System Reliability Evaluation Under Dynamic Operating Conditions

Components in a system work under the same dynamic operating conditions, and their lifetimes are generally positively correlated. Ignorance of the correlation may lead to a significant bias in the evaluation of system reliability. Using the cumulative exposure principle, we model the equivalent operating time of the components, resulting from the cumulative effects of the dynamic environments, as a monotone increasing stochastic time scale. Commonly-used models, such as the compound Poisson, gamma, and the inverse Gaussian processes, are adopted for the stochastic time scale. Based on the above settings, reliability models for multicomponent systems are developed. We investigate how the stochastic time scale influences the system reliability and the correlations between component lifetimes. Under the stochastic time scale, the component lifetimes are shown to be positively quadrant dependent. Overlook of the correlation would overestimate the reliability of a parallel system but underestimate the reliability of a series system. When the stochastic time scale degenerates to a deterministic function of the calendar time, on the other hand, the system reliability becomes the reliability of the system where components work independently. The proposed models are successfully applied to lifetime data of brake pads in the automobile braking system.