Multi-State Reliability Analysis Based on General Wiener Degradation Process and Random Shock

A multi-state reliability analysis model suffering from a dependent competing failure process is developed in this study, where the soft failure is described by general nonlinearity random effect. Wiener degradation process with measurement error and the hard failure is caused by random shock. Considering that the shock process not only may cause abrupt damage but also can accelerate degradation, there are some correlations between soft failure and hard failure. Based on the proposed new model, the multi-state functions are obtained under the cumulative shock model and the extreme shock model, and the system state probabilities are given under the different degradation state points. The fatigue cracks growth data example and MEMS oscillator example are given to demonstrate the proposed new model. At last, some sensitivity analyses are given to illustrate the influence of parameters on the state probability and the system reliability.