living_planet_report/ )
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reliable forecast vs. foretelling
R1-: difficult to obtain; difficult to disseminate (to convince stakeholders)
R1+: Easy to sell any ideas as forecast;Easy to disseminate commonsense concepts
R2-: Lack of time and resources to respond for coming changes; - from difficult to impossible to fix problems; - regular emergency situations ask inventive solutions
V: available
Λ: is not available
R2+: time to develop adequate solutions for coming changes; possibility to solve problems; no emergency situation
Reliable forecast Desired result
[reliable forecast and efficient problem solving]
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why do we need to know about future?
R1-: Way to get knowledge should be changed (cognitive method problem)
R1+: No changes for getting knowledge (cognitive method is the same)
R2-: Regular conflicts with super-systems; A lot of problems to be solved
V: know about future
Λ: doesn’t know about future
R2+: Consistency with changes in super-system;Possible problems are dissolved in advance
Human (e.g. decision maker) Desired result
[harmonization vs. brute-force approach]
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Alternatives to a forecast
• No forecast;
• Anything can happen;
• There is no attempts to anticipate future
• There are attempts to build as multiple scenarios
• Seduced by success (ignore the future);
• Future will be like the past (higher, faster, and father);
• Emergency service (waiting until the problem arrives)…
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what are the objectives of a TF?
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scope of a TF
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We fail more often because we solve the wrong problem than
because we get the wrong solution to the right problem.
Russell Ackoff
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We have to ask ourselves hard questions:
Are we designing for the world that WE WANT?
Are we designing for the world that WE HAVE?
Are we designing for the world THAT'S COMING,
whether we're ready or not?
source: Timothy Prestero: Design for people, not awards, http://www.ted.com/talks/timothy_prestero_design_for_people_not_awards.html
Why is it difficult to forecast?
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why is it difficult to forecast reliably?
Please, discuss and arrange a list of causes.
Place the most important causes high on the list:
1. ____________________________________________
2. ____________________________________________
3. ____________________________________________
4. ____________________________________________
………………………………………………………………………………….
………………………………………………………………………………….
………………………………………………………………………………….
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why is it difficult to forecast reliably? ‐ lack of information for time
being & past;‐ impossible to validate;
‐ variable socioeconomic and political factors;
‐ possibility of unexpected changes at related sectors;
‐ future trends may not follow the regular path (past
behaviour)
‐ lack of knowledge;‐ subjective approach;‐ other technological development (replacement of function);
‐ dynamic environment (e.g. wars, economic crises, regulations, etc.)
‐ uncertainty of super‐system (social, economic, industrial, natural factors);
‐ since forecast itself based on subjective opinion;‐ lack of knowledge about sub‐systems for present
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why is it difficult to forecast reliably?
1. Too many DATA to compile2. Prediction can IMPACT THE FUTURE
3. UNPREDICTABLE (Eisenberg) events can change the forecast
4. Mechanic of EVOLUTION unknown
5. LITTLE CHANGE (Butterfly effect!!) impacts the forecast
1. Lack of knowledge about the EFFECTIVE ELEMENTS (data)
2. Lack of knowledge about the INTERACTIONS between them (effective elements)
3. They (effective elements and interactions) appear GRADUALLY
4. Lack of knowledge about GATHERING / ANALYSING / INTERPRETING DATAS (Methods?)
2012‐03‐06:
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why is it difficult to forecast?
assumption: For strategic decision‐making it is necessary to have reliable knowledge about distant future
[cognitive contradiction]
R1‐: How to access these knowledge? ‐ knowledge by definition comes from past experience by learning
R1+: Learning process to access to knowledge “as usual”
R2‐: Reliable long‐term forecast is impossible;Strategic decision are not secure and suppose to be changed regularly
R2+: Reliable long‐term forecast;Secure strategic decisions
knowledge about future Desired result
Λ: are not available
V: available
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a question
...Allow me to ask you, then, how man can govern, if he is not only deprived of the opportunity of making a plan for at least some ridiculously short period –well, say, a thousand years – but cannot even vouch for his own tomorrow?
–Mikhail Bulgakov [The Master and Margarita]
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why is it difficult to predict?[numerous relationships… over long time horizon]
The forecasting models should
<capture and simulate numerous relationships >, in order
to represent changes in product market, in product use, and in product production;
to characterize the activity of an economic system;
to imitate the feedback characteristics.
However, the forecasting model should
<apply minimum characteristics>, in order
to minimize errors owing by data (e.g. synergy effect);
to minimize inaccuracy of results due to model complexity;
to provide a clear unambiguous interpretation of results.
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complexity vs. design capacity
'a portion of the food web for the Benguela ecosystem (Buchanan, 2002)
This map appeared in the December 1998 Wired (Internet Mapping Project, http://www.cheswick.com/ches/map/index.html)
Efficiency is doing things right;
effectiveness is doing the right things… Peter Drucker
What are the existing approaches?
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Forecasting and TRIZ [timeline fragment #1]
Rogers, E.M. Diffusion of Innovations.
Knight, F.H. Risk, Uncertainty and Profit
Mensch, G. Stalemate in Technology: Innovations Overcome the Depression
Altshuller, G.S. About forecasting of technical systems development
Foundation for the Study of Cycles (FSC)
Altshuller, G.S. The Innovation Algorithm
Thermoeconomics
Tchijevsky, A. Physical factors of the historical process.
Kondratieff, N.D. The Long Waves in Economic Life.
Ogburn, W.F., Merriam, J. and Elliott, E.C. Technological Trends and National Policy…
Altshuller, G.S. and Shapiro, R.V. About a Technology of Creativity
Jantsch, E. Technological Forecasting in Perspective.
