Failure time and rate constant of degradation: An argument for the inverse relationship

Abstract

In the field of reliability engineering, the failure time is usually taken to be inversely proportional to the rate constant for the reaction that leads to failure. This relationship is then used to derive the accelerated life model. We show this assumption to be valid for any elementary reaction leading to failure, provided that the differential equation for the reaction rate is independent of any explicit time dependence, i.e. is autonomous in the variable representing time. We argue that such a form for the differential equation describing the rate of reaction that leads to failure is rather generally valid.