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How do we give our product owners access to V1?
Should we give them a "Customer" role on their projects and add the contact person for each backlog item as an additional owner?
What's really the intended use of "product owner" and "owner"?
Terminology differences can be a confusing factor here, so we'll start with those. In this article, we will use the term "Product Owner". You can translate as appropriate into the term used in your methodology.
Product Owner (in Scrum) = Customer (in XP, DSDM, Agile UP)
Product Owners who are members of the project team (e.g., they define the backlog groups in the system and present them to the rest of the team) are generally the owner of a portfolio item and are defined as the product owner on a backlog item. This is helpful if a team is working with multiple product owners representing different parts of the system. If there is only one product owner for the project team, there is less of a need to identify the same person on each and every backlog item, so many teams will opt not to enter this.
Some teams establish owners at the backlog item level to coordinate the various task and/or test work to be completed on the backlog item. Owners at this level are optional, so only define them if they present some value. Owners are also defined at the tracking level within the system (by default for most organizations, tracking on backlog items occurs down at the task and acceptance test level). One or a pair of owners are typically defined here for each task. Some groups track their progress at the backlog item level, in which case they will probably want to identify an owner for each backlog group that is in a current sprint.