Ayres, R.U. Technological Forecasting and Long-Range Planning.
Fisher, J.C. and Pry, R.H. A simple substitution model of technological change. Technological Forecasting and Social Change, 1971, 3(1), 75-78.
Toffler, A. Future Shock
Martino, J.P. Technological Forecasting for Decision Making
Lotka, A.J. Elements of Physical Biology (Biophysical economics)
Altshuller, G.S. Creativity as an Exact Science.
Altshuller, G.S. Register of contemporary ideas from science-fiction literature
1920 1930 1940 1950 1960 1970 1980 1990
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TRIZ and Forecasting [timeline fragment #2]
Altshuller, Genrich S., Rubin, Michael. What will happen after the final Victory...
Zlotin, B.L. and Zusman, A.V. Searching for New Ideas in Science
Stewart, H.B. Recollecting the Future: A View of Business, Technology, and Innovation in the Next 30 Years.
Y.P.Salamatov, I.M.Kondrakov, Idealization of Technical systems…Heat pipe
Armstrong, J.S. Long Range Forecasting. From Crystal Ball to Computer.
Altshuller, G.S., Zlotin, B.L. and Philatov, V.I. Profession: to Search for New
Naisbitt, J. Megatrends. Ten New Directions Transforming Our Lives
Mensch, G. Theory of Innovation
Toffler, A. The Third Wave
Altshuller, G.S. Creativity as an Exact Science.
Mensch, G. Stalemate in Technology: Innovations Overcome the Depression
Altshuller, G.S. About forecasting of technical systems development
Altshuller, G.S., Zlotin, B.L., Zusman, A.V. and Philatov, V.I. Search for New Ideas: From Insight To Technology…
Ayres, R.U. Technological transformations and long waves. Technological Forecasting and Social Change, 1990, 37(1,2)
Schnaars, S.P. Megamistakes: forecasting and the myth of rapid technological change.
Altshuller, G.S. To Find an Idea:…
Salamatov, Y.P. System of The Laws of Technical Systems Evolution. In Chance to Adventure…
1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:35 29
Clarkesr, D.W. Strategically Evolving the Future: Directed Evolution... Technological Forecasting and Social Change, 2000, 64(2-3), 133-153.
Prushinskiy, V., Zainiev, G. and Gerasimov, V. HYBRIDIZATION
Mann, D.L. Better technology forecasting using systematic innovation methods. Technological Forecasting and Social Change, 2003, 70(8), 779-795.
Keenan, M., Abbott, D., Scapolo, F. and Zappacosta, M. Mapping Foresight Competence in Europe
Modis, T. Predictions - 10 Years Later.335Grubler, A. Technology and Global Change.
Modis, T. Predictions - Society's Telltale Signature Reveals the Past and Forecasts the Future
Modis, T. Conquering Uncertainty
Ackoff, R.L. and Rovin, S. REDESIGNING SOCIETY
PRINCIPLES OF FORECASTING: A Handbook for Researchers and Practitioner.
Directed Evolution Techniques. In TRIZ IN PROGRESS. Ideation International Inc.
Terninko, J., Zusman, A.V. and Zlotin, B.L. Patterns of Evolution. In Systematic Innovation: An Introduction to TRIZ
Makridakis, S., Wheelwright, S.C. and Hyndman, R.J. FORECASTING: methods and applications. 642.
Ayres, R.U. Technological Progress: A Proposed Mesure. Technological Forecasting and Social Change, 1998, 59(3), 213-233.
Fey, V.R. and Rivin, E.I. The Science of Innovation: A Managerial Overview of the TRIZ Methodology.
Kaplan, S. An Introduction to TRIZ, the Russian Theory of Inventive Problem Solving.
Kondrakov, I.M. From Fantasy to Invention
Altshuller, G.S. and Vertkin, I.M. How to Become a Genius: The Life Strategy of a Creative Person.
Kaplan, L.A. et al. Project Cassandra: work guidelines, perspectives. Journal of TRIZ. 94(1). International TRIZ association. 1994. pp.37-42
Tsurikov, V.M. Project "Inventive Machine" as engineering activity-aiding intellectual environment. Journal of TRIZ 2.1 (3). 1991 pp.17-34
Drucker, P.F. Management Challenges for the 21st Century.
Godet, M. Creating Futures. Scenario Planning as a Strategic Management Tool
Rubin, M.S. Forecasting Methods Based on TRIZ
Kostoff, R.N. and Schaller, R.R. Science and Technology Roadmaps
Zlotin, B.L. and Zusman, A.V. DIRECTED EVOLUTION. Philosophy, Theory and Practice.
1990 1992 1994 1996 1998 2000 2002 2004 2006
Technological forecasting & TRIZ[timeline fragment #3]
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many technology forecasting methods…
Source: Cascini G. 2012
What is suggested
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why is it difficult to forecast? [cognitive contradiction]
R1‐: How to access these knowledge? ‐ knowledge by definition comes from past experience by learning
R1+: Learning process to access to knowledge “as usual”
R2‐: Reliable long‐term forecast is impossible;Strategic decision are not secure and suppose to be changed regularly
R2+: Reliable long‐term forecast;Secure strategic decisions
knowledge about future Desired result
Λ: are not available
V: available
Problems are more important than solutions.
Solutions can become obsolete when
PROBLEMS remain.
– attributed to Niels Bohr
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Researching Future
RESEARCHING
FUTURE
Logistic Curve models
OTSM-TRIZ models
Limits of Resources
Waves and Cycles
Knowledge management
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specific (particular) vs. generic (universal) methods
R1‐: unflexible; different problems need specific methods;reliability of method; easy to make errors for applying; can we solve problem with this method?
