A donor's giving totals on the household record are wrong. How would you troubleshoot it?

I work from the definition outward rather than from the number inward.

1. First I confirm what the number is supposed to mean. “Wrong” usually turns out to be a definition mismatch — does it include soft credits, refunds, pledged-but-unpaid commitments, or gifts designated to a particular fund?
2. Then I check the rollup definition itself: its rollup object, join condition and filter conditions. A filter that excludes refunded gifts, for example, will produce a legitimately different number from the one finance has in their spreadsheet.
3. Next I check execution. Rollup definitions generate a Data Processing Engine definition on activation, so I look at whether it has run, when, and whether it errored. A stale number and a wrong number look identical to a user.
4. Then the data: is the constituent actually related to the household through the relationship record the rollup traverses, or was the relationship never created? Missing membership is a common cause of a suspiciously low total.
5. Finally I feed the definition back to the business in words, because half the time the correct fix is to agree what the number should mean, not to change the configuration.