Maximum Entropy and Reliability Distributions

An effort is made to show the relevance and usefulness of the principle of maximum entropy to reliability considerations. The constraints entering into the maximum entropy principle are identified as a class of sufficient statistics which determine the unknown parameters in the probability densities that occur in the most commonly used reliability models. In this way, the maximum entropy principle is shown to be completely compatible with prevailing practice in failure analysis. It is also pointed out that the differential entropy is equal to unity minus the expectation of the natural logarithm of the hazard rate. Maximization of the differential entropy is therefore equivalent to minimization of the expectation of the logarithm of the hazard rate. Behavior of the differential entropy under transformation of variable is used as an indicator of change or lack of change of conditions of failure.