R1+: flexible; apply one algorithm for multiple problems; reliable method; low probability of mistakes to apply; problem is solved in any case
R2‐: abstraction is high; a lot of time to learn how to apply; difficulties in application, user is specialist in method; difficult to integrate into existing toolbox of methods
R2+: precise; easy‐to‐learn, easy to memorize; applicable, user‐friendly; easy to integrate with other methods
Method description Desired result
Λ: long (redundant) and complexgeneralization
V: short (just as needed) and plainspecialisatiton
METHOD – 1) is a process by which a task is completed; a way of doing something [wiktionary]2) is a systematic procedure by which a complex scientific or engineering task is accomplished;
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source of information vs. reliability
R1‐: Reliability? Reproducible? How to be confident with?A lot of personal biases and expert’s opinions
R1+: Reliability. Reproducible. Trustworthy .No personal biases, but laws of nature
R2‐: Only proved data and information from past. How to clean forecast from biases of specialists?
R2+: Apply expert knowledge and intuition; Relatively easy to organize (e.g. Delphi methods)
Forecast (as result) Desired result
Λ: objective
V: subjective
[how to get objective knowledge from subjective sources?]
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a problem of a method forexploratory LONG‐TERM forecast
R1‐: difficult to achieve repeatable results from experts; it costs a lot; it takes a lot of time (low frequency to update results); the results contains a lot of biases
R1+: the results can be obtained a reproducible way; the process is cost effective; it is possible to update result frequently; the results consist less biases R2‐: it is not compatible with law of transformation 'quantity to quality', consequently it is mostly applied for short‐term forecast.
V: applies qualitative method
Λ: applies quantitative method
R2+: it can be applied for long‐term forecast due to conformity with law (of dialectic**) of transformation quantity to qualityForecasting process Desired result
** The law of transformation of quantity into quality: "For our purpose, we could express this by saying that in nature, in a manner exactly fixed for each individual case, qualitative changes can only occur by the quantitative addition or subtractionof matter or motion (so‐called energy)." [Engels' Dialectic of Nature. II. Dialectics. 1883]
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:35 38
flowchart of the suggested method
B. Prepare project
C. Define objectives
of TF
D. Perform analysis
and develop TF
E. Validate results F. Apply TF
A. Identify needs in
Technology Forecast (TF)
D.2. Capitalize Set of
Problems
D.4. Build the Time Diagram
(timing)
D.1. Define Boundaries of
System
D.3. Analyze limitation of resources
D.2.2. Define Critical-to-X
Features
D.2.4. Map Contradictions
as Network
D.2.1. Reformulate Discontents into Contradictions
D.2.3. Revise Sets of Contradictions
D.1.2. Law of System
Completeness Description
D.1.4. Analysis of Drivers and
Barriers (discontents)
D.1.1. Define Key Functions and Key Features
D.1.3. Impact Analysis of
Contexts and Alternatives
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It is not a pencil that is making a letter‐childish saying
It is not a method that is making a forecast‐inspired by childish saying
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flow chart of method
B. Prepare project
C. Define objectives
of TF
D. Perform analysis
and develop TF
E. Validate results F. Apply TF
A. Identify needs in
Technology Forecast (TF)
“…providing a consensual vision of the future science and technology landscape to decision makers.” [Kostoff and Schaller, 2001]
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before studying the trends
• a) What are main objectives and expected outputs?• b) How it will be applied for decision making process?• c) Can we satisfy formulated needs without TF? ‐> Go / Not to Go
A. Identify needs
• a) What are available and necessary resources to perform study?• b) What is an optimal time span to realize project?• c) Who are clients, core team, and necessary external participants? ‐> Detailed plan of project.
B. Prepare project
• a) What kind of question should be answered? • b) What would we need a technology forecast for? • c) How would we like to use the forecast? • d) What are the data sources…? ‐> Validated project specification
C. Define objectives
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identify the Levels for the Forecast
R1‐: large variation in the data may decrease accuracy ; inaccuracy may be magnified in the aggregated forecast (aggregation issue)
R1+: low variation in the data; consistent forecast data can be arranged at all levels (allocation issue)
R2‐: the aggregated forecast may smooth out local trends and/or allocate them incorrectly.
V: too low in sub-systems
Λ: too high in super-systems
R2+: local trends can be identified and the details for practical application can be projected
Levels for forecasts Desired result
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D. Perform a study and develop TF
D.2. Capitalize Set of
Problems
D.4. Build the Time Diagram
(timing)
D.1. Define Boundaries of
System
D.3. Analyze limitation of resources
D.2.2. Define Critical-to-X
Features
D.2.4. Map Contradictions
as Network
D.2.1. Reformulate Discontents into Contradictions
D.2.3. Revise Sets of Contradictions
D.1.2. Law of System
Completeness Description
D.1.4. Analysis of Drivers and
Barriers (discontents)
D.1.1. Define Key Functions and Key Features
D.1.3. Impact Analysis of
Contexts and Alternatives
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D.1. define boundaries of a system
• What are main function (set of major functions) and what are significant traits? ‐> First approximation to boundaries of system to be studied.
D.1.1. Define key functions and key
features
• What are four major components of system? What are product and tool? How energy passes through system? ‐> Defined system with boundaries and major sub‐systems.
D.1.2. Law of System Completeness
• How system is positioned according to Economic, Social, Environmental and Technological contexts?‐> Definition of system and major super‐systems.
