A Probabilistic Interpretation of Miner’s Rule

Abstract

Miner’s rule for the cumulative damage due to fatigue, a deterministic formula which is well known in engineering practice, was examined earlier from a probabilistic point of view with Birnbaum in [2]. Here the assumptions of that model are weakened. Previously the basic assumptions were that crack growth was stochastic in nature with incremental extensions having a distribution with increasing failure rate, and that the spectrum of load fluctuations was fixed and then repeated under program. We now assume, instead of the distributions of incremental crack extension having increasing failure rate, only that for a given load fluctuation, the expected residual damage increment either in crack initiation or extension, given the damage exceeds a preassigned amount, is less than the damage increment which was expected for that load fluctuation before it was imposed. We also weaken the assumptions concerning the type of loading spectra which are admitted, considering the case of random load fluctuations which a...