Play time is worth considering, but perhaps bulk hours aren't really the way (or at least, they shouldn't be the only way) to go about measuring faction activity.
Perhaps "when" is more important than "how long", by which I mean we should turn an eye to when factions are playing. Now, this is a metric we have to take with a grain of salt due to the sinusoidal nature of the server's population and the fact that people live in different time zones, but we should pay some attention to the spread of a faction's activity across a week. Have they logged any time during peak server hours, or do they only play during the dead hours when maybe a dozen people are online? Do they play on a few different days of the week, or is all their activity clustered on Tuesday morning?
If a faction's activity is restricted to a narrow portion of the week, then they're not really exposing the server to their roleplay. Now, granted, small factions (and these days most factions are small) don't necessarily have the manpower to cover multiple time zones and people's work schedules are a thing, so this definitely shouldn't be the deciding factor in a faction's officialdom unless other factors (like forum roleplay presence or total hours clocked) are also very telling.
Now, to long-windedly build on a point Croft made:
Part of a bigger problem here at Discovery is an aversion to specialization, which means that factions that have a wide breadth of privileges and large ZOIs are more attractive to players. Part of this is unavoidable, since, for example, the Liberty Navy and the Liberty Police are both permitted to deal with unlawfuls with their guns or fines or what have you. You can't limit the LPI to fighting off Rogues and Xenos and designate LN purely for fighting Hellfire Legion and Outcast threats, obviously -- it's utter nonsense. Police factions having TLAGSNET and Military factions having access to larger capital ships are reasonable attempts at specialization, so this is the sort of thing we should strive for.
But we look at the Outcasts as a counterexample -- as an instance of where maybe we don't have things tuned quite right. The Outcasts have an absolutely immense ZoI. Based in the Omicrons and Taus, the Outcasts have presence in the Sigmas, Kusari, Bretonia, and Liberty. They are drug dealers and warmongers and pirates and every other feather that fits under their cap. The Maltese engine is monolithic in terms of roleplay documentation, but you can actually play an Outcast many different ways.
Perhaps, in the interests of treating the Outcasts like a House, we should split them up into smaller factions. Given their roles as cardamine smugglers, it's easy to imagine a trade corporation originating in Malta. They can fly fighters, bombers, freighters, and transports up to 4300 cargo space (or we could throw them a bone and get them a faction 5k). Give them a military faction which polices their core systems and leads battle fleets into deep space, let them fly everything from fighters to battleships, but limit the cargo capacity on their transports to 3.6k. Then give them an intelligence faction, responsible for piracy activities in far-reaching places, which specializes in fighters, bombers, freighters, and gunships. No sense drawing oodles of attention down in house space, right?
The Outcasts are merely an example of this. We could effect similar changes with the Corsairs. The Hellfire Legion already has the seeds of a new house sewn in Kansas with the Commonwealth of Liberty -- a welcome split between military and civilian roles.
In breaking up factions with great reach and disproportionate powers, we will open up new opportunities for players to have official factions (which I suppose could be a good or bad thing, depending on your point of view). In the case of the Outcasts, we could have three official factions each with portions of the previous monolithic one's roles. This also pushes players to choose factions (NPC or player) that are more specialized, which I suspect will have two effects: A) players make characters better suited to a specific role instead of polymath pilots with knowledge of smuggling routes and battleship attack strategies and B) encourage the use of generic IDs for factions with more wanderlust and less central organization in mind.
A less on-topic idea would be to break up large faction alliances (cf. Outcasts with Rogues and Hackers) since friendly NPC ties are often seen as a reason to share ZoIs. Obviously many Rogue and Hacker characters are cardamine addicts and rely on good relations with the Outcasts to get their fix at dealer cost, but these factions don't have to be green to each other on the repsheet for this to happen. The Rogues seem to be more interested in maintaining control of their territory (since they want the lion's share of trader wealth) and the Hackers want to bother Liberty's corporations.
There can be a mutual agreement between the Rogues and Outcasts where the former insinuates cardamine into the Libertonian economy and the Outcasts keep their hands out without these factions needing to be allied, especially since this precludes any opportunities for Rogues to deal with Corsairs (which happened in vanilla -- the whole artifact sequence early in the game was evidence of that). In this particular instance, we would be broadening the scope of the Rogues' faction, but only because we are stopping another faction from overshadowing them.
