A Generalized Limit Theorem for Reliability

A new and more general limit theorem is proposed in place of the exponential limit theorem of Drenick. First it is shown that as time goes to zero, the hazard rate can be made to approach an almost arbitrary function. Next it is pointed out that in the exponential limit theorem (and others) the only practical and necessary effect of having the number of elements ``go to infinity'' is to force time to go to zero. Therefore the limit theorems are not as useful as was once thought.