D.1.3. Impact analysis of Contexts and Alternatives
• What are driving forces and obstacles on evolution of system? ‐> Preliminary lists of resources and dissatisfactions.
D.1.4. Analysis of Drivers and Barriers
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D.1. boundaries of a system (example)Law of System Completeness: Distributed Energy Generation system
* Information provided courtesy of EIFER, Karlsruhe [Henckes, L. et al., 2006]
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what is the future of some “X” technology?
intuitive prediction extrapolation of trends
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CONTEXTS
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D.1. boundaries of a system (example)List of Drivers and Barriers: Stationary Fuel cell
* Information provided courtesy of EIFER, Karlsruhe [Gautier, L. et al., 2005]
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D.2. Capitalize Set of Problems
• What are the problems behind of discontents and barriers? ‐> List of contradictions (technical contradictions – TRIZ).
D.2.1. Reformulate Discontents into Contradictions
• What are root causes of discontents and contradictions? ‐> Set of metrics to measure evolution of system.
D.2.2. Define Critical‐to‐X Features
• How root causes are relevant to formulated contradictions?‐> Prototypes of contradictions of parameters (physical contradiction ‐ TRIZ).
D.2.3. Revise Sets of Contradictions
• How formulated contradictions are linked? What is the network of contradictions? ‐> ‘one page’ presentation of interconnected contradictions.
D.2.4. Map Contradictions as
Network
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capitalize set of problemsCritical‐to‐Market features: Stationary Fuel Cell
* Information provided courtesy of EIFER, Karlsruhe [Gautier, L. et al., 2005]
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* Information provided courtesy of EIFER, Karlsruhe [Gautier, L. et al., 2005]
what are we doing to cope with unknown?
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D.3. Analyze the limitations of resourcesTechnological barriers assessment:
• What are Science and Technology + Research and Development activities addressed to identified problems?
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how to map unknown?
* Information provided courtesy of EIFER, Karlsruhe [Gautier, L. et al., 2005]
1. Cost = Installed
cost+ Operational
cost
2. Durability
5. Maintenance
intervals
3. Electrical Efficiency in
use (including
load variation)
6. Adequacy to user
requirements
Fuel Processor Stack
Jan. 2018Noble metal
catalyst in each Cell of
Stack - amount
Jan. 2006
Jan. 2016
Control – Structure/Management
Balance of Plant
Membrane and Bipolar plate –
type of materials
Fuel processor – fuel purification
H2 Rich gas + oxygen in Stack -
Flow rate
Cell of Stack - Humidity rate and
Temperature variation
Fuel processor - hydrogen
purification
Jan. 2012
Fuel processor - Operation
temperature of Reforming
step
Fuel Processor – Energy
consumptions
Catalyst in Fuel
Processor - amount
H2 Rich gas + oxygen in each Cell of
Stack - distribution
Cell of Stack - Current
distribution
Adaptability to fuels (For High Hydrogen
quality)
Stack – Pressure inside
Jan. 2010
Balance of Plant (BOP) - Structure
Stack - Operating
temperature
Jan. 2008
Jan. 2014
4. Emission
Highest priority
Jan. 2020
Product: Electricity + Heat
Water management in the system – External Water
Supply
Load – Output Current
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E. validate and F. apply the forecast
• For consistent validation of TF the major clients and partners should agree on: ‐ key functions of the analyzed system, ‐ key enabling technologies‐major trends in the evolution of the surrounding super‐systems
E. Validate results
• Depends on: ‐ needs and formulated objectives, ‐ transparency and intelligibility, ‐ credibility and consistency of the technology prediction.
F. Apply the forecast
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flowchart of the suggested method
B. Prepare project
C. Define objectives
of TF
D. Perform analysis
and develop TF
E. Validate results F. Apply TF
A. Identify needs in
Technology Forecast (TF)
D.2. Capitalize Set of
Problems
D.4. Build the Time Diagram
(timing)
D.1. Define Boundaries of
System
D.3. Analyze limitation of resources
D.2.2. Define Critical-to-X
Features
D.2.4. Map Contradictions
as Network
D.2.1. Reformulate Discontents into Contradictions
D.2.3. Revise Sets of Contradictions
D.1.2. Law of System
Completeness Description
D.1.4. Analysis of Drivers and
Barriers (discontents)
D.1.1. Define Key Functions and Key Features
D.1.3. Impact Analysis of
Contexts and Alternatives
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 56
US music recording media
* Sources [5, 6]:
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what are we doing to learn unknown?
Extrapolation of past trends in accordance with laws of evolution:
• simple logistic S‐curve, component logistic model, logistic
substitution model, time series analysis…
• Genrich Altshuller, Cesar Marchetti, …
What is different: study of the key problems but not the solutions
• analysis of contradictions, networks of contradictions, learning
the future limits of resources;
• social, economic, environmental and technological contexts.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 58
Those who have knowledge, don't predict.
Those who predict, don't have knowledge.
