Alchemiracle
Alchemiracles (錬金大成功) are incidents in which the alchemical process undergoes a tremendous surge in power during the creation of elite four-star gear, pushing the equipment in question past its limits and resulting in the most supreme object of its type.
Improving the odds
Though the default chance is a lowly 10% to begin with, each item's chance to ascend corresponds to a particular stat of the protagonist and can be raised to a maximum of 40%. The benchmarks for each stat are 20% 533~765, 30% at 766~998, and 40% at 999--keep in mind that the success percentages do not scale incrementally and will only improve upon reaching the next benchmark: a stat of 764 will not raise the rate to 29%, for example.