Aging, of biological and mechanical systems, is well described as ‘deterioration of the power to withstand destruction.’ The failure-rate concept is the mathematical way of describing aging. Failure rates have been defined for discrete and continuous time and used extensively, particularly in actuarial science and reliability. This paper assumes an arbitrary scale on which an object encounters stress, and develops a theory of failure rate with respect to ‘stress-time’ in analogy with the discrete- and continuous-time cases.