‐Lao Tzu
LOGISTIC EQUATION and logistic S‐curve
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 60
simple logistic S‐curve
α – growth rate parameter, time required for growth trajectory from 10% to 90% of limit κ characteristic duration (∆t=2.2 days); β – parameter specifies the time (tm) when the curve reaches 0.5κ midpoint of the growth trajectory; (tm = 2.5 days)κ – is the asymptotic limit of growth. (κ=50 species)
tetN
1)(
)( NN
dtdN
Pop
ulat
ion
/ Per
form
ance
inde
x
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 61
brief HISTORY of logistic models1825 - Benjamin Gompertz published work developing the Malthusian growth
model for demographic study (law of mortality);
1838, 1845, 1847 ‐ logistic curve introduced by Belgian mathematician Pierre‐Francois Verhulst as a model of population growth;
1923 – Robertson, T.B. was the first to use the function for describing the growth process in a single organism or individual;
1924, 1925 – Raymond Pearl rediscovered the function and used it extensively to describe the growth of populations, including human population;
1925, 1926 ‐ Alfred J. Lotka and Vito Volterra independently generalized growth equation to model competition among different species (the predator‐prey equations);
1957 ‐ Griliches, Z. showed that technological substitution can be described by an S‐shaped curve;
1961 – Mansfield, E. developed a model to explain the rate at which firms follow an innovator;
1971 – Fisher, J.C. and Pry, R.H. formulated model of binary technological substitution; it uses the two‐parameter logistic function to describe the substitution process;
1979 – Marchetti C. proposed logistic substitution model to describe several technologies in dynamics of competition.
1994 – Meyer P.S. proposed component logistic model (bi‐logistics, multiple logistics)…
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 62
what is the future of some “X” technology?
new‐to‐the‐world new family of product
new market penetration
Popu
latio
n:th
ousa
nds,
mill
ions
Perf
orm
ance
:kW
h/€,
kW
/m3
Popu
latio
n:th
ousa
nds,
mill
ions
Overwhelming majority of inventions will never become innovations (profitable market products) thanks to the
phenomena of competition and adaptation.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 63
The model of growth under competition
• Natural growth of autonomous systems in competitionmight be described by LOGISTIC EQUATION and logistic S‐curve.
• Natural growth is defined as ability of a 'species' to multiply inside finite 'niche capacity' through time period.
• For socio‐technical systems the three‐parameter S‐shaped growth model is applied for describing "trajectories" of growth or decline through time.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 64
rate of growth, cumulative growth
* S-curve fit on data by Loglet Lab Version 1.1.4
Bell‐shaped (“normal” distribution) Simple logistic (symmetric) S‐curve
Data sources: The TRIZ Journal (1996‐2006), proceedings of the TRIZCON (1999‐2006), proceedings of the ETRIA TFC (2001‐2006). The same articles from different sources
where taken into account just once.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 65
Fisher‐Pry transform. Confidence intervals
* S-curve fit on data by Loglet Lab Version 1.1.4
Forecast with confidence intervals
Fisher-Pry transform
)
)(1)(()(tF
tFtFP
where
)()( tNtF
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 66
Five steps to get an S‐curve
1. To define what is necessary to predict.
2. Define growing variable (parameter).
3. Select data to be applied:• to gather data;• to refine data;• to adapt and arrange data;
4. Fit logistic curve(s) to the data: • to determine upper limit (ceiling) for growing variable;• fit and bootstrap logistic curve to data (mono‐, bi‐, multiple‐
logistics?)5. To build consistent and reasonable interpretation of
obtained curves.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 67
Some rules to fit a logistic curve to the data1. It is crucial to examine the residuals after a fit .
o when a fit is “good,” the residuals are non‐uniformly distributed around the zero axis; that is, they appear to be random in magnitude and sign.
o a substantial or systematic deviation from the zero axis indicates some phenomenon is not being modeled or fitted correctly.
o If the residuals are large or systematically distributed, better fits are likely to be attainable, or perhaps the growth is not logistic.
o "residual analysis could also identify "slices" of data that are especially noise‐free and might be more heavily weighted when fitting. "
2. "…it is helpful to treat the data from … “quiet” years, when growth appears to be unfolding without external disturbances such as war or depression…"
3. ".. behavior is often irregular when a market share is less than 5%..“
4. External evidence supports a set value for a particular parameter: o the growth of a bacteria culture is limited by the size of the petri dish;o because no nuclear tests preceded 1945, leave 0 as the displacement.
* Source: Meyer, P.S., Yung, J.W. and Ausubel, J.H. A Primer on Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software. Technological Forecasting and Social Change, 1999, 61(3), 247‐271.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 68
why does it possess forecasting power?
Logistic S‐curve describes evolution of system under limitation of resources through time
Strength:• Properly established logistic growth reflects the action of a natural law. • Relatively easy to apply. Clear concept and working mechanism.• Can be applied for systems where the growth mechanisms are understood and where the mechanisms are hidden.
…and Weakness:o What is growing variable (species) and what is underlying competing mechanism in particular case? Lack of formal procedure to define.
o Bias towards low or high ceiling: ‘no two people, working independently, will ever get EXACTLY the same answer for an S‐curve fit’.
o Should we fit S‐curve to the raw data or to cumulative number? Fitting technique errors and uncertainties.
How to improve reliability of forecast?
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 70
How to improve reliability of forecast?
1. Adaptation of logistic models of growth for emerging
technologies (towards quantitative methods).
2. Adaptation of knowledge about cycles, trends and
patterns in super‐systems (towards system approach).
3. Improvement of repeatability and reproducibility of
forecasting with evolutionary computation methods
(towards independency of expert’s biases).
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 71
how the stable elements were discovered
* Source: Modis, T. Predictions - 10 Years Later. (Growth Dynamics, Geneva, Switzerland, 2002), pp. 149. ISBN 2-9700216-1-7.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 72
COMPONENT LOGISTIC MODEL
* Source: Modis, T. Predictions - 10 Years Later. (Growth Dynamics, Geneva, Switzerland, 2002), pp. 149. ISBN 2-9700216-1-7.
