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I am interested in mathematically describing as well as formalising a manufacturing plant so that other people in the engineering field understand how the system works. I am not from the engineering field, and so I don't know what the typical standards for this type of task are.

Suppose the manufacturing plant consists of three work units: A warehouse, a transport system and a processing station. The materials are transported from the warehouse to the processing station, where they are processed and then stored again. This process repeats itself indefinitely. What is the best and most professional way how an engineer would describe this system?

So far, I have described the process textually, but I shall only explain it by mathematical formulas or figures. Are there various specifications or guidelines in the engineering environment? I don't know what a good starting point is.

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    $\begingroup$ block diagram is one possibility - will you want to model feedback... $\endgroup$ – Solar Mike Feb 14 '19 at 12:49
  • $\begingroup$ @SolarMike are there any "languages" such as UML that are typically used in the engineering domain for specifying, visualising, constructing, and documenting the manufacturing systems? $\endgroup$ – user3352632 Feb 14 '19 at 12:58
  • $\begingroup$ Never come across UML... but have used many languages French, Fortran, Basic, Pascal, and now vba .... $\endgroup$ – Solar Mike Feb 14 '19 at 13:00
  • $\begingroup$ There is sysML, but might not fit your needs $\endgroup$ – joojaa Feb 15 '19 at 5:25
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Solar Mike is correct (as usual); the block diagram approach is the classic method for "formalizing" the dynamics inside a large and complicated system.

However, it is important to realize that this paradigm is of limited utility in analyzing the actual behavior of a big factory in that it fails to take into account the behavior of the humans that manage the flow of material and information inside that factory, in particular when the factory enters an out-of-control state.

In that case the system can enter a death spiral called "ISOC" or in specification but out of control, about which great volumes of literature could be written... by me, a recovering ex-engineer, for example.

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To represent it, like already mentioned, a diagram would be a good tool to use. If you wanted to go a little deeper, some type of simulation software would be of value. For example, Arena is a program that allows you to simulate a process. You could watch a few videos on YouTube about Arena to see if the program would be helpful to you.

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