"A Li Ion battery is fairly unstable piece of kit, and to control its reliability, manufacturers add very sophisticated controllers to them, the exact way SSD or RAM controllers are added. A bad controller cause poor behaviour, as much as a poorly working battery. A cheap battery without a controller costs 1/3 price (think OWC products) but die in days or weeks. At the extreme of the spectrum you also have Li Ion batteries in aeronautics. As the Boeing fire incidents proved, even at that level they can be troublesome.
Depending how these batteries were built, whom manufactured the controller chips etc, miriad of variables pop over 230 millions iPhone sold a year. And, because the 99.9999999% of users out there have no issues (or Apple's 488 worldwide stores would be flooded) it means that few unlucky people will discover, one day, their battery not working."
All good info to think about, but not necessarily playing a role in this current issue being experienced by posters on this thread.
As you say batteries are complicated things these days, however the issue being experienced may or may not have anything to do with the actual battery at all.
Phones are complicated pieces hardware. OS's are complicated pieces of code. There is a myriad of things which could be going on.
The issue of this thread also may or may not have anything to do with iOS. It may or may not have to do with some other component.
"Quite likely even a factory reset would have revealed your issue."
Actually this phone I have has been factory reset 3 times before as it filtered through different people.
No problem until the iOS 10.1.1 upgrade.
Therefore, what revealed the issue was the iOS 10.1.1 upgrade in our case and the case of many others I personally know as I have previously mentioned. I feel that many experiencing the issue who are savvy enough to understand that something dramatic changed for them and bothered to seek out any info on their issue are a tiny number of the people experiencing this issue.
"So Apple already has a replacement program for iPhones 6 affected by a known physical flaw (BATTERY DEFECT), just batteries not the phone. Outside this small group, there is no indication of high battery failure rates."
But the battery replacement was for 6S's with a known defect in the Battery which affected all iPhones manufactured during a specific date from Sept-Oct 2015. What this thread is about is phones demonstrating similar behavior after a specific upgrade to 10.1.1 and has also spread upwards with those who wished to remediate the issue with by upgrading to 10.2 only to find the problem to be worse.
"All this says is likely they shared and bought the same batch of iPhones, and, possibly, exact same battery manufacturer."
And yet those visiting me over the holidays with the issue are from all over the country and have different models which are affected exactly in time with the 10.1.1 upgrade.
This was a step off that was suddenly noticeable.
Anyhow... what caused it?
Bad controller as you assert. Glitch in iOS. or some other hardware issue may or may not be determined.
For some they will never know. Some will have a useless phone. Some will upgrade their battery and be fine. Some will upgrade their battery and still have a useless phone. Some will wait for an iOS upgrade in hopes that this somehow will fix things. Some will just get another phone.
But this thread will continue on until there is or isn't a solution and over time nobody will care except those affected.
Some will still buy Apple phones. Some will buy other phones.