THE STABLE ELEMENTS WERE DISCOVERED IN CLUSTERS
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 73
growth of knowledge and logistic models What kind of information about knowledge should be measured ?
before system passes the 'infant mortality' threshold;before having enough data for growing variable trend.
invention innovation
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 74
from invention to innovation (1)
Source: Mensch, G. Stalemate in Technology: Innovations Overcome the Depression (Ballinger Pub Co, Cambridge, Massachusetts, 1978), 241. 088410611X.
NAME INVENTION INNOVATION YEARS LEADTIME
High voltage generator 1820 1849 29Electro‐medical stimulator 1831 1846 15Deep sea cable 1847 1866 19Electricity production 1708 1800 92Insulated conductors 1744 1820 76Arc lights 1810 1844 34Pedal bicycle 1818 1839 21Rolled rails 1773 1835 62Rolled wires 1773 1820 47Pudding furnace 1783 1824 41Blast furnace with coke 1713 1796 83Crucible steel 1740 1811 71Locomotives 1769 1824 55Telegraph 1793 1833 40Lead chamber process 1740 1819 79Pharmaceutical industries 1771 1827 56Quinine industries 1790 1820 30Hard rubber 1832 1852 20Portland cement 1756 1824 68Potassium chloride 1777 1831 54Photography 1727 1838 111
Basic Innovations in the First Half of the Nineteen Century
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 75
from invention to innovation (2)
Source: Mensch, G. Stalemate in Technology: Innovations Overcome the Depression (Ballinger Pub Co, Cambridge, Massachusetts, 1978), 241. ISBN 088410611X.
The case of Locomotive
1769 Watt: Low pressure machine1770 Cugnot: Steam gun vehicle1790 Read: Steam road vehicle1800 Watt's: Patent on steam engines expires1801 Trevithick starts work on locomotives1804 Evans: Road locomotive1811 Blenkinskop: First toothed gear locomotive1813 Hadley: Locomotive on rails1814 Stephenson: starts work1824 Stephenson: built first locomotive plant1825 Stephenson: open Stockton‐Darlington line
“…a technical event is a technological basic innovation when the newly discovered material or newly developed technique is being put into regular production for the first time, or when an organized market for the new product is first created."
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 76
Three engineersThree engineers are riding in a car: an electrical
engineer, a chemical engineer and a Microsoft engineer. Suddenly the car stalls and stops by the side of the road. The three engineers look at each other with bewilderment, wondering what could be wrong.
The electrical engineer, not knowing about mechanics, suggests: “Lets strip down the electronics of the car and try to trace where the fault might have occurred.”
The chemical engineer, not knowing much about mechanical or electronic things suggests: “Maybe the fuel has become emulsified and is causing a blockage somewhere in the system.”
The Microsoft engineer suggests: “Why don't we close all the windows, get out, get back in, open the windows again, and maybe it'll work!?”
source: Solo Typing Tutor 9 (www.ergosolo.ru)
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 77
patented but not innovated[smoke-spark arrestors]
* Source: Grubler, A. Technology and Global Change. (International Institute of Applied System Analysis, Cambridge, 2003), p.452 ISBN 0 521 54332 0.
A few examples of the more than 1000 patented ‘smoke‐spark arresters’ for wood‐burning steam locomotives in the USA.
Source: Basalla, G. The Evolution of Technology, p. 136. Copyright © 1988
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 78
"…the distance [between invention and innovation] decreases regularly inside a certain wave, but starts larger again
in the next [wave]…”*
* Marchetti, C. Time Patterns of Technological Choice Options. p. 20 (International Institute for Applied Systems Analysis, Laxenburg, Austria, 1985).
The distance between center points of invention‐innovation waves (1‐2; 3‐4; 5‐6; 7‐8) is always about 55 years, one Kondratiev cycle.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 79
long‐run of technology change
* Source: Modis, T. Predictions ‐ 10 Years Later. (Growth Dynamics, Geneva, Switzerland, 2002), 335. ISBN 2‐9700216‐1‐7.
When many technological processes reach saturation together they produce a recession
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 80
technologies tunnel through the economic growth and recessions
* Source: Modis, T. Predictions ‐ 10 Years Later. (Growth Dynamics, Geneva, Switzerland, 2002), 335. ISBN 2‐9700216‐1‐7.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 81
Kondratieff cycles and US economy
* Source: http://www.thelongwaveanalyst.ca/cycle.html
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 82
trajectories of transport infrastructures
* Source: Modis, T. Predictions ‐ 10 Years Later. (Growth Dynamics, Geneva, Switzerland, 2002), 335. ISBN 2‐9700216‐1‐7. *Adapted from a graph by Arnulf Grubler (originally drawn by Nakicenovic) in The Rise and Fall of Transport Infrastructures, (Heidelberg: Physica‐Verlag, 1990), excluding the lines labeled “Airways” and “Maglev?”
AN ORDERLY PRECESSION OF U.S. TRANSPORT INFRASTRUCTURES
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 83
LOGISTIC SUBSTITUTION MODEL and CYCLES
Primary energy sources substitution and cycles of energy consumption. Adapted from (Modis, 2002)
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 84
Conclusions
Results:
Why it matters:
Methods:
Next steps:
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 85
THANK YOU ! :)
LICIA / LGECO ‐ Design Engineering LaboratoryINSA Strasbourg, 24 bd de la Victoire,
67084 STRASBOURG, FRANCE
www.seecore.org
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 86
REFERENCES: 1. http://www.seecore.org/id1.htm [Publications]2. Kucharavy, D. TRIZ instruments for forecasting: past, present, and future. p. 80
(INSA Strasbourg ‐ Graduate School of Science and Technology, Strasbourg, 2007).
