After the statistics utility generates the Plesk statistics and the webalizer statistics it begins to delete the logs. The statistics utility runs daily at 4:07 am. If you set the logs to be deleted weekly the logs will be deleted at the beginning of the following week or month. If you choose weekly the logs will be deleted at 4:07am on Monday. If you choose monthly the logs will be deleted at 4:07am on the 1st of the upcoming month.