The favored class option system says..
Finally, some of these alternate favored class benefits only add +1/2, +1/3, +1/4, or +1/6 to a roll (rather than +1) each time the benefit is selected [...]
In most cases, these benefits are gained on a level-by level basis—your character gains the specified incremental benefit each time she gains a level. Unless otherwise noted, these benefits always stack with themselves.
And they present an example:
Finally, some of these alternate favored class benefits only add +1/2, +1/3, +1/4, or +1/6 to a roll (rather than +1) each time the benefit is selected; when applying this result to the die roll, round down (minimum 0). For example, a dwarf with Rogue as his favored class adds +1/2 to his trap sense ability regarding stone traps each time he selects the alternate Rogue favored class benefit; though this means the net effect is +0 after selecting it once (because +1/2 rounds down to +0), after 20 levels this benefit gives the dwarf a +10 bonus to his trap sense (in addition to the base value from being a 20th-level Rogue).
I bold both parts of interest. Can I select a +1/2, +1/3, +1/4 bonus benefit multiple times?
Some FCO flat bonuses clearly say what their caps are:
Paladin: Add +1 to the paladin's energy resistance to one kind of energy (maximum +10).
And even some other +x/y got that (bolded):
Mesmerist: Increase the mesmerist's towering ego bonus by 1/3 point (to a maximum increase of +2)
Now if I got for example the rogue's of the example
Rogue: Add a +1/2 bonus on Disable Device checks […]
This mean that … I can take it multiple time, it's got no cap and it stacks with itself?
So what happen if I chose to select each level in the favored class the "Favored class option"?
Ll 1 - ( +1/2 ) bonus to Disable device = lvl * 1/2 = +0
Lv 2 - ( +1/2 ) bonus to Disable device = lvl * 2/2 = +2
Lv 3 - ( +1 HP) bonus to disable device = lvl * 2/2 = 3 * 2/2 = 3
Lv 4 - ( +1/2 ) bonus to disable device = lvl * 3/2 = 4 * 3/2 = 6
Am I overlooking something in this otherwise OP mechanic?