BPMN is the effective process modelling standard. There are some BPMN modelling tools that are open source or that have open source editions, such as:

ADONIS:Community Edition

ARIS Express

BeePMN

Bizagi Modeler

BPMN.io

Camunda

Flowable

Imixs-Workflow

MID Innovator for Business Analysts

The full BPMN language can be unnecessarily complex. So you may want to use a subset, at least initially, to document processes.

There are other business process modelling approaches such as:

Flow Charting

Swim Lanes

Event Process Chain (EPC)

Value Chain

Unified Modelling Language (UML)

IDEF-0

LOVEM-E

SIPOC

Systems Dynamics

Value Stream Mapping

These might be worth exploring.

There are some notes I have written on the topic of BPM:

https://www.researchgate.net/publication/333486082_Introduction_to_Business_Process_Management https://www.researchgate.net/publication/333486171_Process_Oriented_Architecture https://www.researchgate.net/publication/333486169_RPA_Robotic_Process_Automation_POA_Process_Oriented_Architecture_And_BPM_Business_Process_Management https://www.researchgate.net/publication/333486176_BPM_Business_Process_Management_CRM_and_Cross-Functional_Enterprise-Level_Customer-Focussed_Business_Processes https://www.researchgate.net/publication/333486382_Business_Process_Analysis_and_Design_-_Importance_of_Having_a_Common_Language_Between_Business_and_IT

Thank you very much Alan McSweeney . Your response is quite helpful.

I was told to try with draw.io which can be use as a plug in for a software called Confluence which is actually implemented within the project I am working.

Now, I need to figure out if these kinds of solutions allow to create a familiy of processus with the aim to be able to reuse a "Parent" process to inherite some elements to the child's processes.

The idea is to be able to easily modify part of sub-processes linked to a particular Main Process by directly editing targeted elements of the Main Process which will automatically change in the sub-processes.

Does it makes sense to you?

Thanks in advance

draw.io is a fairly simple drawing tool, like a easier version of Visio.

It has the concept of containers which is a shape that contains other shapes. This can be used to model subprocesses. It also has the concept of libraries which are simply sets of custom shapes. These shapes can be containers.

So you could use libraries and containers to create some crude process/structure hierarchy, with difficulty.

It does not have the concept of a process organisation structure with a hierarchy of processes, resources, business functions and so on. You would need to use a more functional product to have access to these features.

There are BPMN add-ons for Confluence:

https://marketplace.atlassian.com/apps/1215543/bpmn-modeler-free https://www.viadee.de/business-process-management/bpmn-modeler-for-confluence-en

These are related products. The free one is a limited version of the BPMN-Modeler Enterprise tool from Viadee. This version may do what you are looking for, at a cost. It also supports DMN and CMMN which may be of use. DMN in particular is good for defining decision rules.

I have never used either.

Do you have some experience with BPMN and machines within industrial processes?