The PlayStation 3 does not have a "Red Ring of Death." That term refers to a specific hardware failure on the Xbox 360, indicated by three red lights on the console's power ring.
The PS3 has its own set of hardware issues, often called the "Yellow Light of Death" (YLOD), "Green Light of Death", or other colored light errors, which signal various internal problems. While the PS3 experienced hardware failures, it never had an issue officially known as the "Red Ring of Death."