System fatigue reliability modelling under stochastic cyclic load

Based on a mathematically insightful interpretation of the 'statistical average' meaning of the traditional stress-strength interference model for reliability calculation, this paper puts the issue of interference analysis of two random variables into a more general framework. Under such a framework, what is expressed by the traditional stress-strength interference model is a statistical stress-weighted average of the 'reliability conditioning to stress', which is a function of the random stress. Thus, the same form of expression as the load-strength interference equation, which traditionally can be applied only in the case of the same system-of-units parameters (e.g., stress and strength, both are measured in the same unit, MPa), can be applied to more general situations involving parameters of different system-of-units. In this way, the traditional stress-strength interference model was extended to deal with any two random variables, as long as one of the variables is a function of the other. Such an extended interference analysis model has the ability to calculate fatigue reliability under cyclic stress with uncertainty in stress amplitude. Using the order statistic of component lives to describe system life, fatigue reliability models for different types of system were developed based on the statistical average algorithm.