3. Kucharavy, D. and De Guio, R. Anticipation of Technology Barriers in border of Technological Forecasting. Part 3. Project IGIT (Instrumentation de la Gestion de l’Innovation Technologique à haut risque), p. 47 (INSA Strasbourg, Strasbourg, 2008).
4. Kucharavy, D., Schenk, E. and De Guio, R. Long‐Run Forecasting of Emerging Technologies with Logistic Models and Growth of Knowledge. Competitive Design, 19th CIRP Design Conference, pp. 277‐284Cranfield, UK, 2009).
5. Meyer, P.S., Yung, J.W. and Ausubel, J.H. A Primer on Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software. Technological Forecasting and Social Change, 1999, 61(3), 247‐271.
6. IIASA – Logistic Substitution Model II: Data Source: RIAA (Recording Industry Association of America), yearend market reports (var. vols.) http://www.riaa.com/News/marketingdata/yearend.asp
7. Kucharavy D. and De Guio R. Tutorial at CBC: Forecasting the Problems, Presentation materials. Santiago, Chili, 2011. p.126
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 87
Graduate School of Science and Technology
http://www.insa‐strasbourg.fr/en/
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 88
About 20 years experience in TRIZ as engineer, researcher,
consultant, and instructor
www.seecore.orgwww.trizminsk.org
1987‐1988: the first acquaintance with TRIZ; 1989‐1993: research engineer at IMLab, Minsk, Belarus; 1994‐1998: freelance TRIZ‐consultant, entrepreneur;1997‐1998: invited instructor in SADT, IDEF0, and TRIZ at Belarusian state and private universities; 1998‐2001: professional TRIZ consultant & instructor at LG‐Production and Research Center (LG‐PRC, Pyeongtaek, S.Korea); 2001 ‐ : research engineer, instructor, adviser and consultant at LGECO, INSA Strasbourg, France.2003 ‐ : restart of research for method of Reliable Technological Forecasting...
• Project_1 (2004 – 2005) Technological forecasting of Fuel Cells for small stationary applications
• Project_2 (2005‐2006) Technological forecast of Distributed Generation (DG)
• 4 days course (2008) Vinci, Italy
• 3 days course (2010) Istanbul, Archelik, Turkey
• Project_3 (2011 – 2012) Forecasting the parameters of the technological dynamics of a technological core area of Chilean mining industry (BHP Billiton)
• Project_4 (2012 – 2015) FOrecast and Roadmapping for MAnufacturingTechnologies (FORMAT)
KUCHARAVY Dmitry
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 89
Innovation of different degree of Radicalness(in the period 1953-1973*)
Type of innovation (according to degree of radicalness)Weighting (according to
degree of radicalness)
Frequency (in the
period 1953-1973)
1 Basic innovation 32 to 35 7
2 Radical innovation 28 to 31 29
3 Very important improvement innovations 24 to 27 62
4 Important improvement innovations 20 to 23 145
5 Mundane improvements 16 to 19 239
6 Minor product or process differentiation with new technology 0 to 15 760
* Mensch, G. (1978). Stalemate in Technology: Innovations Overcome the Depression Cambridge, Massachusetts: Ballinger Pub Co. p.p. 31.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 90
we don't see things as they are, we see things as we are…
‐about two thousand years ago
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 91
forecasting & inventive problem solving
… 1975… 1991… 2008… 2015…
Strategic planning & Decision making;Management of technologies;Innovation management;Diffusion of Innovations
Technological Forecast
Data, Methods, Experts,Customers
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 92
2010 Haiti earthquake (12 January)Magnitude 7.0 Mw
Depth 13 km (8.1 miles)
On 10 February the Haitian government reported the death
toll to have reached 230,000*
An investigation by Radio Netherlands has questioned the
official death toll, reporting an estimate of 92,000 deaths as
being a more realistic figure.**
* "Haiti quake death toll rises to 230,000". BBC News. 10 February 2010.** Melissen, Hans Jaap (23 February 2010). "Haiti quake death toll well under 100,000". Radio Netherlands Worldwide. Retrieved 28 February 2010.
Population- 2009 estimate
9,035,600- Density
361.5/km2
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 93
2010 Chile earthquake (February 27)
This was the strongest earthquake affecting Chile since the magnitude 9.5 1960 Valdivia earthquake (the most energetic earthquake ever measured in the world), and it is the strongest earthquake worldwide since the 2004 Indian Ocean earthquake.* It is tied with the 1906 Ecuador‐Colombia and 1833 Sumatra earthquakes as the seventh strongest earthquake ever measured, five hundred times more forceful than the 7.0 Mw earthquake in Haiti in January of 2010.**
* "Historic World Earthquakes". Earthquake.usgs.gov. United States Geological Survey. November 23, 2009. Retrieved February 27, 2010.** "Huge quake hits Chile; tsunami threatens Pacific". February 26, 2010. Retrieved February 26, 2010.*** Gobierno aumenta a 486 los fallecidos por terremoto y posterior tsunami http://www.latercera.com/contenido/680_240084_9.shtml****Ya suman 802 los fallecidos por el terremoto y tsunami http://www.elmostrador.cl/noticias/pais/2010/03/03/ya-suman-802-los-fallecidos-por-el-terremoto-y-tsunami/
Population:- April 2010 estimate
17,063,000- Density22/km2
Magnitude 8.8 Mw
Depth 35 kilometres (22 mi)
The latest death toll as of April 7, 2010 is 486 victims***
(down from 802 reported by the previous administration on March 3).
