Series System Failure Rate Modeling and the Mechanism to Yield Bathtub Curve

Abstract

Failure rate functions were usually constructed in terms of life distribution. The present paper defines “discrete failure rate”, analyzes the dependence of failure rate curve shape on the probabilistic property of load-strength interaction, and develops load-strength-interaction based system failure rate model. For the majority of mechanical equipment, operation load is normally a random process, components are subjected to a large number of stochastic load actions during its service life. Meanwhile, material property degrades continuously owing to the failure mechanisms such as fatigue. It is the ever changing load-strength relationship that yields the variation in failure rate. Based on the criterion that failure occurs when a load higher than the relevant strength appears, failure rate model is developed based on the interaction mechanism between load and residual strength, and their statistical characteristics as well. Based on the interpretation to the variation of failure rate in terms of load uncertainty and strength uncertainty, the effect of statistical risk of load and the effect of strength degradation on failure rate curve shape are highlighted.