Subscriptions still active at month x are represented as `l(x)` and subscriptions that "die" (cancel/expire) in a given month are represented as `d(x)`.
This gives you a "life expectancy" and a "mortality rate" (so, churn) for any given number of months that a customer has been subscribed. So I can project how long someone will stay subscribed when they're brand new (at month 0) and how long they likely still have when they're at month 8 (longer than at month 0, funnily enough).
With those subscriptions where the month-specific churn will largely decrease the longer someone's subscribed (after passing the initial high-churn first months), this allows measuring/projecting churn on a much more granular level.
Segmenting this data by signup date is useful as well.
If I'm not mistaken, you're aligning all time periods to the same imaginary start date. This gives you the grand perspective but ignores very real changes in your application, team, marketplace, advertising, and product-fit over time.
Yes, you should absolutely segment into cohorts. Ideally you can tag users such that you can slice them not just by time, but what funnel they used or what marketing they've been exposed to (emails, etc.)
Just measuring the grand perspective, as you say, can be a very poor indicator for what is working well, and what isn't.
Subscriptions still active at month x are represented as `l(x)` and subscriptions that "die" (cancel/expire) in a given month are represented as `d(x)`.
This gives you a "life expectancy" and a "mortality rate" (so, churn) for any given number of months that a customer has been subscribed. So I can project how long someone will stay subscribed when they're brand new (at month 0) and how long they likely still have when they're at month 8 (longer than at month 0, funnily enough).
With those subscriptions where the month-specific churn will largely decrease the longer someone's subscribed (after passing the initial high-churn first months), this allows measuring/projecting churn on a much more granular level.