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 94
competition and technological substitution
Malthusian case: competition for resources Simple S‐curve
Models for two competitors:
Pure Lotka‐Volterra model1
Predator‐Pry Lotka‐Volterra model
Symbiosis (Mutualism) Lotka‐Volterra model2
Parasitic (Commensalism) Logistic S‐curve
Symbiotic (Amensalism) Logistic S‐curve
No‐competition (Neutralism) Simple S‐curve
Models for multiple competitors:
Spatial arrangement Can be reduced totwo competitorsTime arrangement
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 95
what is the future of some “X” technology?
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 96
Sales of Digital’s VAX 11/750
The VAX‐11/750, code named "Comet", was a more compact, lower‐performance TTL gate array‐based implementation of the VAX architecture introduced in October 1980. The CPU had a 320 ns cycle time (3.125 MHz). [Wikipedia]
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 97
Digital Equipment Corporation (DEC)
was a major American company in the computer industry and a leading vendor of computer systems, software and peripherals from the 1960s to the 1990s. Also known as DEC and using the trademark DIGITAL, its PDP and VAX products were the most successful minicomputers*.
* Source: Digital Equipment Corporation. (2012, September 28). In Wikipedia, The Free Encyclopedia. Retrieved 16:30, October 9, 2012, from http://en.wikipedia.org/w/index.php?title=Digital_Equipment_Corporation&oldid=515026592
Industry Computer manufacturing
Fate Assets were sold to various companies. What remained was sold to Compaq.
Successor(s)
Hewlett-Packard(2002 – present)Compaq(1998–2002)
Founded 1957
Defunct 1998
Headquarters Maynard, Massachusetts, United States
Key people
Ken Olsen (founder, president, and chairman)Harlan Anderson (co-founder)C. Gordon Bell (VP Engineering, 1972-1983)
Products
PDP minicomputersVAX minicomputersAlpha servers and workstationsDECnetVT100 terminalStrongARM microprocessorsDigital Linear Tape
Employees over 140,000 (1987)
Existing forecasting approaches
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 99
How does one forecast a technology change? Technological forecasting and long‐range planning
99* Ayres R.U. (1969)
Types of Forecasts• Exploratory projection (possible future)• Target projection
Families of methods
• Morphological analysis
• Extrapolation of trends (quantitative)
• Heuristic forecasts
• Intuitive methods of forecasting (qualitative)
• Policy and Strategic planning
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 100
How does one forecast a technology change? Technological forecasting for decision making
100* Martino J.P (1972)
Types of Forecasts• Normative Methods• Exploratory Methods • Combining Forecasts
Major methods• Delphi surveys
• Forecasting by Analogy• Growth curves
• Trend Extrapolation• Analytical Models
• Monitoring for Breakthroughs
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 101
How does one forecast a technology change? Long Range Forecasting. From Crystal Ball to Computer.
101* Armstrong, Jon Scott (1985)
Three continuums:• Subjective vs. Objective methods
• Naïve vs. Causal methods
• Linear vs. Classification methods
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 102
How does one forecast a technology change? Forecasting: methods and applications
102* S.Makridakis (1998)
advanced forecasting methods‐ dynamic regression; ‐ neural networks; ‐ state space modeling; ‐ new ideas for combining
statistical and judgmental forecasting
traditional time series methods‐decomposition; ‐ exponential smoothing; ‐ simple and multiple linear regression; ‐ Box‐
Jenkins' ARIMA models
judgmental forecasting‐ Bayesian approach
major statistical combination methods‐ `optimal' combination; ‐ outperformance; ‐ quasi‐Bayes
approach to long‐term forecasting‐ based on mega trends; ‐ based on analogies; ‐ based on scenarios
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 103
How does one forecast a technology change? Methodology tree
103http://www.forecastingprinciples.com/methodologytree.html J. Scott Armstrong (2002)
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 104
How does one forecast a technology change? Technology Future Inc. (consulting company)
Vanston, J.H. (2003)
Extrapolations (quantitative)• Technology Trend Analysis• Fisher‐Pry Analysis• Gompertz Analysis• Growth Limit Analysis• Learning Curve
Pattern Analysts / Causal models• Analogy analysis• Precursor Trend Analysis• Morphological Matrices• Feedback Models
Goal Analysis / Scenarios• Impact Analysis• Content Analysis• Stakeholder Analysis
• Patent Analysis• Roadmaps• Value Models
Counter Punchers / Monitoring• Scanning, Monitoring, Tracking• Scenarios• Terrain Mapping• Decision Tree• Strategic Games
Intuitions (qualitative)• Delphi Surveys• Nominal Group Conferencing• Structured and Unstructured Interviews
• Competitor Analysis
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 105
How does one forecast a technology change? Futures Research Methodology (AC/UNU Millennium Project)
105
Quantitative
Qualitative
Normative
Exploratory
Jerome C. Glenn (2003)
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 106
How does one forecast a technology change? Technology Future Analysis
106Porter, A.L. (2004)
Two groups:Exploratory ‐ beginning the process with extrapolation of current
technological capabilities;Normative ‐ beginning the process with a perceived future need.
Two classes:Hard ‐ quantitative: empirical, numerical;Soft ‐ qualitative: judgmentally based, reflecting tacit knowledge;
Nine families:Creativity; Descriptive and matrices; Statistical; Expert Opinion; Monitoring and Intelligence; Modeling & Simulation; Scenarios; Trend Analyses; Valuing/Decision/Economic.
Researching FutureKUCHARAVY Dmitry 12/10/2012 14:36 107
growth rate function
S-curve function(cumulative growth)
t0
Midpoint: inflection point (point of symmetry)
K/2
K
Growth time: the time needed to grow from 10% of K to 90% of K
Saturation: a priory unknown asymptotic limit of growth