Just wondering, is an epic meant to show the total time spent on all its stories linked to it? like how an issue type e.g. a task usually sums up the amount of time logged for its sub-tasks which is displayed against that task?
Nope. Epic is meant to capture a large chunk of work. See https://confluence.atlassian.com/display/AGILE/Working+with+Epics
An epic can span more than one project, if multiple projects are included in the board to which the epic belongs.
I think this is a math question not a definition of an Epic. Is an Epic supposed to show the Sigma Total Time Spent of Items linked to it with Epic Link? Like a Story shows the Sigma Total Time Spent of the Story itself and the Sub-tasks underneath it in the Sigma Time Spent Field (or Displayed Data as it were)
If you would be interested in a ready made solution you can try out our add-on to track progress of issues in Epic hierarchy on time estimates and at story points as well.
The add-on allows you to manage and visualize your Epics with rolled up estimate progress reports along with multiple Time in Status Reports ( more than 6 reports).
Key features of Epic Hierarchy:
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