In this paper it is shown that the bathtub-curve (BTC) based time-derivative of the failure rate at the initial moment of time can be considered as a suitable criterion of whether burn-in testing (BIT) should or does not have to be conducted. It is also shown that the above criterion is, in effect, the variance of the random statistical failure rate (SFR) of the mass-produced components that the product manufacturer received from numerous vendors, whose commitments to reliability were unknown, and their random SFR might vary therefore in a very wide range, from zero to infinity. A formula for the non-random SFR of a product comprised of mass-produced components with random SFRs was derived, and a solution for the case of the normally distributed random SFR was obtained.