S-curve

S-curve is an S-shaped curve that represents the typical dependence of a main parameter of value (MPV) of an evolving engineering system on time.

Overview

The S-curve is a graphical representation illustrating the life cycle of a system’s main parameter of value (MPV) over time. It shows how a parameter evolves from its initial development through maturity to its eventual decline. The horizontal axis of the S-curve represents time, while the vertical axis represents the value or performance of a specific MPV.

The concept of the S-curve was originally adapted from biology into other fields of knowledge. In early 20th-century research, scientists discovered that bacterial colony growth followed a distinct pattern: a slow start, a phase of rapid growth, stabilization, and eventual decline due to resource limitations. This pattern resembled the shape of the letter S.

During his research, Altshuller examined and confirmed that various MPVs in engineering systems also evolve along their own specific S-curves over time.

To analyze and understand the evolutionary stage of an engineering system, Altshuller recommended using specific indicators. These indicators are a fundamental part of classical TRIZ and undoubtedly contribute significantly to the methodology. However, over time, it became clear that their practical application has serious limitations, and the results of analyses based on them were not always reliable. The Altshuller’s classical approach was further developed and served as the foundation for the creation of a pragmatic S-curve analysis.

Stages of the S-curve

Every system goes through 4 main stages during its life cycle:

STAGE 1:	A “newborn” system has not yet entered the market. It may even exist in the form of an idea, a sketch, or a prototype. MPV is almost flat.
	If the system survives stage 1, it enters the TRANSITIONAL STAGE. Due to specific characteristics, the transitional stage is sometimes considered a separate Stage in TRIZ, in fact it is the very end the stage 1. The system is still very young and vulnerable to external factors, but it is nearly ready to go to market or occupies small, strictly limited market niches. MPV starts growing noticeably.
STAGE 2:	A stage of intensive growth and expansion – the system moves into mass production, it is adapted for use in different applications, its variations and applications become more widely differentiated, the supersystem begins to adapt to the system, etc. MPV grows fast.
STAGE 3:	The mature system reaches some development limits. It is still in mass production, successfully infiltrates new applications and market niches, consumes highly specialized resources. Its incremental improvement requires disproportionate resources. The supersystem components intensively adapt to the system. MPV stabilizes and grows slowly.
STAGE 4:	The phase of decline. The system loses its utilitarian purpose, so it becomes an entertainment artifact, a decoration, a toy, sports equipment, etc., or it continues to function only in highly specialized fields or within a supersystem. MPV goes down.

The Altshuller's indicators of the S-curve stages

The indicators advised by Altshuller are the following:

Main parameter of value behavior is usually the easiest to be measured.
Number of inventions usually expressed as the number of patents. It is an indicator for which data can be easily obtained; they can be provided by patent databases (now, available online).
Level of invention is an indicator that has some subjectivity.
Profitability is probably the most difficult of the four measures. For a subsystem of a larger system, analysis can sometimes be even impossible.

The following chart illustrates a comparison of how individual indicators change as the system evolves:

MPV value

During the early stages, MPV value tends to be low as the system is refined and improved. During the rapid growth, it increases significantly due to the optimization for mass production and market demands. During the mature stage, it may plateau or increase more slowly, and it can decline in the final stage as the system becomes obsolete or less competitive.

Number of patents

The number of patents is an indicator for which data can be relatively easily obtained from patent databases available online.
It usually experiences two significant spikes:

during the introduction of the system into mass production, and
during efforts to extend the system’s lifecycle.

In the first stage of the system’s development in the context of a specific MPV, the number of patents is relatively low due to a lack of practical applications. As the system enters Stage 2, demand increases for technologies that enable mass production and widespread adoption. Companies and inventors race to secure intellectual property rights, leading to a rapid rise in patent filings.

In the third stage, patent activity continues to grow but for different reasons. The system is now mature, and engineers focus on extending its lifespan and improving profitability. Innovations mainly target optimization, performance enhancement, and new applications. In this phase, the motivation for patents is often to maintain market relevance and profitability.

In the fourth stage, a noticeable decline in patent activity occurs. The technology has reached its peak, and opportunities for further innovation are limited. The drop in patent filings reflects the phase in which the system is either being phased out or replaced by newer technologies, and the drive for new patents significantly weakens compared to the active pursuit seen in the previous two stages.

Level of invention

The level of invention is more difficult to obtain. The indicator depends on the individual assessment of patents, making it a subjective measure. Additionally, analyzing the history of a given system in the context of the given parameter is usually a very time-consuming process.

Young systems are characterized by a very high level of invention, which decreases over time. A temporary increase occurs during the period of mass application, only to revert to a downward trend.

In his research, Altshuller observed that not all inventions possess the same inventive level. By using the criteria of how contradictions are resolved and the scope of introduced inventions, he identified five levels:

Level 1 involves simple optimizations that do not resolve any contradictions and typically include minor improvements, usually of a structural nature, introduced through experimentation. These solutions often refine existing systems without introducing new principles. Developing these requires knowledge and resources (devices, methods, materials) related to the specific system.

Level 2 encompasses inventions that resolve contradictions, but these contradictions are simple and relatively easy to solve. The solutions typically involve still minor, but more significant changes than those at Level 1. These changes remain within the same engineering field, although they may require knowledge and resources from other areas of industry.

Level 3 is characterized by advanced and non-obvious solutions; however, both the problem and the solution still originate from the same field. These inventions are more sophisticated and already involve the use of knowledge from other branches of industry.

Level 4 includes more groundbreaking solutions that synthesize new systems by applying knowledge from one field of science to solve problems in another (e.g., solving a mechanical problem using principles from biology). By integrating different fields, this level reflects a significant leap in innovation.

Level 5 is the highest. It involves breakthrough solutions often resulting from fundamental scientific research. These introduce new principles that can revolutionize entire industries, such as the invention of the laser or radio. These inventions typically go beyond the scope of conventional problem-solving methods, such as TRIZ.

Profitability

Profitability is probably the most difficult to obtain. For a subsystem of a larger system, analysis can sometimes be almost impossible.

Young systems, despite their very high level of invention, do not generate income – they often exist only on paper or in single prototypes. They have many flaws and inconveniences. Income begins to appear once they transition to mass application. During this period, even small improvements can yield significant profits.