I suggest you create a new relationship from the parent table (invoices?) to the log, adding a "<=" predicate to the graph. Set a global date field equal to the date you want, and the related records will be only those items occurring on or before that date.
It will then be a simple matter to aggregate whatever field you want; just put a summary field in the log table and call it from the parent.
If you're scripting it, you can also set $$Variables that will show up as merge fields on your report.
You will set them via ExecuteSQL's, like
Set Variable $$TotalFailures;
ExecuteSQL("SELECT SUM(Failures) FROM ProductLog WHERE LogEntryDate < ?";"";""; gChosenDate + 1)