System Reliability Models with Random Shocks and Uncertainty: A State-of-the-Art Review

Reliability evaluation is an important task in safety–critical applications. The failure of a system is generally caused by random shocks resulting from adverse events or internal degradations. This chapter thus mainly focuses on the review of system reliability models with random shocks and the uncertainty of the degradation process. In the category of system reliability models with random shocks, we review system reliability models based on five random shock models that are commonly used in Reliability Engineering, cumulative shock model, extreme shock model, run shock model, $$\delta$$ δ -shock model, and mixed shock model. In addition, three sources of variabilities, commonly discussed in the literature, can result in the uncertainty of the degradation process, which are temporal variability in the degradation process, unit-to-unit variability, and measurement error caused by imperfect instruments or imperfect inspection. In the category of system reliability model with uncertainty, we review system reliability models using stochastic degradation models in terms of three stochastic processes, Wiener process, gamma process, and inverse Gaussian process.