Reliability Assessment for Products Subject to Generalized δ-Shock Considering the Threshold of Shock Magnitude

Some products may subject to degradation process with shocks, and shocks can affect degradation process. Generalized δ-shock model is one of the basic shock models in this field, and it is defined that the degradation rate of products can be increased when the interval of two sequential shocks is less than a threshold. Existing work on degradation modeling considering the effect of generalized δ-shock on degradation rate only focus on the time interval of two sequential shocks. However, for some products, if magnitudes of the two shock are too small, generalized δ-shock may not increase the degradation rate of products, even the time interval is less than the threshold. Thus, the threshold of magnitudes for generalized δ-shock is also a factor need to be considered. That is, generalized δ-shock can speed up the deterioration by increasing the degradation rate, only when time interval of two sequential shocks is less than a threshold, and magnitudes of the two shocks are above a critical value. According to existing work, a degradation modeling and lifetime prediction method considering the effect of generalized δ-shock on degradation rate is proposed. The model is established based on Wiener process which combines changing degradation rate function and generalized δ-shock function. A simulation study is presented to verify the application of the method, and a case study for miniature bulbs are used to verify the effectiveness and practicality of the proposed model.