Each production category has a certain attribute linked to it.
Chasing - light - white - DEX
Alchemy - dark - black - INT
Cooking - water - blue - CRT
Smithing - fire - red - STR
Tailoring - wind - green - AGI
Carpentry - earth - yellow - VIT
To increase your success rate you need to add the stat which is linked to that production.
For example adding STR if you're doing smithing.
If I remember correctly every 25 of a stat gives you one point; the more points you have the better your success rate will be.
Another thing to keep in mind is the use of elemental advantage:
Every 5% adds a point.
Smithing is fire, so use either equipment with 'melee to fire' or 'ice/water element' and perhaps even stuff with '4 elements' or 'all elements'.
The first 2 options are the most recommended ones as they provide large amounts of elemental bonuses.
Element drinks apply to this as well.
(Bonus:
Now if you want to level up your prod with as least materials as possible you might want to consider a 'fail set', so you waste less materials in the process.
For that you want equipment that lowers damage against a certain element. Unmelting Ice, Grim Reaper, Magia Knife etc. are all good examples of such as they have 'no damage to ...' which equals to -100% elemental damage.)
Colour also matters: fortune colour plays a role and even your additional equipment.
I forgot exactly which additionals gave a boost, but I know for sure the ribbon series added points.
Like using Red Ribbon for smithing.
And if you want to do carpentry like a pro:
Any 2S fire/flame weapon Vatendeth Vatendeth
Lava Mail last up Foxxus
Some yellow additional Captain Beelzem
Carpentry Charm Vatendeth
Theru
Theru II
Sauro II
Max your VIT
Have yellow as lucky colour
Use Fire Drink
Have Fire Origin and All Around
Enjoy.