For my project I rewrote how status effects work and made the LUK stat drastically factor in to how well status effects are inflicted and resisted.
Basically, each of the main status effects has 5 stages of severity: 0, 1, 2, 3, and MAX. (Stage 0 doesn't actually inflict any ailments associated with the status effect, but it's different than not having any stage of the status effect in that it makes it easier to at least inflict stage 1 of the status effect on the target during subsequent attempts.) Furthermore, every skill that inflicts a status effect has a "Potency" rating for that status effect, the higher the Potency the better it is at inflicting the status effect. A skill that is completely dedicated to inflicting Poison might have a Potency of 100, while a melee attack that inflicts Poison as a side-effect might have a Potency of 35.
If the user uses a skill with Potency 100 on a target that has roughly the same LUK as the user, the skill will have a good chance of applying stage 1 of the status effect (before resistances are calculated), with a slight chance of inflicting stage 0 or stage 2. If the user subsequently uses the same skill on a target that has stage 1, the skill will have a good chance of advancing the target to stage 2 of the status effect, and a slight chance of advancing to stage 3 or reapplying stage 1.
However, if the user's LUK is double that of the target, the same skill will have a good chance of inflicting stage 2 right off the bat, with a slight chance of inflicting stage 3 or 1. On subsequent attempts on a target with stage 2, the skill will have a good chance of advancing the target to stage MAX or at least stage 3.
And if the user's LUK is half that of the target, the skill will either only apply stage 0, or not apply any stage at all, and after two attempts user would only be able to get the stage as high as stage 1.