We could also merge factions together. I mean, goodness, Rheinland has four unlawful factions and the three that aren't the Hessians are rather niche. This is an issue of too much specialization. Hell, the LWB? "We're angry about Synth Foods on Stuttgart." Even the Gaians -- named for one particular planet in Edinburgh -- have a broader scope than that.
TL;DR: Break up the factions that have power-crept to having lots of power and boost or merge factions who've been overshadowed or overspecialized.
Maybe it´s little late, but here is my opinion and proposal. Please take your hiking boots, Chinese wall of text is incomming (sorry for that).
First, I don´t want to be rude, but if there was problem to maintain even such very simple system as checking logged online time (what takes like ten minutes) for several months, I can´t imagine that any more sophisticated and thus more difficult and time consuming system could work, considering how overloaded the staff is already.
It is impossible to create a system which would be at the same time sophisticated and will consider both objective (logged time) and subjective (overall quality of provided roleplay) criterias, and at same time will be easy to run without need of investing too much time into it from staff. We all know that for example activity summaries were interesting idea, but it went down the drain the moment when many faction leaders got feeling (often justified) that staff do not read what they write, or at least do nothing with issues which are raised there.
So I don´t see issue with keeping the basic system which is in place (24 hours ingame, 3 active players). However, it is true that sometimes even factions which don´t meet 24 hours quota (or three active players) are still beneficial to the community because they still at least do for example forum RP. That´s quite important, because it is annoying for any player when he has some interesting roleplay idea for which he needs cooperation with some official faction (as valid representative of some ID) or their approval for something, but there is not any and thus the roleplay is blocked. And in the same time, we have factions which meet the requirements but otherwise don´t do anything more including ignoring forum RP querries.
So I gave it some thought and tried to propose some better but still reasonably demanding system, which will be more friendly to semi-active factions (which have better and worse months of activity, but they still try to contribute) but in the same time will be friendly to admins which need to overview it. System is still based on monthly checks, however if staff think it would be still too demanding, checks can be done every two months (just multiple mentioned logged times x2). Or even only every three months (and multiple it x3), however flaw of this would be that it leaves dead factions with official status for quite a long time period (especially if inactive factions are going to be warned first).
So, here it is:
Step 1: Separating the factions on the basis of activity
First step is to separate active factions, semi-active factions and alternatively also dead factions, possibly in some very easy way so admins don´t have to invest lot of time into checking (best solution would be some kind of automatic forum plugin if it´s possible technically).
Tracker seems to be best solution for this. Let´s just establish a amount of logged time which constitute active faction. In my opinion it can be like 36 hours (eventually 48 hours, but it should not be more per month). Such faction does not have to prove anything more, because usually if they are that active ingame, they are also active in other ways (like forums) and we all know that it would be nonsense to question status of any faction which has 2+ days of activity these days. These factions don´t have to be judged further in any way and are good to go. This setup also makes activity grinding harder because grinding 36 or even 48 hours per month is much more difficult than 24 hours when faction is not really active.
[Alternative part]
We can also establish absolute minimum of logged time per month to keep officialdom, for example 6 hours (since this is line for removal from tracker for indies). Alternatively it can be 8 hours (as one third of current mandatory 24 hours quota), but should not be more I think.
If faction will not meet this quota, warn them. Warning stay active for next three months and if they won´t meet it again, strip them of officialdom. No ifs or buts, faction whose members can not bother to log this minimal time (with three members it´s literally one evening for whole month) became more virtual than real. Actually we had/have official factions which logged for less than hour for whole month(s), yet they still keep their status technically (see {343} or IC| for example). That´s not right.
[End of alternative part]
So now we have a group which can be called semi-active factions. These will submit their activity summary so admins can judge if they are more just a placeholder which does not contribute at all apart of few logged hours, or they still have some activity (forum RP, events organization or participation etc.) and contribute to the environment. It will be up to adminteam´s judgement to set up when the faction is to be considered inactive (like, one post in message dump per month surely isn´t enough) and community will lose little to nothing by warning it and then revoking its status, or it still is able to play the role at least partially and it will be beneficial for community to keep them their status (especially important when there is not any active unofficial group for this NPC faction).
That´s it, today´s hike over Chinese wall is over, have a nice day.
The idea of keeping semi-active factions around, combined with the "paperwork" necessity is good, as it enables some roleplay possibilities that might be impossible otherwise.
In my opinion, we really need to start cleaning house again. Dead official factions that occupy a spot are bad for Disco. They discourage new initiative systematically, and make Disco feel deader than it is.