I've found some info on them; they're a sllight modification of partials as espoused by Gironda: most of his ideas make more sense than other sources, even today. Gironda and Scott used them on most exercises, including Scott's arm program which IMO is still superior to most others.
Not a new idea, but likely new to most. The X-rep variation concerns where in the ROM the burns are done.
From my own experience, it's true that there is a sweet spot in any ROM which justifies partial ROMs, sometimes it's even better than using full ROMs. Can be used for the full set or after full ROM failure. I'm quite sure that this technique is very effective if you're willing to go through the pain.
The X-rep idea is to do partials at the end of set within the sweet spot they define as after mid-point, around 5/8s-7/8s into the ROM. From experience i agree with their concept and the effectiveness, try different ranges and compare results. Apparently Platz also used this in squat sets. An additional advantage of this is further extension of time under tension TOT. Here's an excerpt:
At the end of a set to failure, when the high-threshold motor units start to kick in, your nervous system fails. That’s when most people stop a set—when they can’t get another full-range rep. But what if instead of stopping, you were to lower the weight to the max-force-generation point and continue to fire out partials? You would leapfrog nervous system failure and continue to recruit fast-twitch fibers, essentially making each set three to five times more efficient at stimulating growth.
Just the way Ronnie Coleman instinctively tries to overload that point on his rows. With X Reps, however, instead of jerking or heaving every rep, wait till the end of the set and attack that key mass-building sweet spot safely and efficiently. Getting more fast-twitch-fiber involvement and energy conservation is only part of X Reps’ extraordinary power, however. There’s occlusion too. Because X Reps are partial movements and create continuous tension, you get some occlusion at the end of every set you use them on, even if it’s a full-range multijoint exercise. Partials create continuous tension. And if you use X-Rep partials at the end of a set of a continuous-tension isolation movement, like leg extensions, you occlude the muscle even longer than if you stop at failure.
At the end of a set right at the max-force-generation point on the exercise stroke. It’s a fairly straightforward concept. Try them near the bottom of incline presses or chins, for example. Or on leg curls. You’ll learn firsthand why it doesn’t take a lot of sets—but it does take some guts (go for the burn).