40 principles of invention
A Contradiction Matrix, accordingly to its cells, (ordered alongside columns and rows with the indicated properties of the analyzed system) collects - in a structured and systematic manner - the basic engineering parameters of common objects, or systems, such as weight, length, and manufacturing tolerances, etc.
TRIZ methodology claims that by studying an individual parameter, which is causing a problem (e.g., the weight of an object needs to be reduced), and the other parameters which are in conflict with it (e.g., lower weight would require thinner material, which is more likely to undergo catastrophic failure if over-stressed), engineering solutions can be created for invention problems.
And this is actually the simplification of some fact. Namely, the structured contents of each of the cells within Contradiction Matrix, (i.e. cells fulfilled with ordered principles and identified by their order numbers) - the principles of inventions have been chosen, due to realized necessary statistical extensive studies. These were the studies led by G. S. Altshuller, based on virtually all known technical solutions up to that time, as well as the registered patents.
In Altshuller's opinion, every technical problem which has not yet any effective or satisfactory solution, nonetheless can be categorized in terms of its Main Technical Contradiction for the analyzed System. Therefore, it could be then analyzed using proper column and row of the Contradiction Matrix indicated, by correctly defined Main Technical Contradiction of the System, finally indicating the dedicated and suggested in process of finding the necessary solution - principles of invention.
Altshuller noticed that process of evolution of any given System is nonetheless ruled by commonly existing general Laws of Systems' Evolution. One such law says, that the very process of finding the necessary solution for the technical problem, can be facilitated and sped up in analogy to solutions which have already been found for another technical problem. However, the main point is to acquire the long-term necessary experience in correct defining of the Main Technical Contradiction for any given analyzed System.
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