Anatomy of the failure rate: A mathematical dissection

摘要

The failure rate function is one of the most commonly used notion in reliability engineering and in survival analysis. The purpose of this expository paper is to point out some mathematical issues connected with this notion, a consequence of which is that under certain circumstances the famous exponentiation formula overestimates the probability of survival. To demonstrate this we point out a scenario that results in Volterra's product integrals, instead of the usual Lebesgue integral for which the exponentiation formula is exact.