I have just purchased 3/16 x 2-3/4" philips head tapcons and the recommended 5/32" drill bit. I drilled the holes using hammer-drill with ease and plenty deep as recommended. Attempting to drive the tapcon it slides right in the hole, No resistance whatsoever. Feels like the hole is to big, Checking the drill bit it states 5/32 therefore - What the heck?
5/32" is just 1/32" smaller than 3/16". My guess is that, either due to a really good hammer-drill or relatively soft or brittle surface, you drilled the holes a little too big. If the location of the holes is critical (i.e., have to be where you already drilled) then get some larger screws - e.g., 1/4". If the location is not so critical then move an inch or two away and use a slightly smaller bit and/or drill a little less aggressively.
Vacuum dust out of hole
Mix some epoxy and inject into hole
Drive in a tight fitting wooden dowel (obviously 3/16 will fit)
Wait for cure