Entropy Maximum Principle and Instantaneous Failure Statistics

摘要

A Shannon entropy for instantaneous failure statistics is defined in terms of an integral over the full epoch of possible failure times. An entropy maximum principle subject only to the normalization of the probability density integral and the existence of a mean time to failure yields an exponential distribution as the fundamental probability distribution for instantaneous failure statistics. It is observed that the time scale of measurements does not necessarily coincide with the time scale on which the probability distribution takes its fundamental form. Time scale transformations are considered. The maximum entropy density is taken to be form-invariant independent of the time scale used in its description, and the resulting epoch entropy is itself taken to be an invariant. This latter invariance leads to a relation between the time unit of a transformed time scale and the time unit of the fundamental scale. The invariance relation is employed in consideration of the effect of parameter scaling in particular devices, and in the discussion of the behavior of parameters that arise in accelerated testing. (Author)