A Unified Model for System Reliability Evaluation under Dynamic Operating Conditions

The working conditions of multicomponent systems are usually dynamic and stochastic. Reliability evaluation of such systems is challenging, since the components are generally positively correlated. Based on the cumulative exposure principle, we model the effects of the dynamic environments on the component lifetimes by a common stochastic time scale, and exponential dispersion process is utilized to describe the stochastic time scale. Then, the component lifetimes are shown to be positively quadrant dependent, and the joint survival function of the component lifetimes is derived, which includes the results of [1] as special cases. In this article, we show that neglecting either the effects of dynamic environments or the correlation among component lifetimes would underestimate the reliability of series systems and overestimate the reliability of parallel systems. We also investigate the problem of parameter redundancy of the model, and give some suggestions for data analysis. Simulation studies show that the unified model is flexible and useful for suggesting an optimal model given observed data.