Metrisable assessment of the course of stream-systemic processes in vector form in industry 4.0

The goal of this paper is to present an innovative conception how to use metrisable vector structure of a manufacturing process, based on quantitative relations between the activity of input streams, features of the product, and effect of losses; all of which are excellent practical solution for Industry 4.0, and in turn intelligent factories. This solution can be a usefull way in the process of building sustainable organization. A vector representation of manufacturing processes was formulated, one which is based in system engineering. Three manufacturing system state vectors were proposed. These are: input stream vector $${\upphi }$$ ϕ , product features vector $$\overrightarrow {{\text{ P}}}$$ P → which is also referred to as quality vector, and losses vector $$\overrightarrow {{\text{ S}}}$$ S → . Scalar, vector, and mixed products of these vectors may form constitutive equations of manufacturing processes. The relations between the vectors $$\upphi$$ ϕ , $$\overrightarrow {{\text{ P}}}$$ P → , $$\overrightarrow {{\text{ S}}}$$ S → provide a possibility for a metrisable, complex analysis and assessment of a contemporary manufacturing process. The paper shows practical methods for defining the size of the vector values within the process. The demonstrated vector description of stream-systemic processes can also be applied to non-material manufacturing.