How low will my ink go before Instant Ink sends new cartridges?

[Joel57]

Printer Model: HP OfficeJet 3830

I have been enrolled in the Instant Ink program since I purchased my printer in July 2016.  My last cartridge shipment was November 6, 2017.  My black cartridge is now only 1/4 full, yet the 'Ink Shipment' page in my account says, "You should have ink available to install. Check around your workspace; it might have arrived some time ago."

I do not have ink available to install, because I installed it 14 months ago.

How low does the cartridge have to be before new ink is sent?

[Valsimot]

https://support.hp.com/lv-en/document/c03760650#AbT4 

• HP monitors the ink levels when your printer is connected to the Internet and Web Services is turned on.
• Replacement ink cartridges are automatically shipped when your ink cartridges have enough ink to print twice the number of pages included in your monthly plan. You do not receive replacement ink cartridges every month, but they should arrive before you run out of ink.
• Replacement ink cartridges can take up to 10 days to arrive, which should be sufficient for customers with regular usage.

[Joel57]

More information than I asked for, and most of which I knew already, but thanks anyway.

However, am I to assume then, that when I no longer have enough ink to print more than twice as many pages as my monthly plan includes, only then  I will get a shipment?  If so, that's cutting it pretty close, because sometimes it takes a while for the cartridges to arrive, and I could run out of ink before then.