We perform an analysis of the derivation of Quantized Inertia (QI) theory, formerly known with the acronym MiHsC, as presented by McCulloch (2007McCulloch ( , 2013. Two major flaws were found in the original derivation. We derive a discrete black-body radiation spectrum, deriving a different formulation for F(a) than the one presented in the original theory. We present a numerical result of the new solution which is compared against the original prediction.