The crew of the B737 were cleared to track via PEPPA for a SPUDO 1 arrival for runway 24 at Perth. At PEPPA the aircraft was observed to turn onto a south-westerly heading instead of continuing towards the west. This turn placed the aircraft in potential conflict with outbound traffic and radar instructions were issued to maintain adequate separation. The crew of the B737 later indicated that they had started to fly a PEPPA 1 (218 degrees) arrival instead of the SPUDO 1 (263 degrees) arrival. Evidence indicates that the B737 crew misunderstood the clearance. As part of the aviation safety net there is a requirement for crews to repeat a clearance back to the controller to confirm they have received it correctly. The crews read-back on this occasion, indicated they would complete a PEPPA 1 arrival rather than a SPUDO 1. This error was not picked up by the controller. The clearance had been given in an abbreviated form and it is possible this contributed to the crews misunderstanding, particularly, as the arrival procedure had only recently been introduced (5 December 1996) and was not yet easily recognised by flight crews.