Reliability modeling of systems with dependent failure when the life measured by the number of loadings

The method for modeling reliability of systems with dependent failure when the life is measured by the number of loadings is developed. Dependent failure existing among components is considered, and reliability models of systems with dependent failure are derived through introducing the conditional reliability of systems. Taking the analysis of static strength failure and fatigue failure as the backgrounds, the models for calculating the reliability and failure rate of systems under repeated random load without strength degeneration and those with strength degeneration are derived respectively. Then, the relationship between the reliability of systems and the number of loadings, and that between the failure rate of systems and the number of loadings are discussed in different cases. The result shows that even though strength doesn't degenerate, both reliability and the failure rate of systems decrease as the number of loadings increases, and the failure rate curves have the partial characteristics of bathtub curve with early failure period and random failure period. When strength degenerates with the number of loadings, the reliability of systems decreases more obviously as the number of loadings, and the failure rate of systems decreases first and then increases as the number of loadings, showing the whole shape of bathtub curve. The models proposed can be applied to guiding the reliability design, reliability test and the whole lifecycle management of systems.