Metrisable assessment of the course of stream-systemic processes in vector form in industry 4.0
Radosław Drozd, Radosław Wolniak
Abstract
Abstract 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 $${\upphi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϕ</mml:mi></mml:math> , product features vector $$\overrightarrow {{\text{ P}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mspace/><mml:mtext>P</mml:mtext></mml:mrow><mml:mo>→</mml:mo></mml:mover></mml:math> which is also referred to as quality vector, and losses vector $$\overrightarrow {{\text{ S}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mspace/><mml:mtext>S</mml:mtext></mml:mrow><mml:mo>→</mml:mo></mml:mover></mml:math> . Scalar, vector, and mixed products of these vectors may form constitutive equations of manufacturing processes. The relations between the vectors $$\upphi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϕ</mml:mi></mml:math> , $$\overrightarrow {{\text{ P}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mspace/><mml:mtext>P</mml:mtext></mml:mrow><mml:mo>→</mml:mo></mml:mover></mml:math> , $$\overrightarrow {{\text{ S}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mspace/><mml:mtext>S</mml:mtext></mml:mrow><mml:mo>→</mml:mo></mml:mover></mml:math> 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.