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Jira has dashboards which can help you with this. They're a collection of gadgets that you define that show you data in different shapes. So, to start with, create a dashboard for your programme.
Many of the gadgets you can use have specific inputs like a project, agile board, or user, but a lot of them report on a saved "filter".
So, your second step should be to go to issue search and create a search for the issues you are interested in. For me, it sounds like you probably want one that says "issuetype in (Story, Customer-issue, Bug)", so run that and then save it, giving it a sensible name.
Then go use it in lots of gadgets on your dashboards!
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