Influence of S-Curves on Use of Inventive Principles

Darrell Mann
Industrial Fellow, Department of Mechanical Engineering
University of Bath
Bath, BA2 7AY, UK
Phone: +44 (1225) 826465
Fax: +44 (1225) 826928



This article discusses emerging correlations between evolutionary S-curves and the 40 Inventive Principles contained within TRIZ. The position of a system - be it technical or non-technical - on its current S-curve plays a significant role in determining which TRIZ tools may be deployed to improve the system. We may see, for example, that our approaches when the system are markedly different at the two extreme ends of the curve - Figure 1.

Figure 1: Position on S-Curve Influences Problem Solution Strategy

Given the two ends of the S-curve, it is commonly observed that the Substance-Field Analysis method is more effective at the bottom of the curve, and that the Contradictions toolkit is most effective at the top of the curve. That being said, it is also clear that contradictions exist throughout the life of the S-curve - indeed, as long as the system exists, it will contain contradictions.

The Contradiction Matrix is of course a commonly applied means of managing the choice of when to use which of the 40 Inventive Principles. Unfortunately, for a good number of engineering problems - particularly electrical-based systems - and for just about all non-technical problems, the Matrix is not a reliable tool. A common response in these situations where the Matrix does not help, is to ask problem solvers to examine each of the 40 Principles. The main problem with this advice is that it tends to dilute the consideration of each Principle to unacceptably low levels.

While research continues to examine updates to the Matrix, there are a number of simple strategies which enable problem solvers to reduce the number of Principles which are likely to be relevant to a given situation. This article discusses one such method.


S-Curves and Trimming Trend

A previous article has discussed the correlation between an S-curve and the Trimming evolution trend (Reference 1). Figure 2 reproduces the main correlation suggested in that article.

Figure 2: Approximate Relationship Between S-Curve and System Part Count

The main message from the graph is that during the initial stages of the S-curve, part count (NB phrase is intended to apply to both technical and non-technical systems again) may have to rise; and during the latter stages, the part count will become reduced.

With this increasing-then-decreasing part count idea in mind, examination of the Inventive Principles suggests that certain of the 40 involve inventive directions which also correlate to either increasing or decreasing part count:


Principles Associated With Increasing Part Count
(In numerical order)

Principles Associated With Decreasing Part Count
(In numerical order)



Figure 3: Relationship Between S-Curve and Inventive Principle Applicability

Bringing the ‘increasing’ and ‘decreasing’ Principles together onto one picture gives the reference image shown in Figure 3. It is hoped that this picture will be of some value to problem owners working in areas - particularly non-technical - where the Contradiction Matrix is not effective.

Note that some of the Principles cannot be categorised into either ‘increasing’ or ‘decreasing’ part count usage because they are either part-count neutral (‘Colour Changes’) or may cause part count to change in either direction depending on the particular circumstances of the system.

Health Warning

Care should be applied when employing the recommendations contained in this article in cases where systems and sub-systems are shifting to new S-curves. More will be written about the importance of S-curves and S-curve families in a future article.


  1. Mann, D.L., ‘Trimming Evolution Patterns For Complex Systems’, TRIZ Journal, February 2000.