That is my Two-stage forge PID control setup. The plans for a PID controlled forge and lots of forge info is in the metallurgy Sticky. They work very well. The video looks like a good explanation. There are many threads in ShopTalk about my system. Use the custom search engine to read them.
As far as accuracy, it will easily keep +/- 5 degrees*, and on a well-built forge that has had run long enough to soak the refractory, it can get down to =/- 2* degrees. I consider it very accurate once it is tuned for a target temperature.
*Those numbers are the reading on the PID. The REAL temperature is based on the range of error on your setup. A good type K thermocouple is +/- .75% of the reading. at 1500°F that is +/- 11 degrees, and your PID is likely +/-.3 to +/- .5% accuracy
The point is - People often don't realize that the maximum total efficiency of any system is dependent on the combined inefficiency. If the TC is .75% inefficient, and the PID control is .5% inefficient, the resulting accuracy can be as much as 1.25% inaccurate. It may be zero off, but it could be as much as 19 degrees off from what the readout on the PID says. This is similar to Heisenberg's Uncertainty Principal (Before I get jumped by a rouge gang of nerds, I said "similar", not, "the same".)
I have seen many posts here in Shop Talk and get regular emails from folks who are panicked over a difference of 15 degrees between two recommended programs for HT. I tell them that it is most likely off more than that for everyone ... even Larrin has to deal with the same inefficiencies. He gives you his best average numbers of many tests as his recommendation .... based on his equipment.
This is why we say in HT advice - YMMV - because my reading of 1500° and someone else's 1500° may be almost 40° apart.
Check YOUR results and adjust YOUR parameters up or down to find YOUR correct HT regime for the desired hardness/toughness results. Any numbers based on another shop's equipment are just a suggested starting point (even Larrin's book).