“Hot Pixels” defects in digital imaging sensors accumulate as the camera ages over time at a rate that is highly dependent on pixel size. Previously we developed an empirical formula that projects hot pixel defect growth rates in terms of defect density (defects/year/mm2)
via a power law, with the inverse of the pixel size raised to the power of ˜3, multiplied by the square root of the ISO (gain) We show in this paper that this increasing defect rate results in a higher probability that two defects will occur within a 5x5 pixel box. The demosaicing and
JPEG image compression algorithms may greatly amplify the impact of two defective pixels within a 5x5 pixel box, spreading it into a 16x16 pixel box thus resulting in a very noticeable image degradation. We develop both analytical (generalized birthday problem formula) and Monte Carlo simulations
to estimate the number of hot pixels required to achieve a given probability of having two defective pixels occur within a 5x5 square. For a 20 Mpix DSLR camera (360 mm2) only 128 hot pixels generate a 4% probability of two such defective pixels, which for pixels of size 4 μm may occur
in 1.4 years at ISO 6400, and in 3.2 years at ISO 3200.