How aging laws influence parametric and catastrophic reliability distributions

In this paper we describe how these physics of failure aging laws influence reliability distributions, not only the type of distribution, but the rate of failure as it relates to the aging rate. We illustrate how one can predict parametric failure rates based on the physics of failure aging laws when known. A number of statements are concluded. We show that when a manufactured part has a key parameter that is distributed normally, and the physics of failure aging for this key parameter ages in log-time, its failure rate is lognormally distributed. When the physics of failure is a power law, we illustrate how the Weibull beta and eta can be obtained from the physics of failure aging law exponent and amplitude in the parametric case. We use the example of creep, and make direct comparisons between the full creep `rate' curve and the bathtub curve. Although the example of creep is used many aging laws have a similar power law forms and can be applied in a similar manner. Although we work though parametric failure rate statistics, one can relate it to the catastrophic case.