Did some digging in the lua code and found that the chance for an autorepair is evaluated every time the drill is upgraded as "Drill:set_skill_upgrades(upgrades)" should be called every time that happens.

First this happens:

local auto_repair_level_1 = upgrades.auto_repair_level_1 or 0
local auto_repair_level_2 = upgrades.auto_repair_level_2 or 0
local current_auto_repair_level_1 = self._skill_upgrades.auto_repair_level_1 or 0
local current_auto_repair_level_2 = self._skill_upgrades.auto_repair_level_2 or 0

Further down this happens if one of the local variables above is greater than 0

upgrades.auto_repair_level_1 = current_auto_repair_level_1
upgrades.auto_repair_level_2 = current_auto_repair_level_2
local drill_autorepair_chance = 0

if auto_repair_level_1 > current_auto_repair_level_1 then
current_auto_repair_level_1 = auto_repair_level_1
upgrades.auto_repair_level_1 = auto_repair_level_1
end

if auto_repair_level_2 > current_auto_repair_level_2 then
current_auto_repair_level_2 = auto_repair_level_2
upgrades.auto_repair_level_2 = auto_repair_level_2
end

if current_auto_repair_level_1 > 0 then
drill_autorepair_chance = drill_autorepair_chance + tweak_data.upgrades.values.player.drill_autorepair_2[1]
end

if current_auto_repair_level_2 > 0 then
drill_autorepair_chance = drill_autorepair_chance + tweak_data.upgrades.values.player.drill_autorepair_1[1]
end

if Network:is_server() and drill_autorepair_chance > math.random() then
self:set_autorepair(true)
end

So what I get out of it is that if a drill has already upgraded autorepair1 and/or autorepair2, the autorepair chance is evaluated once again if another upgrade happens. And it can only become an autorepair drill not the other way around.

Therefore the way to have the best chance for an autorestarter should be if the drill gets upgraded by players who have the skills in this order:
1. Kickstarter Basic(+20%; 0.2 restart chance so far)
2. Hardware Expert Ace (+10%; 0.2 + 0.8*0.3 = 0.44 restart chance so far)
3. Drill Sawgeant Basic (+0%; 0.2 + 0.8*0.3 + 0.8*0.7*0.3 = 0.608 restart chance so far)
4. Drill Sawgeant Ace (+0%; 0.2 + 0.8*0.3 + 0.8*0.7*0.3 + 0.8*0.7*0.7*0.3 = 0.7256 restart chance)

So it is possible to have a chance of 73% that a drill restarts if you upgrade in that order with 4 players. Usefullness is questionable as it takes around 33 seconds to perform that action for every drill.

Confirmations and counters are welcome.