Solution : https://service.sap.com/sap/support/notes/166092 (SAP Service marketplace login required)
Key words : 
convert existing invoice documents, item category 'tad service', item category tad, sales information system, field vbrp-posar, attached report zzposar1, parameter 'item category', 'maintain item category', incorrect item type, service materials
Related Notes : 
       
| 1597096 | FAQ: Statistics update in Sales Information System | 
| 368011 | SIS/BW: Statistics update for value items, quantities | 
| 365922 | Incorrect update of value-only items in billing document | 
| 314486 | FSD: Billing document does not remove sales order | 
| 210330 | Statistics update for value items | 
| 204130 | SIS update: Collective note | 
| 197769 | Statistics update for value items | 
| 174141 | SIS: Collective note - Customizing | 
| 145701 | Statistics update for value items |