For "containing" those process definitions (and managing them) you can use a combination of tools such as CMS and productivity tools such as MS Office (to produce process documents, which contain process activities and reference to additional - documents - templates, procedures, check lists, etc). But you'll have some difficulty with traceability between those QMS elements/artifacts.
Traceability is most relevant to answer questions like: What is the impact of/What shall be updated when I update this process, task, template? Who should I notify? Who is using this process, this template? And much more. MS Word (and PDF) documents can include hyperlinks but from a bunch of them it is not easy to tell how many activities/roles/processes/et. do I have "buried" on those PDFs (for example).
So this is why you can find in the market, market for (most of them) expensive tools that allow you to manage the Process Definitions (metamodels) and, for some cases, at a second stage, allow you to perform QMS process instantiations (a specific project can be seen as a concrete instantiation of the generic definition of the QMS, tailored for the specific project). With that process instantiation feature you can have additional insight (times elapsed, next steps to be done, notifications per life cycle phase, ...), like in Business Process Management (BPM) tools.
QMS Process Management tools ideally shall support the SPEM notation (Software Process Engineering Metamodel); BPMN support only (Business Process Modeling Notation) lacks capacity of relation between some objects/concepts that are much needed for full QMS Processes Definition.
Some tools found in the market include (the list is not extensive, google for more please):
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These are some possible valid solutions for self-hosted QMS Management tools. If cloud based is acceptable for your organization, the offer widens. Again, google for it.
About SPEM and BPMN you can see the PDF here (valid at 2017-05-08)
About SPEM support in Sparx Systems' EA: http://www.sparxsystems.com/enterprise_architect_user_guide/10/domain_based_models/spem.html
About SPEM support in Sparx Systems' EA: http://www.sparxsystems.com/enterprise_architect_user_guide/10/domain_based_models/spem.html