According to the depth of field (DOF) fomula, the DOF is linearly proportional to the circle of confusion (C), in which C is also linearly proportional to the pixel size. Thus DOF is linearly proportional to the pixel size.
If that assumption is correct, then does that means some of the DSLR with APS-C sensor size and low pixel number would have a shallower DOF than some of the full frame DSLR with a high pixel number, assuming using full frame equivalent lens by considering the crop factor and same distance to the capturing subject?
For example the Pentax K-100D has 6 Mega pixels with an aps-C sized sensor, comparing to Pentax K-1 with a full frame sensor and 36 Mega pixels.
The DOF of K-1 would be about 4 times deeper than that of K-100D.
Please correct me if I my logic is not sound. Thank you for your time and effort!
the DOF is linearly proportional to the circle of confusion (C), in which C is also linearly proportional to the pixel size.
No. The CoC criterion is the largest blur that will be perceived by the viewer as a point. At low resolutions, this may be limited by pixel size, but generally in real world use other factors are dominant — display size, distance of viewer, etc.
Keep in mind also that we usually assume a same size print regardless of recording media size (so, greater enlargement for APS-C than full-frame), and when doing comparisons, we generally mean for the same framing, not for the same focal length. (More on this at Why do depth of field calculators show *more* DOF for larger formats with the same lens parameters?)
Since this is one of your basic assumptions, and it is not correct... everything after that falls apart from there.