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Rogers' bell curve. Similarly, in the later stages, the opposite mistakes can be made relating to the possibilities of technology maturity and market saturation. The technology adoption life cycle typically occurs in an S curve, as modelled in diffusion of innovations theory. This is because customers respond to new products in different ways.
It is used heavily in statistical physics, statistical analysis, information theory, data science, neural networks, finance and marketing. A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion.
A similar theory about the stability of fixed points can also be applied to periodic points. That is, a periodic point that attracts surrounding orbits is called an asymptotically stable periodic point, and a periodic point where the surrounding orbits move away is called an unstable periodic point.
The Bass model or Bass diffusion model was developed by Frank Bass. It consists of a simple differential equation that describes the process of how new products get adopted in a population. The model presents a rationale of how current adopters and potential adopters of a new product interact.
The blue curve is broken into sections of adopters. Diffusion of innovations is a theory that seeks to explain how, why, and at what rate new ideas and technology spread. The theory was popularized by Everett Rogers in his book Diffusion of Innovations, first published in 1962. [1]
A process capability analysis may be performed on a stable process to predict the ability of the process to produce "conforming product" in the future. A stable process can be demonstrated by a process signature that is free of variances outside of the capability index. A process signature is the plotted points compared with the capability index.
The rate of diffusion is the speed with which the new idea spreads from one consumer to the next. Adoption is the reciprocal process as viewed from a consumer perspective rather than distributor; it is similar to diffusion except that it deals with the psychological processes an individual goes through, rather than an aggregate market process.
The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. [ 1 ] [ 2 ] Of the four parameters defining the family, most attention has been focused on the stability parameter, α {\displaystyle \alpha } (see panel).