I made this as a personal challenge. In roleplaying games, the main problem with Mad Science themed mechanics is finding ways to deal with players possessing unlimited free-form creative abilities - preventing deus ex machina, keeping game balance, assigning costs, construction times and needed resources all while trying not to stifle player freedom. Hopefully, this system deals with those potential issues while keeping the process fun and creative for players, all while not ruining your campaign world too much. Still, this is a decadent system. I’d love to hear your thoughts and questions so I can amend and update this post and get it in a more realisable state.
Overview
+1 for each 1000gp invested in the Scientist’s laboratory. 
Mad Science is a downtime activity, from research to construction the process will always take 1 month and is accessible to all player classes. Mad Science must be performed in a laboratory. The end goal of the downtime is the construction of a Creation. This Creation is inspired by Ideas. Ideas are words that are randomly rolled and combined to form an initial Creation concept. Once the concept is decided upon, the DM can apply drawbacks to balance the Creation. Then resources and funds are gathered and the Creation is constructed. This funding/construction phase is the most dangerous and the potential for mishaps is high!
The first step of Mad Science is research. At this stage the Scientist is gathering Ideas and inspiration in his laboratory. The player rolls to discover what Ideas they will be working with. These Ideas will form the basis for their Creation. There is a d200 table of Idea words included alongside this post and here.
The base amount of Ideas to be rolled is 4. This score is modified by;
+1 if the Scientist is a Magic-User (or Specialist with 6/6 Tinker skill)
+/- the Scientist’s Intelligence modifier.
+1? At this stage the Scientist may also reverse-engineer a device/invention/thing to gain an additional Idea. An Idea specific to the thing being reverse-engineered. At its simplest, a laser-gun could be reverse engineered to produce the Idea laser or gun, a thermonuclear missile could give the Idea atomic or just bomb. This way the Scientist might be able to impart some direction into his Creation but they will have to go out adventuring to find a device related to the thing they want to create.
There are 200 words here. Use an online number generator or use a d20 for the 100's die (with a result of 20 being 00) and a d10 for the tens and digits. These words are generic and intended for a fantasy or science-fantasy game. 50 words list possible forms for the Creation, 75 words are fantastic and the final 75 words are more scientific. Players should be encouraged to reverse engineer items they already possess to choose a bonus Idea. Rewrite this table to better fit your setting.
An Example. A Scientist rolls the Ideas; Implant, Blade, Ray, Disintegration, Gestate and reverse-engineers a necromantic magic item to gain the bonus Idea; Death. The Scientist combines the Ideas Death and Ray - Death-Ray - simple. Other combinations could be Blade-Implants, Blade-Disintegration-Ray... Death-Implant (a kind of cyanide pill?) there are many possibilities but only one concept can be selected and detailed. Idea words can be altered to a degree; plurals, synonyms, changes in grammar are acceptable. The words do not have to form the name of the Creation, they simply inform the Creation's function.
Once the Creation is described the DM adds drawbacks. The drawback(s) must be worded in a way that uses half the word count of the Creation’s description (rounded up). This way, any Creation can be balanced by the DM and encourages players not to be too verbose or overladen their Creation with features. Drawbacks shouldn't render an invention useless but should hinder or wrinkle its usage in a way unintended by its creator. An unimpeded doomsday device, like a death ray could massively throw off a campaign - a huge, slow-charging death ray would throw off a campaign slightly less and prove more interesting logistically. A smoke bomb with the description 'explodes into concealing smoke' doesn't need so much of a drawback, 'really stinks' would suffice. For the sake of evenness, all inventions must have DM attached drawbacks, be fair and consistent - don't annoy your players but don't let your game be thrown out of balance either.
A simple example:
Creation name: Death Ray
Description: A gun that kills everything it shoots (7 words, half rounded up to 4)
Drawback: Colossal and charges slowly (4 words)
Construction Table
2-4: A mishap, a disaster! Follow this flowchart or apply the most applicable outcome. There is an industrial accident, the Creation goes rogue, turns out evil or is stolen. The Creation is complete but something must be done or dealt with before it can be used - retrieved from a huge acid spill, from an exploding workshop, from a thief. Perhaps the Creation, if sentient, rebels against its creator. Perhaps the Creation fuses with the Creator?
5-6: A detestable success. Your weird science has destroyed your reputation, the locals hate you and barely tolerate your presumably diabolical Creation. Any slight or provocation would see them gladly take up torches and pitch forks against you, your lab and your Creation. Maybe it's time to leave town?
7-9: Success, the Creation is completed without an issue.
10-11: Excess resources. Creation is completed. The process was inspiring. Gain an additional word during your next mad science downtime.
12: Very successful. You have made 2 copies of your Creation rather than one.
Once this table has been rolled on, the downtime is over and the Creation (though it's status might be fraught) is complete and adventuring may resume. The DM determines the mechanical properties and effects of the Creation based on its description and drawbacks if necessary.
Other Rules
Assistants: For each assistant hired an additional copy of a Creation can be constructed per month of downtime. Assistants can also be used to create previously invented Creations of which the blue print is available. Assistants cost 100gp for each month of Mad Science in which they are involved and 10gp a month when otherwise maintaining the laboratory. Assistants cannot produce Creations without the oversight of a PC.
Not all devices can be mass-produced by lab assistants. As a rule of thumb, if a Creation is man-sized or larger and non-consumable only one of it can be produced per downtime. Many grenades can be manufactured but flying cars cannot be.
Laboratories: Laboratories should have everything a mad scientist would need - electrodes, bubbling vials, operating tables. They cost 10,000gp and 1 month to set up. It's easier and cheaper if the adventuring party just take one over.
The Mad Science Process - takes 1 month
1. Roll 4 Ideas/Words. +1 word if Magic-User, +1 for each 1000gp invested in the laboratory being used, +/- intelligence modifier. +1 custom Idea if player reverse-engineers something.
2. Combine 2 or more Ideas into a Creation concept
4. Name the Creation and describe what it does, keep the description's word count low.
5. DM applies appropriate drawback(s) to the Creation using half the word count of the Creation’s description (rounded up)
6. Roll on the Construction Table (2d6+CHA modifier, -2 if Creation is abhorrent)
7. The Creation is complete. Deal with the resultant situation caused by a low roll on the Construction table using this flowchart or DM fiat if applicable.
